Consensus (computer science)

Concept in computer science
A fundamental problem in distributed computing and multi agent systems is to achieve overall system reliability in the presence of a number of faulty processes. This often requires coordinating processes to reach consensus, or agree on some data value that is needed during computation. Example applications of consensus include agreeing on what transactions to commit to a database in which order, state machine replication, and atomic broadcasts. Real world applications often requiring consensus include cloud computing, clock synchronization, PageRank, opinion formation, smart power grids, state estimation, control of UAVs (and multiple robots/agents in general), load balancing, blockchain, and others.

The consensus problem requires agreement among a number of processes (or agents) on a single data value. Some of the processes (agents) may fail or be unreliable in other ways, so consensus protocols must be fault tolerant or resilient. The processes must put forth their candidate values, communicate with one another, and agree on a single consensus value. The consensus problem is a fundamental problem in controlling multi agent systems. One approach to generating consensus is for all processes (agents) to agree on a majority value. In this context, a majority requires at least one more than half of the available votes (where each process is given a vote). However, one or more faulty processes may skew the resultant outcome such that consensus may not be reached or may be reached incorrectly. Protocols that solve consensus problems are designed to deal with a limited number of faulty processes. These protocols must satisfy several requirements to be useful. For instance, a trivial protocol could have all processes output binary value 1. This is not useful; thus, the requirement is modified such that the production must depend on the input. That is, the output value of a consensus protocol must be the input value of some process. Another requirement is that a process may decide upon an output value only once, and this decision is irrevocable. A method is correct in an execution if it does not experience a failure. A consensus protocol tolerating halting failures must satisfy the following properties.[1]. Termination Eventually, every correct process decides some value. Integrity If all the correct processes proposed the same value , then any correct process must decide Agreement Every correct process must agree on the same value. Variations on the definition of integrity may be appropriate, according to the application. For example, a weaker type of integrity would be for the decision value to equal a value that some correct process proposed – not necessarily all of them. The two different authentication models are often called oral communication and written communication models. In an oral communication model, the immediate source of information is known, whereas in stronger, written communication models, every step along the receiver learns not just the immediate source of the message, but the communication history of the message.

In the most traditional single value consensus protocols such as Paxos, cooperating nodes agree on a single value such as an integer, which may be of variable size so as to encode useful metadata such as a transaction committed to a database. A special case of the single value consensus problem, called binary consensus, restricts the input, and hence the output domain, to a single binary digit {0,1}. While not highly useful by themselves, binary consensus protocols are often useful as building blocks in more general consensus protocols, especially for asynchronous consensus. In multi valued consensus protocols such as Multi Paxos and Raft, the goal is to agree on not just a single value but a series of values over time, forming a progressively growing history. While multi valued consensus may be achieved naively by running multiple iterations of a single valued consensus protocol in succession, many optimizations and other considerations such as reconfiguration support can make multi valued consensus protocols more efficient in practice.

The consensus problem may be considered in the case of asynchronous or synchronous systems. While real world communications are often inherently asynchronous, it is more practical and often easier to model synchronous systems, given that asynchronous systems naturally involve more issues than synchronous ones. In synchronous systems, it is assumed that all communications proceed in rounds. In one round, a process may send all the messages it requires, while receiving all messages from other processes. In this manner, no message from one round may influence any messages sent within the same round.

In a fully asynchronous message passing distributed system, in which at least one process may have a crash failure, it has been proven in the famous 1985 FLP impossibility result by Fischer, Lynch and Paterson that a deterministic algorithm for achieving consensus is impossible. This impossibility result derives from worst case scheduling scenarios, which are unlikely to occur in practice except in adversarial situations such as an intelligent denial of service attacker in the network. In most normal situations, process scheduling has a degree of natural randomness.

Consensus algorithms traditionally assume that the set of participating nodes is fixed and given at the outset: that is, that some prior (manual or automatic) configuration process has permissioned a particular known group of participants who can authenticate each other as members of the group. In the absence of such a well defined, closed group with authenticated members, a Sybil attack against an open consensus group can defeat even a Byzantine consensus algorithm, simply by creating enough virtual participants to overwhelm the fault tolerance threshold. A permissionless consensus protocol, in contrast, allows anyone in the network to join dynamically and participate without prior permission, but instead imposes a different form of artificial cost or barrier to entry to mitigate the Sybil attack threat. Bitcoin introduced the first permissionless consensus protocol using proof of work and a difficulty adjustment function, in which participants compete to solve cryptographic hash puzzles, and probabilistically earn the right to commit blocks and earn associated rewards in proportion to their invested computational effort. Motivated in part by the high energy cost of this approach, subsequent permissionless consensus protocols have proposed or adopted other alternative participation rules for Sybil attack protection, such as proof of stake, proof of space, and proof of authority.

Three agreement problems of interest are as follows.

There is a t resilient anonymous synchronous protocol which solves the Byzantine Generals problem, if and the Weak Byzantine Generals case The proof is constructed by first showing the impossibility for the three node case and using this result to argue about partitions of processors. In the written messages model there are protocols that can tolerate However, FLP does not state that consensus can never be reached: merely that under the model's assumptions, no algorithm can always reach consensus in bounded time. In practice it is highly unlikely to occur.

The Paxos consensus algorithm by Leslie Lamport, and variants of it such as Raft, are used pervasively in widely deployed distributed and cloud computing systems. These algorithms are typically synchronous, dependent on an elected leader to make progress, and tolerate only crashes and not Byzantine failures. An example of a polynomial time binary consensus protocol that tolerates Byzantine failures is the Phase King algorithm by Garay and Berman. The algorithm solves consensus in a synchronous message passing model with n processes and up to f failures, provided n > 4f. In the phase king algorithm, there are f + 1 phases, with 2 rounds per phase. Each process keeps track of its preferred output (initially equal to the process's own input value). In the first round of each phase each process broadcasts its own preferred value to all other processes. It then receives the values from all processes and determines which value is the majority value and its count. In the second round of the phase, the process whose id matches the current phase number is designated the king of the phase. The king broadcasts the majority value it observed in the first round and serves as a tie breaker. Each process then updates its preferred value as follows. If the count of the majority value the process observed in the first round is greater than n/2 + f, the process changes its preference to that majority value; otherwise it uses the phase king's value. At the end of f + 1 phases the processes output their preferred values. Google has implemented a distributed lock service library called Chubby. Chubby maintains lock information in small files which are stored in a replicated database to achieve high availability in the face of failures. The database is implemented on top of a fault tolerant log layer which is based on the Paxos consensus algorithm. In this scheme, Chubby clients communicate with the Paxos master in order to access/update the replicated log; i. e., read/write to the files. Many peer to peer online real time strategy games use a modified lockstep protocol as a consensus protocol in order to manage game state between players in a game. Each game action results in a game state delta broadcast to all other players in the game along with a hash of the total game state. Each player validates the change by applying the delta to their own game state and comparing the game state hashes. If the hashes do not agree then a vote is cast, and those players whose game state is in the minority are disconnected and removed from the game (known as a desync.) Another well known approach is called MSR type algorithms which have been used widely from computer science to control theory. Source Synchrony Authentication Threshold Rounds Notes Pease Shostak Lamport Asynchronous Oral (expected) expected rounds when Dolev et al. Synchronous Oral total communication Dolev Strong Synchronous Oral (expected) Katz Koo Synchronous Written (expected) Requires Public Key Infrastructure (PKI) PBFT Asynchronous (safety)Synchronous (liveness) Oral HoneyBadger Asynchronous Oral (expected) per tx communication requires public key encryption Abraham et al. Synchronous Written Byzantine Agreement Made Trivial Synchronous Signatures (expected) Requires digital signatures

To solve the consensus problem in a shared memory system, concurrent objects must be introduced. A concurrent object, or shared object, is a data structure which helps concurrent processes communicate to reach an agreement. Traditional implementations using critical sections face the risk of crashing if some process dies inside the critical section or sleeps for an intolerably long time. Researchers defined wait freedom as the guarantee that the algorithm completes in a finite number of steps. The consensus number of a concurrent object is defined to be the maximum number of processes in the system which can reach consensus by the given object in a wait free implementation. Objects with a consensus number of can implement any object with a consensus number of or lower, but cannot implement any objects with a higher consensus number. The consensus numbers form what is called Herlihy's hierarchy of synchronization objects. Consensusnumber Objects atomic read/write registers, mutex test and set, swap, fetch and add, wait free queue or stack n register assignment compare and swap, load link/store conditional, memory to memory move and swap, queue with peek operation, fetch&cons, sticky byte

According to the hierarchy, read/write registers cannot solve consensus even in a 2 process system. Data structures like stacks and queues can only solve consensus between two processes. However, some concurrent objects are universal (notated in the table with ), which means they can solve consensus among any number of processes and they can simulate any other objects through an operation sequence.