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Mdshobu / Liberty House Club Whitepaper# Liberty House Club **A Parallel Binance Chain to Enable Smart Contracts** _NOTE: This document is under development. Please check regularly for updates!_ ## Table of Contents - [Motivation](#motivation) - [Design Principles](#design-principles) - [Consensus and Validator Quorum](#consensus-and-validator-quorum) * [Proof of Staked Authority](#proof-of-staked-authority) * [Validator Quorum](#validator-quorum) * [Security and Finality](#security-and-finality) * [Reward](#reward) - [Token Economy](#token-economy) * [Native Token](#native-token) * [Other Tokens](#other-tokens) - [Cross-Chain Transfer and Communication](#cross-chain-transfer-and-communication) * [Cross-Chain Transfer](#cross-chain-transfer) * [BC to BSC Architecture](#bc-to-bsc-architecture) * [BSC to BC Architecture](#bsc-to-bc-architecture) * [Timeout and Error Handling](#timeout-and-error-handling) * [Cross-Chain User Experience](#cross-chain-user-experience) * [Cross-Chain Contract Event](#cross-chain-contract-event) - [Staking and Governance](#staking-and-governance) * [Staking on BC](#staking-on-bc) * [Rewarding](#rewarding) * [Slashing](#slashing) - [Relayers](#relayers) * [BSC Relayers](#bsc-relayers) * [Oracle Relayers](#oracle-relayers) - [Outlook](#outlook) # Motivation After its mainnet community [launch](https://www.binance.com/en/blog/327334696200323072/Binance-DEX-Launches-on-Binance-Chain-Invites-Further-Community-Development) in April 2019, [Binance Chain](https://www.binance.org) has exhibited its high speed and large throughput design. Binance Chain’s primary focus, its native [decentralized application](https://en.wikipedia.org/wiki/Decentralized_application) (“dApp”) [Binance DEX](https://www.binance.org/trade), has demonstrated its low-latency matching with large capacity headroom by handling millions of trading volume in a short time. Flexibility and usability are often in an inverse relationship with performance. The concentration on providing a convenient digital asset issuing and trading venue also brings limitations. Binance Chain's most requested feature is the programmable extendibility, or simply the [Smart Contract](https://en.wikipedia.org/wiki/Smart_contract) and Virtual Machine functions. Digital asset issuers and owners struggle to add new decentralized features for their assets or introduce any sort of community governance and activities. Despite this high demand for adding the Smart Contract feature onto Binance Chain, it is a hard decision to make. The execution of a Smart Contract may slow down the exchange function and add non-deterministic factors to trading. If that compromise could be tolerated, it might be a straightforward idea to introduce a new Virtual Machine specification based on [Tendermint](https://tendermint.com/core/), based on the current underlying consensus protocol and major [RPC](https://docs.binance.org/api-reference/node-rpc.html) implementation of Binance Chain. But all these will increase the learning requirements for all existing dApp communities, and will not be very welcomed. We propose a parallel blockchain of the current Binance Chain to retain the high performance of the native DEX blockchain and to support a friendly Smart Contract function at the same time. # Design Principles After the creation of the parallel blockchain into the Binance Chain ecosystem, two blockchains will run side by side to provide different services. The new parallel chain will be called “**Binance Smart Chain**” (short as “**BSC**” for the below sections), while the existing mainnet remains named “**Binance Chain**” (short as “**BC**” for the below sections). Here are the design principles of **BSC**: 1. **Standalone Blockchain**: technically, BSC is a standalone blockchain, instead of a layer-2 solution. Most BSC fundamental technical and business functions should be self-contained so that it can run well even if the BC stopped for a short period. 2. **Ethereum Compatibility**: The first practical and widely-used Smart Contract platform is Ethereum. To take advantage of the relatively mature applications and community, BSC chooses to be compatible with the existing Ethereum mainnet. This means most of the **dApps**, ecosystem components, and toolings will work with BSC and require zero or minimum changes; BSC node will require similar (or a bit higher) hardware specification and skills to run and operate. The implementation should leave room for BSC to catch up with further Ethereum upgrades. 3. **Staking Involved Consensus and Governance**: Staking-based consensus is more environmentally friendly and leaves more flexible option to the community governance. Expectedly, this consensus should enable better network performance over [proof-of-work](https://en.wikipedia.org/wiki/Proof_of_work) blockchain system, i.e., faster blocking time and higher transaction capacity. 4. **Native Cross-Chain Communication**: both BC and BSC will be implemented with native support for cross-chain communication among the two blockchains. The communication protocol should be bi-directional, decentralized, and trustless. It will concentrate on moving digital assets between BC and BSC, i.e., [BEP2](https://github.com/binance-chain/BEPs/blob/master/BEP2.md) tokens, and eventually, other BEP tokens introduced later. The protocol should care for the minimum of other items stored in the state of the blockchains, with only a few exceptions. # Consensus and Validator Quorum Based on the above design principles, the consensus protocol of BSC is to fulfill the following goals: 1. Blocking time should be shorter than Ethereum network, e.g. 5 seconds or even shorter. 2. It requires limited time to confirm the finality of transactions, e.g. around 1-min level or shorter. 3. There is no inflation of native token: BNB, the block reward is collected from transaction fees, and it will be paid in BNB. 4. It is compatible with Ethereum system as much as possible. 5. It allows modern [proof-of-stake](https://en.wikipedia.org/wiki/Proof_of_stake) blockchain network governance. ## Proof of Staked Authority Although Proof-of-Work (PoW) has been recognized as a practical mechanism to implement a decentralized network, it is not friendly to the environment and also requires a large size of participants to maintain the security. Ethereum and some other blockchain networks, such as [MATIC Bor](https://github.com/maticnetwork/bor), [TOMOChain](https://tomochain.com/), [GoChain](https://gochain.io/), [xDAI](https://xdai.io/), do use [Proof-of-Authority(PoA)](https://en.wikipedia.org/wiki/Proof_of_authority) or its variants in different scenarios, including both testnet and mainnet. PoA provides some defense to 51% attack, with improved efficiency and tolerance to certain levels of Byzantine players (malicious or hacked). It serves as an easy choice to pick as the fundamentals. Meanwhile, the PoA protocol is most criticized for being not as decentralized as PoW, as the validators, i.e. the nodes that take turns to produce blocks, have all the authorities and are prone to corruption and security attacks. Other blockchains, such as EOS and Lisk both, introduce different types of [Delegated Proof of Stake (DPoS)](https://en.bitcoinwiki.org/wiki/DPoS) to allow the token holders to vote and elect the validator set. It increases the decentralization and favors community governance. BSC here proposes to combine DPoS and PoA for consensus, so that: 1. Blocks are produced by a limited set of validators 2. Validators take turns to produce blocks in a PoA manner, similar to [Ethereum’s Clique](https://eips.ethereum.org/EIPS/eip-225) consensus design 3. Validator set are elected in and out based on a staking based governance ## Validator Quorum In the genesis stage, a few trusted nodes will run as the initial Validator Set. After the blocking starts, anyone can compete to join as candidates to elect as a validator. The staking status decides the top 21 most staked nodes to be the next validator set, and such an election will repeat every 24 hours. **BNB** is the token used to stake for BSC. In order to remain as compatible as Ethereum and upgradeable to future consensus protocols to be developed, BSC chooses to rely on the **BC** for staking management (Please refer to the below “[Staking and Governance](#staking-and-governance)” section). There is a **dedicated staking module for BSC on BC**. It will accept BSC staking from BNB holders and calculate the highest staked node set. Upon every UTC midnight, BC will issue a verifiable `ValidatorSetUpdate` cross-chain message to notify BSC to update its validator set. While producing further blocks, the existing BSC validators check whether there is a `ValidatorSetUpdate` message relayed onto BSC periodically. If there is, they will update the validator set after an **epoch period**, i.e. a predefined number of blocking time. For example, if BSC produces a block every 5 seconds, and the epoch period is 240 blocks, then the current validator set will check and update the validator set for the next epoch in 1200 seconds (20 minutes). ## Security and Finality Given there are more than ½\*N+1 validators are honest, PoA based networks usually work securely and properly. However, there are still cases where certain amount Byzantine validators may still manage to attack the network, e.g. through the “[Clone Attack](https://arxiv.org/pdf/1902.10244.pdf)”. To secure as much as BC, BSC users are encouraged to wait until receiving blocks sealed by more than ⅔\*N+1 different validators. In that way, the BSC can be trusted at a similar security level to BC and can tolerate less than ⅓\*N Byzantine validators. With 21 validators, if the block time is 5 seconds, the ⅔\*N+1 different validator seals will need a time period of (⅔\*21+1)*5 = 75 seconds. Any critical applications for BSC may have to wait for ⅔\*N+1 to ensure a relatively secure finality. However, besides such arrangement, BSC does introduce **Slashing** logic to penalize Byzantine validators for **double signing** or **inavailability**, which will be covered in the “Staking and Governance” section later. This Slashing logic will expose the malicious validators in a very short time and make the “Clone Attack” very hard or extremely non-beneficial to execute. With this enhancement, ½\*N+1 or even fewer blocks are enough as confirmation for most transactions. ## Reward All the BSC validators in the current validator set will be rewarded with transaction **fees in BNB**. As BNB is not an inflationary token, there will be no mining rewards as what Bitcoin and Ethereum network generate, and the gas fee is the major reward for validators. As BNB is also utility tokens with other use cases, delegators and validators will still enjoy other benefits of holding BNB. The reward for validators is the fees collected from transactions in each block. Validators can decide how much to give back to the delegators who stake their BNB to them, in order to attract more staking. Every validator will take turns to produce the blocks in the same probability (if they stick to 100% liveness), thus, in the long run, all the stable validators may get a similar size of the reward. Meanwhile, the stakes on each validator may be different, so this brings a counter-intuitive situation that more users trust and delegate to one validator, they potentially get less reward. So rational delegators will tend to delegate to the one with fewer stakes as long as the validator is still trustful (insecure validator may bring slashable risk). In the end, the stakes on all the validators will have less variation. This will actually prevent the stake concentration and “winner wins forever” problem seen on some other networks. Some parts of the gas fee will also be rewarded to relayers for Cross-Chain communication. Please refer to the “[Relayers](#relayers)” section below. # Token Economy BC and BSC share the same token universe for BNB and BEP2 tokens. This defines: 1. The same token can circulate on both networks, and flow between them bi-directionally via a cross-chain communication mechanism. 2. The total circulation of the same token should be managed across the two networks, i.e. the total effective supply of a token should be the sum of the token’s total effective supply on both BSC and BC. 3. The tokens can be initially created on BSC in a similar format as ERC20 token standard, or on BC as a BEP2, then created on the other. There are native ways on both networks to link the two and secure the total supply of the token. ## Native Token BNB will run on BSC in the same way as ETH runs on Ethereum so that it remains as “native token” for both BSC and BC. This means, in addition to BNB is used to pay most of the fees on Binance Chain and Binance DEX, BNB will be also used to: 1. pay “fees“ to deploy smart contracts on BSC 2. stake on selected BSC validators, and get corresponding rewards 3. perform cross-chain operations, such as transfer token assets across BC and BSC ### Seed Fund Certain amounts of BNB will be burnt on BC and minted on BSC during its genesis stage. This amount is called “Seed Fund” to circulate on BSC after the first block, which will be dispatched to the initial BC-to-BSC Relayer(described in later sections) and initial validator set introduced at genesis. These BNBs are used to pay transaction fees in the early stage to transfer more BNB from BC onto BSC via the cross-chain mechanism. The BNB cross-chain transfer is discussed in a later section, but for BC to BSC transfer, it is generally to lock BNB on BC from the source address of the transfer to a system-controlled address and unlock the corresponding amount from special contract to the target address of the transfer on BSC, or reversely, when transferring from BSC to BC, it is to lock BNB from the source address on BSC into a special contract and release locked amount on BC from the system address to the target address. The logic is related to native code on BC and a series of smart contracts on BSC. ## Other Tokens BC supports BEP2 tokens and upcoming [BEP8 tokens](https://github.com/binance-chain/BEPs/pull/69), which are native assets transferrable and tradable (if listed) via fast transactions and sub-second finality. Meanwhile, as BSC is Ethereum compatible, it is natural to support ERC20 tokens on BSC, which here is called “**BEP2E**” (with the real name to be introduced by the future BEPs,it potentially covers BEP8 as well). BEP2E may be “Enhanced” by adding a few more methods to expose more information, such as token denomination, decimal precision definition and the owner address who can decide the Token Binding across the chains. BSC and BC work together to ensure that one token can circulate in both formats with confirmed total supply and be used in different use cases. ### Token Binding BEP2 tokens will be extended to host a new attribute to associate the token with a BSC BEP2E token contract, called “**Binder**”, and this process of association is called “**Token Binding**”. Token Binding can happen at any time after BEP2 and BEP2E are ready. The token owners of either BEP2 or BEP2E don’t need to bother about the Binding, until before they really want to use the tokens on different scenarios. Issuers can either create BEP2 first or BEP2E first, and they can be bound at a later time. Of course, it is encouraged for all the issuers of BEP2 and BEP2E to set the Binding up early after the issuance. A typical procedure to bind the BEP2 and BEP2E will be like the below: 1. Ensure both the BEP2 token and the BEP2E token both exist on each blockchain, with the same total supply. BEP2E should have 3 more methods than typical ERC20 token standard: * symbol(): get token symbol * decimals(): get the number of the token decimal digits * owner(): get **BEP2E contract owner’s address.** This value should be initialized in the BEP2E contract constructor so that the further binding action can verify whether the action is from the BEP2E owner. 2. Decide the initial circulation on both blockchains. Suppose the total supply is *S*, and the expected initial circulating supply on BC is *K*, then the owner should lock S-K tokens to a system controlled address on BC. 3. Equivalently, *K* tokens is locked in the special contract on BSC, which handles major binding functions and is named as **TokenHub**. The issuer of the BEP2E token should lock the *K* amount of that token into TokenHub, resulting in *S-K* tokens to circulate on BSC. Thus the total circulation across 2 blockchains remains as *S*. 4. The issuer of BEP2 token sends the bind transaction on BC. Once the transaction is executed successfully after proper verification: * It transfers *S-K* tokens to a system-controlled address on BC. * A cross-chain bind request package will be created, waiting for Relayers to relay. 5. BSC Relayers will relay the cross-chain bind request package into **TokenHub** on BSC, and the corresponding request and information will be stored into the contract. 6. The contract owner and only the owner can run a special method of TokenHub contract, `ApproveBind`, to verify the binding request to mark it as a success. It will confirm: * the token has not been bound; * the binding is for the proper symbol, with proper total supply and decimal information; * the proper lock are done on both networks; 10. Once the `ApproveBind` method has succeeded, TokenHub will mark the two tokens are bounded and share the same circulation on BSC, and the status will be propagated back to BC. After this final confirmation, the BEP2E contract address and decimals will be written onto the BEP2 token as a new attribute on BC, and the tokens can be transferred across the two blockchains bidirectionally. If the ApproveBind fails, the failure event will also be propagated back to BC to release the locked tokens, and the above steps can be re-tried later. # Cross-Chain Transfer and Communication Cross-chain communication is the key foundation to allow the community to take advantage of the dual chain structure: * users are free to create any tokenization, financial products, and digital assets on BSC or BC as they wish * the items on BSC can be manually and programmingly traded and circulated in a stable, high throughput, lighting fast and friendly environment of BC * users can operate these in one UI and tooling ecosystem. ## Cross-Chain Transfer The cross-chain transfer is the key communication between the two blockchains. Essentially the logic is: 1. the `transfer-out` blockchain will lock the amount from source owner addresses into a system controlled address/contracts; 2. the `transfer-in` blockchain will unlock the amount from the system controlled address/contracts and send it to target addresses. The cross-chain transfer package message should allow the BSC Relayers and BC **Oracle Relayers** to verify: 1. Enough amount of token assets are removed from the source address and locked into a system controlled addresses/contracts on the source blockchain. And this can be confirmed on the target blockchain. 2. Proper amounts of token assets are released from a system controlled addresses/contracts and allocated into target addresses on the target blockchain. If this fails, it can be confirmed on source blockchain, so that the locked token can be released back (may deduct fees). 3. The sum of the total circulation of the token assets across the 2 blockchains are not changed after this transfer action completes, no matter if the transfer succeeds or not.  The architecture of cross-chain communication is as in the above diagram. To accommodate the 2 heteroid systems, communication handling is different in each direction. ## BC to BSC Architecture BC is a Tendermint-based, instant finality blockchain. Validators with at least ⅔\*N+1 of the total voting power will co-sign each block on the chain. So that it is practical to verify the block transactions and even the state value via **Block Header** and **Merkle Proof** verification. This has been researched and implemented as “**Light-Client Protocol**”, which are intensively discussed in [the Ethereum](https://github.com/ethereum/wiki/wiki/Light-client-protocol) community, studied and implemented for [Cosmos inter-chain communication](https://github.com/cosmos/ics/blob/a4173c91560567bdb7cc9abee8e61256fc3725e9/spec/ics-007-tendermint-client/README.md). BC-to-BSC communication will be verified in an “**on-chain light client**” implemented via BSC **Smart Contracts** (some of them may be **“pre-compiled”**). After some transactions and state change happen on BC, if a transaction is defined to trigger cross-chain communication,the Cross-chain “**package**” message will be created and **BSC Relayers** will pass and submit them onto BSC as data into the "build-in system contracts". The build-in system contracts will verify the package and execute the transactions if it passes the verification. The verification will be guaranteed with the below design: 1. BC blocking status will be synced to the light client contracts on BSC from time to time, via block header and pre-commits, for the below information: * block and app hash of BC that are signed by validators * current validatorset, and validator set update 2. the key-value from the blockchain state will be verified based on the Merkle Proof and information from above #1. After confirming the key-value is accurate and trustful, the build-in system contracts will execute the actions corresponding to the cross-chain packages. Some examples of such packages that can be created for BC-to-BSC are: 1. Bind: bind the BEP2 tokens and BEP2E 2. Transfer: transfer tokens after binding, this means the circulation will decrease (be locked) from BC and appear in the target address balance on BSC 3. Error Handling: to handle any timeout/failure event for BSC-to-BC communication 4. Validatorset update of BSC To ensure no duplication, proper message sequence and timely timeout, there is a “Channel” concept introduced on BC to manage any types of the communication. For relayers, please also refer to the below “Relayers” section. ## BSC to BC Architecture BSC uses Proof of Staked Authority consensus protocol, which has a chance to fork and requires confirmation of more blocks. One block only has the signature of one validator, so that it is not easy to rely on one block to verify data from BSC. To take full advantage of validator quorum of BC, an idea similar to many [Bridge ](https://github.com/poanetwork/poa-bridge)or Oracle blockchains is adopted: 1. The cross-chain communication requests from BSC will be submitted and executed onto BSC as transactions. The execution of the transanction wil emit `Events`, and such events can be observed and packaged in certain “**Oracle**” onto BC. Instead of Block Headers, Hash and Merkle Proof, this type of “Oracle” package directly contains the cross-chain information for actions, such as sender, receiver and amount for transfer. 2. To ensure the security of the Oracle, the validators of BC will form anothe quorum of “**Oracle Relayers**”. Each validator of the BC should run a **dedicated process** as the Oracle Relayer. These Oracle Relayers will submit and vote for the cross-chain communication package, like Oracle, onto BC, using the same validator keys. Any package signed by more than ⅔\*N+1 Oracle Relayers’ voting power is as secure as any block signed by ⅔\*N+1 of the same quorum of validators’ voting power. By using the same validator quorum, it saves the light client code on BC and continuous block updates onto BC. Such Oracles also have Oracle IDs and types, to ensure sequencing and proper error handling. ## Timeout and Error Handling There are scenarios that the cross-chain communication fails. For example, the relayed package cannot be executed on BSC due to some coding bug in the contracts. **Timeout and error handling logics are** used in such scenarios. For the recognizable user and system errors or any expected exceptions, the two networks should heal themselves. For example, when BC to BSC transfer fails, BSC will issue a failure event and Oracle Relayers will execute a refund on BC; when BSC to BC transfer fails, BC will issue a refund package for Relayer to relay in order to unlock the fund. However, unexpected error or exception may still happen on any step of the cross-chain communication. In such a case, the Relayers and Oracle Relayers will discover that the corresponding cross-chain channel is stuck in a particular sequence. After a Timeout period, the Relayers and Oracle Relayers can request a “SkipSequence” transaction, the stuck sequence will be marked as “Unexecutable”. A corresponding alerts will be raised, and the community has to discuss how to handle this scenario, e.g. payback via the sponsor of the validators, or event clear the fund during next network upgrade. ## Cross-Chain User Experience Ideally, users expect to use two parallel chains in the same way as they use one single chain. It requires more aggregated transaction types to be added onto the cross-chain communication to enable this, which will add great complexity, tight coupling, and maintenance burden. Here BC and BSC only implement the basic operations to enable the value flow in the initial launch and leave most of the user experience work to client side UI, such as wallets. E.g. a great wallet may allow users to sell a token directly from BSC onto BC’s DEX order book, in a secure way. ## Cross-Chain Contract Event Cross-Chain Contract Event (CCCE) is designed to allow a smart contract to trigger cross-chain transactions, directly through the contract code. This becomes possible based on: 1. Standard system contracts can be provided to serve operations callable by general smart contracts; 2. Standard events can be emitted by the standard contracts; 3. Oracle Relayers can capture the standard events, and trigger the corresponding cross-chain operations; 4. Dedicated, code-managed address (account) can be created on BC and accessed by the contracts on the BSC, here it is named as **“Contract Address on BC” (CAoB)**. Several standard operations are implemented: 1. BSC to BC transfer: this is implemented in the same way as normal BSC to BC transfer, by only triggered via standard contract. The fund can be transferred to any addresses on BC, including the corresponding CAoB of the transfer originating contract. 2. Transfer on BC: this is implemented as a special cross-chain transfer, while the real transfer is from **CAoB** to any other address (even another CAoB). 3. BC to BSC transfer: this is implemented as two-pass cross-chain communication. The first is triggered by the BSC contract and propagated onto BC, and then in the second pass, BC will start a normal BC to BSC cross-chain transfer, from **CAoB** to contract address on BSC. A special note should be paid on that the BSC contract only increases balance upon any transfer coming in on the second pass, and the error handling in the second pass is the same as the normal BC to BSC transfer. 4. IOC (Immediate-Or-Cancel) Trade Out: the primary goal of transferring assets to BC is to trade. This event will instruct to trade a certain amount of an asset in CAoB into another asset as much as possible and transfer out all the results, i.e. the left the source and the traded target tokens of the trade, back to BSC. BC will handle such relayed events by sending an “Immediate-Or-Cancel”, i.e. IOC order onto the trading pairs, once the next matching finishes, the result will be relayed back to BSC, which can be in either one or two assets. 5. Auction Trade Out: Such event will instruct BC to send an auction order to trade a certain amount of an asset in **CAoB** into another asset as much as possible and transfer out all the results back to BSC at the end of the auction. Auction function is upcoming on BC. There are some details for the Trade Out: 1. both can have a limit price (absolute or relative) for the trade; 2. the end result will be written as cross-chain packages to relay back to BSC; 3. cross-chain communication fees may be charged from the asset transferred back to BSC; 4. BSC contract maintains a mirror of the balance and outstanding orders on CAoB. No matter what error happens during the Trade Out, the final status will be propagated back to the originating contract and clear its internal state. With the above features, it simply adds the cross-chain transfer and exchange functions with high liquidity onto all the smart contracts on BSC. It will greatly add the application scenarios on Smart Contract and dApps, and make 1 chain +1 chain > 2 chains. # Staking and Governance Proof of Staked Authority brings in decentralization and community involvement. Its core logic can be summarized as the below. You may see similar ideas from other networks, especially Cosmos and EOS. 1. Token holders, including the validators, can put their tokens “**bonded**” into the stake. Token holders can **delegate** their tokens onto any validator or validator candidate, to expect it can become an actual validator, and later they can choose a different validator or candidate to **re-delegate** their tokens<sup>1</sup>. 2. All validator candidates will be ranked by the number of bonded tokens on them, and the top ones will become the real validators. 3. Validators can share (part of) their blocking reward with their delegators. 4. Validators can suffer from “**Slashing**”, a punishment for their bad behaviors, such as double sign and/or instability. 5. There is an “**unbonding period**” for validators and delegators so that the system makes sure the tokens remain bonded when bad behaviors are caught, the responsible will get slashed during this period. ## Staking on BC Ideally, such staking and reward logic should be built into the blockchain, and automatically executed as the blocking happens. Cosmos Hub, who shares the same Tendermint consensus and libraries with Binance Chain, works in this way. BC has been preparing to enable staking logic since the design days. On the other side, as BSC wants to remain compatible with Ethereum as much as possible, it is a great challenge and efforts to implement such logic on it. This is especially true when Ethereum itself may move into a different Proof of Stake consensus protocol in a short (or longer) time. In order to keep the compatibility and reuse the good foundation of BC, the staking logic of BSC is implemented on BC: 1. The staking token is BNB, as it is a native token on both blockchains anyway 2. The staking, i.e. token bond and delegation actions and records for BSC, happens on BC. 3. The BSC validator set is determined by its staking and delegation logic, via a staking module built on BC for BSC, and propagated every day UTC 00:00 from BC to BSC via Cross-Chain communication. 4. The reward distribution happens on BC around every day UTC 00:00. ## Rewarding Both the validator update and reward distribution happen every day around UTC 00:00. This is to save the cost of frequent staking updates and block reward distribution. This cost can be significant, as the blocking reward is collected on BSC and distributed on BC to BSC validators and delegators. (Please note BC blocking fees will remain rewarding to BC validators only.) A deliberate delay is introduced here to make sure the distribution is fair: 1. The blocking reward will not be sent to validator right away, instead, they will be distributed and accumulated on a contract; 2. Upon receiving the validator set update into BSC, it will trigger a few cross-chain transfers to transfer the reward to custody addresses on the corresponding validators. The custody addresses are owned by the system so that the reward cannot be spent until the promised distribution to delegators happens. 3. In order to make the synchronization simpler and allocate time to accommodate slashing, the reward for N day will be only distributed in N+2 days. After the delegators get the reward, the left will be transferred to validators’ own reward addresses. ## Slashing Slashing is part of the on-chain governance, to ensure the malicious or negative behaviors are punished. BSC slash can be submitted by anyone. The transaction submission requires **slash evidence** and cost fees but also brings a larger reward when it is successful. So far there are two slashable cases. ### Double Sign It is quite a serious error and very likely deliberate offense when a validator signs more than one block with the same height and parent block. The reference protocol implementation should already have logic to prevent this, so only the malicious code can trigger this. When Double Sign happens, the validator should be removed from the Validator **Set** right away. Anyone can submit a slash request on BC with the evidence of Double Sign of BSC, which should contain the 2 block headers with the same height and parent block, sealed by the offending validator. Upon receiving the evidence, if the BC verifies it to be valid: 1. The validator will be removed from validator set by an instance BSC validator set update Cross-Chain update; 2. A predefined amount of BNB would be slashed from the **self-delegated** BNB of the validator; Both validator and its delegators will not receive the staking rewards. 3. Part of the slashed BNB will allocate to the submitter’s address, which is a reward and larger than the cost of submitting slash request transaction 4. The rest of the slashed BNB will allocate to the other validators’ custody addresses, and distributed to all delegators in the same way as blocking reward. ### Inavailability The liveness of BSC relies on everyone in the Proof of Staked Authority validator set can produce blocks timely when it is their turn. Validators can miss their turn due to any reason, especially problems in their hardware, software, configuration or network. This instability of the operation will hurt the performance and introduce more indeterministic into the system. There can be an internal smart contract responsible for recording the missed blocking metrics of each validator. Once the metrics are above the predefined threshold, the blocking reward for validator will not be relayed to BC for distribution but shared with other better validators. In such a way, the poorly-operating validator should be gradually voted out of the validator set as their delegators will receive less or none reward. If the metrics remain above another higher level of threshold, the validator will be dropped from the rotation, and this will be propagated back to BC, then a predefined amount of BNB would be slashed from the **self-delegated** BNB of the validator. Both validators and delegators will not receive their staking rewards. ### Governance Parameters There are many system parameters to control the behavior of the BSC, e.g. slash amount, cross-chain transfer fees. All these parameters will be determined by BSC Validator Set together through a proposal-vote process based on their staking. Such the process will be carried on BC, and the new parameter values will be picked up by corresponding system contracts via a cross-chain communication. # Relayers Relayers are responsible to submit Cross-Chain Communication Packages between the two blockchains. Due to the heterogeneous parallel chain structure, two different types of Relayers are created. ## BSC Relayers Relayers for BC to BSC communication referred to as “**BSC Relayers**”, or just simply “Relayers”. Relayer is a standalone process that can be run by anyone, and anywhere, except that Relayers must register themselves onto BSC and deposit a certain refundable amount of BNB. Only relaying requests from the registered Relayers will be accepted by BSC. The package they relay will be verified by the on-chain light client on BSC. The successful relay needs to pass enough verification and costs gas fees on BSC, and thus there should be incentive reward to encourage the community to run Relayers. ### Incentives There are two major communication types: 1. Users triggered Operations, such as `token bind` or `cross chain transfer`. Users must pay additional fee to as relayer reward. The reward will be shared with the relayers who sync the referenced blockchain headers. Besides, the reward won't be paid the relayers' accounts directly. A reward distribution mechanism will be brought in to avoid monopolization. 2. System Synchronization, such as delivering `refund package`(caused by failures of most oracle relayers), special blockchain header synchronization(header contains BC validatorset update), BSC staking package. System reward contract will pay reward to relayers' accounts directly. If some Relayers have faster networks and better hardware, they can monopolize all the package relaying and leave no reward to others. Thus fewer participants will join for relaying, which encourages centralization and harms the efficiency and security of the network. Ideally, due to the decentralization and dynamic re-election of BSC validators, one Relayer can hardly be always the first to relay every message. But in order to avoid the monopolization further, the rewarding economy is also specially designed to minimize such chance: 1. The reward for Relayers will be only distributed in batches, and one batch will cover a number of successful relayed packages. 2. The reward a Relayer can get from a batch distribution is not linearly in proportion to their number of successful relayed packages. Instead, except the first a few relays, the more a Relayer relays during a batch period, the less reward it will collect. ## Oracle Relayers Relayers for BSC to BC communication are using the “Oracle” model, and so-called “**Oracle Relayers**”. Each of the validators must, and only the ones of the validator set, run Oracle Relayers. Each Oracle Relayer watches the blockchain state change. Once it catches Cross-Chain Communication Packages, it will submit to vote for the requests. After Oracle Relayers from ⅔ of the voting power of BC validators vote for the changes, the cross-chain actions will be performed. Oracle Replayers should wait for enough blocks to confirm the finality on BSC before submitting and voting for the cross-chain communication packages onto BC. The cross-chain fees will be distributed to BC validators together with the normal BC blocking rewards. Such oracle type relaying depends on all the validators to support. As all the votes for the cross-chain communication packages are recorded on the blockchain, it is not hard to have a metric system to assess the performance of the Oracle Relayers. The poorest performer may have their rewards clawed back via another Slashing logic introduced in the future. # Outlook It is hard to conclude for Binance Chain, as it has never stopped evolving. The dual-chain strategy is to open the gate for users to take advantage of the fast transferring and trading on one side, and flexible and extendable programming on the other side, but it will be one stop along the development of Binance Chain. Here below are the topics to look into so as to facilitate the community better for more usability and extensibility: 1. Add different digital asset model for different business use cases 2. Enable more data feed, especially DEX market data, to be communicated from Binance DEX to BSC 3. Provide interface and compatibility to integrate with Ethereum, including its further upgrade, and other blockchain 4. Improve client side experience to manage wallets and use blockchain more conveniently ------ [1]: BNB business practitioners may provide other benefits for BNB delegators, as they do now for long term BNB holders.
fazeelkhalid / Graph Real Time ProblemsPoints: 100 Topics: Graphs, topological sort, freedom to decide how to represent data and organize code (while still reading in a graph and performing topological sort) PLAGIARISM/COLLUSION: You should not read any code (solution) that directly solves this problem (e.g. implements DFS, topological sorting or other component needed for the homework). The graph representation provided on the Code page (which you are allowed to use in your solution) and the pseudocode and algorithm discussed in class provide all the information needed. If anything is unclear in the provided materials check with us. You can read materials on how to read from a file, or read a Unix file or how to tokenize a line of code, BUT not in a sample code that deals with graphs or this specific problem. E.g. you can read tutorials about these topics, but not a solution to this problem (or a problem very similar to it). You should not share your code with any classmate or read another classmate's code. Part 1: Main program requirements (100 pts) Given a list of courses and their prerequisites, compute the order in which courses must be taken so that when taking a courses, all its prerequisites have already been taken. All the files that the program would read from are in Unix format (they have the Unix EOL). Provided files: ● Grading Criteria ● cycle0.txt ● data0.txt ● data0_rev.txt ● data1.txt - like data0.txt but the order of the prerequisite courses is modified on line 2. ● slides.txt (graph image) - courses given in such a way that they produce the same graph as in the image. (The last digit in the course number is the same as the vertex corresponding to it in the drawn graph. You can also see this in the vertex-to-course name correspondence in the sample run for this file.) ● run.html● data0_easy.txt - If you cannot handle the above file format, this is an easier file format that you can use, but there will be 15 points lost in this case. More details about this situation are given in Part 3. ● Unix.zip - zipped folder with all data files. ● For your reference: EOL_Mac_Unix_Windows.png - EOL symbols for Unix/Mac/Windows Specifications: 1. You can use structs, macros, typedef. 2. All the code must be in C (not C++, or any other language) 3. Global or static variables are NOT allowed. The exception is using macros to define constants for the size limits (e.g. instead of using 30 for the max course name size). E.g. #define MAX_ARRAY_LENGTH 20 4. You can use static memory (on the frame stack) or dynamic memory. (Do not confuse static memory with static variables.) 5. The program must read from the user a filename. The filename (as given by the user) will include the extension, but NOT the path. E.g.: data0.txt 6. You can open and close the file however many times you want. 7. File format: 1. Unix file. It will have the Unix EOL (end-of-line). 2. Size limits: 1. The file name will be at most 30 characters. 2. A course name will be at most 30 characters 3. A line in the file will be at most 1000 characters. 3. The file ends with an empty new line. 4. Each line (except for the last empty line) has one or more course names. 5. Each course name is a single word (without any spaces). E.g. CSE1310 (with no space between CSE and 1310). 6. There is no empty space at the end of the line. 7. There is exactly one empty space between any two consecutive courses on the same line. (You do not need to worry about having tabs or more than one empty space between 2 courses.) The first course name on each line is the course being described and the following courses are the prerequisites for it. E.g. CSE2315 CSE1310 MATH1426 ENGL13018. The first line describes course CSE2315 and it indicates that CSE2315 has 2 prerequisite courses, namely: CSE1310 and MATH1426. The second line describes course ENG1301 and it indicates that ENG1301 has no prerequisites. 9. You can assume that there is exactly one line for every course, even for those that do not have prerequisites (see ENGL1301 above). Therefore you can count the number of lines in the file to get the total number of courses. 10.The courses are not given in any specific order in the file. 8. You must create a directed graph corresponding to the data in the file. 1. The graph will have as many vertices as different courses listed in the file. 2. You can represent the vertices and edges however you want. 3. You do NOT have to use a graph struct. If you can do all the work with just the 2D table (the adjacency matrix) that is fine. You HAVE TO implement the topological sorting covered in class (as this assignment is on Graphs), but you can organize, represent and store the data however you want. 4. For the edges, you can use either the adjacency matrix representation or the adjacency list. If you use the adjacency list, keep the nodes in the list sorted in increasing order. 5. For each course that has prerequisites, there is an edge, from each prerequisite to that course. Thus the direction of the edge indicates the dependency. The actual edge will be between the vertices in the graph corresponding to these courses. E.g. file data0.txt has: c100 c300 c200 c100 c200 c100 Meaning: c100-----> c200 \ | \ | \ | \ | \ | \ | V V c300(The above drawing is provided here to give a picture of how the data in the file should be interpreted and the graph that represents this data. Your program should *NOT* print this drawing. See the sample run for expected program output.) From this data you should create the correspondence: vertex 0 - c100 vertex 1 - c300 vertex 2 - c200 and you can represent the graph using adjacency matrix (the row and column indexes are provided for convenience): | 0 1 2 ----------------- 0| 0 1 1 1| 0 0 0 2| 0 1 0 e.g. E[0][1] is 1 because vertex 0 corresponds to c100 and vertex 1 corresponds to c300 and c300 has c100 as a prerequisite. Notice that E[1][0] is not 1. If you use the adjacency list representation, then you can print the adjacency list. The list must be sorted in increasing order (e.g. see the list for 0). It should show the corresponding node numbers. E.g. for the above example the adjacency list will be: 0: 1, 2, 1: 2: 1, 6. 7. In order for the output to look the same for everyone, use the correspondence given here: vertex 0 for the course on the first line, vertex 1 for the course on the second line, etc. 1. Print the courses in topological sorted order. This should be done using the DFS (Depth First Search) algorithm that we covered in class and the topological sorting based on DFS discussed in class. There is no topological order if there is a cycle in the graph; in this case print an error message. If in DFV-visit when looking at the (u,v) edge, if the color of v is GRAY then there is a cycle in the graph (and therefore topological sorting is not possible). See the Lecture on topological sorting (You can find the date based on the table on the Scans page and then watch the video from that day. I have also updated the pseudocodein the slides to show that. Refresh the slides and check the date on the first page. If it is 11/26/2020, then you have the most recent version.) 8. (6 points) create and submit 1 test file. It must cover a special case. Indicate what special case you are covering (e.g. no course has any prerequisite). At the top of the file indicate what makes it a special case. Save this file as special.txt. It should be in Unix EOL format. Part 2: Suggestions for improvements (not for grade) 1. CSE Advisors also are mindful and point out to students the "longest path through the degree". That is longest chain of course prerequisites (e.g. CSE1310 ---> CSE1320 --> CSE3318 -->...) as this gives a lower bound on the number of semesters needed until graduation. Can you calculate for each course the LONGEST chain ending with it? E.g. in the above example, there are 2 chains ending with c300 (size 2: just c100-->c300, size 3: c100-->c200-->c300) and you want to show longest path 3 for c300. Can you calculate this number for each course? 2. Allow the user the enter a list of courses taken so far (from the user or from file) and print a list of the courses they can take (they have all the prerequisites for). 3. Ask the user to enter a desired number of courses per semester and suggest a schedule (by semester). Part 3: Implementation suggestions 1. Reading from file: (15 points) For each line in the file, the code can extract the first course and the prerequisites for it. If you cannot process each line in the file correctly, you can use a modified input file that shows on each line, the number of courses, but you would lose the 15 points dedicated to line processing. If your program works with the "easy files", in order to make it easy for the TAs to know which file to provide, please name your C program courses_graph_easy.c. Here is the modification shown for a new example. Instead of c100 c300 c200 c100 c200 the file would have: 1 c1003 c300 c200 c100 1 c200 1. that way the first data on each line is a number that tells how many courses (strings) follow after it on that line. Everything is separated by exactly one space. All the other specifications are the same as for the original file (empty line at the end, no space at the end of any line, length of words, etc). Here is data0_easy.txt Make a direct correspondence between vertex numbers and course names. E.g. the **first** course name on the first line corresponds to vertex 0, the **first** course name on the second line corresponds to vertex 1, etc... 2. 3. The vertex numbers are used to refer to vertices. 4. In order to add an edge in the graph you will need to find the vertex number corresponding to a given course name. E.g. find that c300 corresponds to vertex 1 and c200 corresponds to vertex 2. Now you can set E[2][1] to be 1. (With the adjacency list, add node 1 in the adjacency list for 2 keeping the list sorted.) To help with this, write a function that takes as arguments the list/array of [unique] course names and one course name and returns the index of that course in the list. You can use that index as the vertex number. (This is similar to the indexOf method in Java.) 5. To see all the non-printable characters that may be in a file, find an editor that shows them. E.g. in Notepad++ : open the file, go to View -> Show symbol -> Show all characters. YOU SHOULD TRY THIS! In general, not necessarily for this homework, if you make the text editor show the white spaces, you will know if what you see as 4 empty spaces comes from 4 spaces or from one tab or show other hidden characters. This can help when you tokenize. E.g. here I am using Notepad++ to see the EOL for files saved with Unix/Mac/Windows EOL (see the CR/LF/CRLF at the end of each line): EOL_Mac_Unix_Windows.png How to submit Submit courses_graph.c (or courses_graph_easy.c) and special.txt (the special test case you created) in Canvas . (For courses_graph_easy.c you can submit the "easy" files that you created.)Your program should be named courses_graph.c if it reads from the normal/original files. If instead it reads from the 'easy' files, name it courses_graph_easy.c As stated on the course syllabus, programs must be in C, and must run on omega.uta.edu or the VM. IMPORTANT: Pay close attention to all specifications on this page, including file names and submission format. Even in cases where your answers are correct, points will be taken off liberally for non-compliance with the instructions given on this page (such as wrong file names, wrong compression format for the submitted code, and so on). The reason is that non-compliance with the instructions makes the grading process significantly (and unnecessarily) more time consuming. Contact the instructor or TA if you have any questions
randlet / To PrecisionFormatting floating point numbers to a specific number of significant digits in Python
flybunctious / The Game Of HogIntroduction In this project, you will develop a simulator and multiple strategies for the dice game Hog. You will need to use control statements and higher-order functions together, as described in Sections 1.2 through 1.6 of Composing Programs. In Hog, two players alternate turns trying to be the first to end a turn with at least 100 total points. On each turn, the current player chooses some number of dice to roll, up to 10. That player's score for the turn is the sum of the dice outcomes. To spice up the game, we will play with some special rules: Pig Out. If any of the dice outcomes is a 1, the current player's score for the turn is 1. Example 1: The current player rolls 7 dice, 5 of which are 1's. They score 1 point for the turn. Example 2: The current player rolls 4 dice, all of which are 3's. Since Pig Out did not occur, they score 12 points for the turn. Free Bacon. A player who chooses to roll zero dice scores one more than the largest digit in the opponent's total score. Example 1: If the opponent has 42 points, the current player gains 1 + max(4, 2) = 5 points by rolling zero dice. Example 2: If the opponent has 48 points, the current player gains 1 + max(4, 8) = 9 points by rolling zero dice. Example 3: If the opponent has 7 points, the current player gains 1 + max(0, 7) = 8 points by rolling zero dice. Swine Swap. After points for the turn are added to the current player's score, if both scores are larger than 1 and either one of the scores is a positive integer multiple of the other, then the two scores are swapped. Example 1: The current player has a total score of 37 and the opponent has 92. The current player rolls two dice that total 9. The opponent's score (92) is exactly twice the player's new total score (46). These scores are swapped! The current player now has 92 points and the opponent has 46. The turn ends. Example 2: The current player has 91 and the opponent has 37. The current player rolls five dice that total 20. The current player has 111, which is 3 times 37, so the scores are swapped. The opponent ends the turn with 111 and wins the game. Download starter files To get started, download all of the project code as a zip archive. You only have to make changes to hog.py. hog.py: A starter implementation of Hog dice.py: Functions for rolling dice hog_gui.py: A graphical user interface for Hog ucb.py: Utility functions for CS 61A ok: CS 61A autograder tests: A directory of tests used by ok images: A directory of images used by hog_gui.py Logistics This is a 2-week project. This is a solo project, so you will complete this project without a partner. You should not share your code with any other students, or copy from anyone else's solutions. Remember that you can earn an additional bonus point by submitting the project at least 24 hours before the deadline. The project is worth 20 points. 18 points are assigned for correctness, and 2 points for the overall composition of your program. You will turn in the following files: hog.py You do not need to modify or turn in any other files to complete the project. To submit the project, run the following command: python3 ok --submit You will be able to view your submissions on the Ok dashboard. For the functions that we ask you to complete, there may be some initial code that we provide. If you would rather not use that code, feel free to delete it and start from scratch. You may also add new function definitions as you see fit. However, please do not modify any other functions. Doing so may result in your code failing our autograder tests. Also, please do not change any function signatures (names, argument order, or number of arguments). Testing Throughout this project, you should be testing the correctness of your code. It is good practice to test often, so that it is easy to isolate any problems. However, you should not be testing too often, to allow yourself time to think through problems. We have provided an autograder called ok to help you with testing your code and tracking your progress. The first time you run the autograder, you will be asked to log in with your Ok account using your web browser. Please do so. Each time you run ok, it will back up your work and progress on our servers. The primary purpose of ok is to test your implementations, but there are two things you should be aware of. First, some of the test cases are locked. To unlock tests, run the following command from your terminal: python3 ok -u This command will start an interactive prompt that looks like: ===================================================================== Assignment: The Game of Hog Ok, version ... ===================================================================== ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Unlocking tests At each "? ", type what you would expect the output to be. Type exit() to quit --------------------------------------------------------------------- Question 0 > Suite 1 > Case 1 (cases remaining: 1) >>> Code here ? At the ?, you can type what you expect the output to be. If you are correct, then this test case will be available the next time you run the autograder. The idea is to understand conceptually what your program should do first, before you start writing any code. Once you have unlocked some tests and written some code, you can check the correctness of your program using the tests that you have unlocked: python3 ok Most of the time, you will want to focus on a particular question. Use the -q option as directed in the problems below. We recommend that you submit after you finish each problem. Only your last submission will be graded. It is also useful for us to have more backups of your code in case you run into a submission issue. The tests folder is used to store autograder tests, so do not modify it. You may lose all your unlocking progress if you do. If you need to get a fresh copy, you can download the zip archive and copy it over, but you will need to start unlocking from scratch. If you do not want us to record a backup of your work or information about your progress, use the --local option when invoking ok. With this option, no information will be sent to our course servers. Graphical User Interface A graphical user interface (GUI, for short) is provided for you. At the moment, it doesn't work because you haven't implemented the game logic. Once you complete the play function, you will be able to play a fully interactive version of Hog! In order to render the graphics, make sure you have Tkinter, Python's main graphics library, installed on your computer. Once you've done that, you can run the GUI from your terminal: python3 hog_gui.py Once you complete the project, you can play against the final strategy that you've created! python3 hog_gui.py -f Phase 1: Simulator In the first phase, you will develop a simulator for the game of Hog. Problem 0 (0 pt) The dice.py file represents dice using non-pure zero-argument functions. These functions are non-pure because they may have different return values each time they are called. The documentation of dice.py describes the two different types of dice used in the project: Dice can be fair, meaning that they produce each possible outcome with equal probability. Example: six_sided. For testing functions that use dice, deterministic test dice always cycle through a fixed sequence of values that are passed as arguments to the make_test_dice function. Before we start writing any code, let's understand the make_test_dice function by unlocking its tests. python3 ok -q 00 -u This should display a prompt that looks like this: ===================================================================== Assignment: Project 1: Hog Ok, version v1.5.2 ===================================================================== ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Unlocking tests At each "? ", type what you would expect the output to be. Type exit() to quit --------------------------------------------------------------------- Question 0 > Suite 1 > Case 1 (cases remaining: 1) >>> test_dice = make_test_dice(4, 1, 2) >>> test_dice() ? You should type in what you expect the output to be. To do so, you need to first figure out what test_dice will do, based on the description above. You can exit the unlocker by typing exit() (without quotes). Typing Ctrl-C on Windows to exit out of the unlocker has been known to cause problems, so avoid doing so. Problem 1 (2 pt) Implement the roll_dice function in hog.py. It takes two arguments: a positive integer called num_rolls giving the number of dice to roll and a dice function. It returns the number of points scored by rolling the dice that number of times in a turn: either the sum of the outcomes or 1 (Pig Out). To obtain a single outcome of a dice roll, call dice(). You should call dice() exactly num_rolls times in the body of roll_dice. Remember to call dice() exactly num_rolls times even if Pig Out happens in the middle of rolling. In this way, we correctly simulate rolling all the dice together. Checking Your Work: Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 01 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 01 If the tests don't pass, it's time to debug. You can observe the behavior of your function using Python directly. First, start the Python interpreter and load the hog.py file. python3 -i hog.py Then, you can call your roll_dice function on any number of dice you want, such as 4. >>> roll_dice(4) In most systems, you can evaluate the same expression again by pressing the up arrow or Control-P, then pressing enter or return. You should find that evaluating this call expression gives a different answer each time, since dice rolls are random. The roll_dice function has a default argument value for dice that is a random six-sided dice function. You can also use test dice that fix the outcomes of the dice in advance. For example, rolling twice when you know that the dice will come up 3 and 4 should give a total outcome of 7. >>> fixed_dice = make_test_dice(3, 4) >>> roll_dice(2, fixed_dice) 7 If you find a problem, you need to change your hog.py file, save it, quit Python, start it again, and then start evaluating expressions. Pressing the up arrow should give you access to your previous expressions, even after restarting Python. Once you think that your roll_dice function is correct, run the ok tests again. Tests like these don't prove that your program is exactly correct, but they help you build confidence that this part of your program does what you expect, so that you can trust the abstraction it defines as you proceed. Problem 2 (1 pt) Implement the free_bacon helper function that returns the number of points scored by rolling 0 dice, based on the opponent's current score. You can assume that score is less than 100. For a score less than 10, assume that the first of the two digits is 0. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 02 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 02 You can also test free_bacon interactively by entering python3 -i hog.py in the terminal and then calling free_bacon with various inputs. Problem 3 (1 pt) Implement the take_turn function, which returns the number of points scored for a turn by the current player. Your implementation should call roll_dice when possible. You will need to implement the Free Bacon rule. You can assume that opponent_score is less than 100. Call free_bacon in your implementation of take_turn. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 03 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 03 Problem 4 (1 pt) Implement is_swap, which returns whether or not the scores should be swapped because one is an integer multiple of the other. The is_swap function takes two arguments: the player scores. It returns a boolean value to indicate whether the Swine Swap condition is met. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 04 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 04 Problem 5 (3 pt) Implement the play function, which simulates a full game of Hog. Players alternate turns, each using their respective strategy function (Player 0 uses strategy0, etc.), until one of the players reaches the goal score. When the game ends, play returns the final total scores of both players, with Player 0's score first, and Player 1's score second. Here are some hints: You should use the functions you have already written! You will need to call take_turn with all three arguments. Only call take_turn once per turn. Enforce all the special rules. You can get the number of the other player (either 0 or 1) by calling the provided function other. You can ignore the say argument to the play function for now. You will use it in Phase 2 of the project. A strategy is a function that, given a player's score and their opponent's score, returns how many dice the player wants to roll. A strategy function (such as strategy0 and strategy1) takes two arguments: scores for the current player and opposing player, which both must be non-negative integers. A strategy function returns the number of dice that the current player wants to roll in the turn. Each strategy function should be called only once per turn. Don't worry about the details of implementing strategies yet. You will develop them in Phase 3. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 05 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 05 The last test for Question 5 is a fuzz test, which checks that your play function works for a large number of different inputs. Failing this test means something is wrong, but you should look at other tests to see where the problem might be. Once you are finished, you will be able to play a graphical version of the game. We have provided a file called hog_gui.py that you can run from the terminal: python3 hog_gui.py If you don't already have Tkinter (Python's graphics library) installed, you'll need to install it first before you can run the GUI. The GUI relies on your implementation, so if you have any bugs in your code, they will be reflected in the GUI. This means you can also use the GUI as a debugging tool; however, it's better to run the tests first. Congratulations! You have finished Phase 1 of this project! Phase 2: Commentary In the second phase, you will implement commentary functions that print remarks about the game, such as, "22 points! That's the biggest gain yet for Player 1." A commentary function takes two arguments, the current score for Player 0 and the current score for Player 1. It returns another commentary function to be called on the next turn. It may also print some output as a side effect of being called. The function say_scores in hog.py is an example of a commentary function. The function announce_lead_changes is an example of a higher-order function that returns a commentary function. def say_scores(score0, score1): """A commentary function that announces the score for each player.""" print("Player 0 now has", score0, "and Player 1 now has", score1) return say_scores def announce_lead_changes(previous_leader=None): """Return a commentary function that announces lead changes. >>> f0 = announce_lead_changes() >>> f1 = f0(5, 0) Player 0 takes the lead by 5 >>> f2 = f1(5, 12) Player 1 takes the lead by 7 >>> f3 = f2(8, 12) >>> f4 = f3(8, 13) >>> f5 = f4(15, 13) Player 0 takes the lead by 2 """ def say(score0, score1): if score0 > score1: leader = 0 elif score1 > score0: leader = 1 else: leader = None if leader != None and leader != previous_leader: print('Player', leader, 'takes the lead by', abs(score0 - score1)) return announce_lead_changes(leader) return say Problem 6 (2 pt) Update your play function so that a commentary function is called at the end of each turn. say(score0, score1) should be called at the end of the first turn. Its return value (another commentary function) should be called at the end of the second turn. Each turn, a new commentary function should be called that is the return value of the previous call to a commentary function. Also implement both, a function that takes two commentary functions (f and g) and returns a new commentary function. This new commentary function returns another commentary function which calls the functions returned by calling f and g, in that order. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 06 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 06 Problem 7 (2 pt) Implement the announce_highest function, which is a higher-order function that returns a commentary function. This commentary function announces whenever a particular player gains more points in a turn than ever before. To compute the gain, it must compare the score from last turn to the score from this turn for the player of interest, which is designated by the who argument. This function must also keep track of the highest gain for the player so far. The way in which announce_highest announces is very specific, and your implementation should match the doctests provided. Notice in particular that if the gain is only 1 point, then the message includes "point" in singular form. If the gain is larger, then the message includes "points" in plural form. Use Ok to test your code: python3 ok -q 07 Hint. The announce_lead_changes function provided to you is an example of how to keep track of information using commentary functions. If you are stuck, first make sure you understand how announce_lead_changes works. When you are done, if play the game again, you will see the commentary. python3 hog_gui.py The commentary in the GUI is generated by passing the following function as the say argument to play. both(announce_highest(0), both(announce_highest(1), announce_lead_changes())) Great work! You just finished Phase 2 of the project! Phase 3: Strategies In the third phase, you will experiment with ways to improve upon the basic strategy of always rolling a fixed number of dice. First, you need to develop some tools to evaluate strategies. Problem 8 (2 pt) Implement the make_averaged function, which is a higher-order function that takes a function fn as an argument. It returns another function that takes the same number of arguments as fn (the function originally passed into make_averaged). This returned function differs from the input function in that it returns the average value of repeatedly calling fn on the same arguments. This function should call fn a total of num_samples times and return the average of the results. To implement this function, you need a new piece of Python syntax! You must write a function that accepts an arbitrary number of arguments, then calls another function using exactly those arguments. Here's how it works. Instead of listing formal parameters for a function, we write *args. To call another function using exactly those arguments, we call it again with *args. For example, >>> def printed(fn): ... def print_and_return(*args): ... result = fn(*args) ... print('Result:', result) ... return result ... return print_and_return >>> printed_pow = printed(pow) >>> printed_pow(2, 8) Result: 256 256 >>> printed_abs = printed(abs) >>> printed_abs(-10) Result: 10 10 Read the docstring for make_averaged carefully to understand how it is meant to work. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 08 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 08 Problem 9 (1 pt) Implement the max_scoring_num_rolls function, which runs an experiment to determine the number of rolls (from 1 to 10) that gives the maximum average score for a turn. Your implementation should use make_averaged and roll_dice. If two numbers of rolls are tied for the maximum average score, return the lower number. For example, if both 3 and 6 achieve a maximum average score, return 3. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 09 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 09 To run this experiment on randomized dice, call run_experiments using the -r option: python3 hog.py -r Running experiments For the remainder of this project, you can change the implementation of run_experiments as you wish. By calling average_win_rate, you can evaluate various Hog strategies. For example, change the first if False: to if True: in order to evaluate always_roll(8) against the baseline strategy of always_roll(4). You should find that it wins slightly more often than it loses, giving a win rate around 0.5. Some of the experiments may take up to a minute to run. You can always reduce the number of samples in make_averaged to speed up experiments. Problem 10 (1 pt) A strategy can take advantage of the Free Bacon rule by rolling 0 when it is most beneficial to do so. Implement bacon_strategy, which returns 0 whenever rolling 0 would give at least margin points and returns num_rolls otherwise. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 10 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 10 Once you have implemented this strategy, change run_experiments to evaluate your new strategy against the baseline. You should find that it wins more than half of the time. Problem 11 (2 pt) A strategy can also take advantage of the Swine Swap rule. The swap_strategy rolls 0 if it would cause a beneficial swap. It also returns 0 if rolling 0 would give at least margin points and would not cause a swap. Otherwise, the strategy rolls num_rolls. Before writing any code, unlock the tests to verify your understanding of the question. python3 ok -q 11 -u Once you are done unlocking, begin implementing your solution. You can check your correctness with: python3 ok -q 11 Once you have implemented this strategy, update run_experiments to evaluate your new strategy against the baseline. You should find that it gives a significant edge over always_roll(4). Optional: Problem 12 (0 pt) Implement final_strategy, which combines these ideas and any other ideas you have to achieve a high win rate against the always_roll(4) strategy. Some suggestions: swap_strategy is a good default strategy to start with. There's no point in scoring more than 100. Check whether you can win by rolling 0, 1 or 2 dice. If you are in the lead, you might take fewer risks. Try to force a beneficial swap. Choose the num_rolls and margin arguments carefully. You can check that your final strategy is valid by running Ok. python3 ok -q 12 You can also check your exact final winrate by running python3 calc.py At this point, run the entire autograder to see if there are any tests that don't pass. python3 ok Once you are satisfied, submit to Ok to complete the project. python3 ok --submit You can also play against your final strategy with the graphical user interface: python3 hog_gui.py -f The GUI will alternate which player is controlled by you. Congratulations, you have reached the end of your first CS 61A project! If you haven't already, relax and enjoy a few games of Hog with a friend.
KlazikCZ / SignificantDigitsPrintFiles for printed version of the Significant Digits fanfic
george-steel / Sigdigs EbookWork in progress of ebook for "Significant digits" by Alexander D. http://www.anarchyishyperbole.com/p/significant-digits.html
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