Consensus (computer science)

Consensus is a problem in distributed computing that encapsulates the task of group agreement in the presence of faults.^[1]

In particular, any process in the group may fail at any time. Consensus is fundamental to core techniques in fault tolerance, such as state machine replication.

Problem description

A process is called "correct" if it does not fail at any point during its execution. Unlike Terminating Reliable Broadcast, the typical consensus problem does not label any single process as a "sender". Every process "proposes" a value; the goal of the protocol is for all correct processes to choose a single value from among those proposed. Valid consensus protocols must provide important guarantees to all processes involved. All correct processes must eventually decide the same value, for example, and that value must be one of those proposed. A correct process is therefore guaranteed that the value it decides was also decided by all other correct processes, and can act on that value accordingly.

More precisely, a consensus protocol must satisfy the four formal properties below.

Termination

every correct process decides some value.

Validity

if all processes propose the same value v, then every correct process decides v.

Integrity

every correct process decides at most one value, and if it decides some value v, then v must have been proposed by some process.

Agreement

if a correct process decides v, then every correct process decides v.

The possibility of faults in the system makes these properties more difficult to satisfy. A simple but invalid consensus protocol might have every process broadcast its proposal to all others, and have a process decide on the smallest value received. Such a protocol, as described, does not satisfy Agreement if faults can occur: if a process crashes after sending its proposal to some processes, but before sending it to others, then the two sets of processes may decide different values.

Failure model

The consensus problem is challenging primarily because one or more of the processes involved may fail at any time. Consensus protocols typically make one of two assumptions about how processes may fail:

• In a fail-stop or fail-crash model, a failed process simply stops participating in the protocol. This models a communication failure (e.g., network partition) or a system crash. A variant is the crash-recovery model, where halted processes can restart and restore their state previous to the crash, through stable storage.
• In a Byzantine failure model, a failed process may behave in an arbitrary fashion. In particular, a failed process may collaborate with other failed processes in order to deliberately subvert the operations of the consensus protocol. Because failed processes are allowed to behave arbitrarily and to collaborate, this models both software bugs and the possibility of attack by a hostile adversary.

Impossibility

Consensus has been shown to be impossible to solve in several models of distributed computing.

In an asynchronous system, where processes have no common clock and run at arbitrarily varying speeds, the problem is impossible to solve if one process may crash and processes communicate by sending messages to one another.^[2] The technique used to prove this result is sometimes called an FLP impossibility proof, named after its creators, Michael J. Fischer, Nancy A. Lynch and Michael S. Paterson, who won the Dijkstra Prize for this result. The technique has been widely used to prove other impossibility results. For example, a similar proof can be used to show that consensus is also impossible in asynchronous systems where processes communicate by reading and writing shared variables if one process may crash.^[3]

A notable exception to the FLP impossibility proof is in quantum computing, where it has been shown that asynchronous consensus can always be achieved even in the presence of faults, crashes, or deliberate efforts to undermine the consensus by participating processes.^[4]

The FLP result 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. There exist algorithms, even under the asynchronous model, that can reach consensus with probability one. The FLP proof hinges on demonstrating the existence of an order of message receipts that causes the system to never reach consensus. This "bad" input however may be vanishingly unlikely in practice.

In a synchronous system, where all processes run at the same speed, consensus is impossible if processes communicate by sending messages to one another and one third of the processes can experience Byzantine failures.^[5]

Important consensus protocols

Google has implemented a distributed lock service library called Chubby.^[6] 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.^[7]

Bitcoin uses proof of work to maintain consensus in its peer-to-peer network. Nodes in the bitcoin network attempt to solve a cryptographic proof-of-work problem, where probability of finding the solution is proportional to the computational effort, in hashes per second, expended, and the node that solves the problem has their version of the block of transactions added to the peer-to-peer distributed timestamp server accepted by all of the other nodes. As any node in the network can attempt to solve the proof-of-work problem, a Sybil attack becomes unfeasible unless the attacker has over 50% of the computational resources of the network.

• Chandra-Toueg consensus algorithm
• Randomized consensus

References

1. ^ Lamport, Leslie; Marshall Pease and Robert Shostak (April 1980). "Reaching Agreement in the Presence of Faults". Journal of the ACM 27 (2): 228–234. doi:10.1145/322186.322188. 10.1145/322186.322188. http://research.microsoft.com/users/lamport/pubs/reaching.pdf. Retrieved 2007-07-25. 
2. ^ Fischer, Michael J.  ; Nancy A. Lynch; Michael S. Paterson (April 1985). "Impossibility of Distributed Consensus with One Faulty Process". Journal of the ACM 32 (2): 374–382. doi:10.1145/3149.214121. http://portal.acm.org/citation.cfm?doid=3149.214121. Retrieved 2007-04-29  . 
3. ^ Loui, M. C.; Abu-Amara, H. H. (1987). "Memory requirements for agreement among unreliable asynchronous processes". In Preparata, F. P.. Advances in Computing Research. 4. Greenwich, Connecticut: JAI Press. pp. 163–183. 
4. ^ Helm, Louis K. (2008). "Quantum distributed consensus". Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing (ACM) 1 (1): 445. doi:10.1145/1400751.1400841. ISBN 9781595939890. http://portal.acm.org/citation.cfm?id=1400841. 
5. ^ Fischer, Michael J.; Nancy A. Lynch; Michael Merritt (1986). "Easy impossibility proofs for distributed consensus problems". Distributed Computing (Springer) 1 (1): 26–39. doi:10.1007/BF01843568. 
6. ^ Burrows, M. (2006). "The Chubby lock service for loosely-coupled distributed systems". Proceedings of the 7th Symposium on Operating Systems Design and Implementation. USENIX Association Berkeley, CA, USA. pp. 335–350. http://labs.google.com/papers/chubby.html. 
7. ^ C., Tushar; Griesemer, R; Redstone J. (2007). "Paxos Made Live - An Engineering Perspective". Proceedings of the Twenty-sixth Annual ACM Symposium on Principles of Distributed Computing. Portland, Oregon, USA: ACM Press New York, NY, USA. pp. 398–407. doi:http://doi.acm.org/10.1145/1281100.1281103. http://delivery.acm.org/10.1145/1290000/1281103/p398-chandra.pdf?key1=1281103&key2=4382532021&coll=GUIDE&dl=GUIDE&CFID=15324100&CFTOKEN=95510390. Retrieved 2008-02-06. 

Further reading

• Herlihy, M.; Shavit, N. (1999). "The topological structure of asynchronous computability". Journal of the ACM 46 (6): 858. doi:10.1145/331524.331529.  edit
• Saks, M.; Zaharoglou, F. (2000). "Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge". SIAM Journal on Computing 29 (5): 1449. doi:10.1137/S0097539796307698.  edit