The Problem of Distributed Consensus: A Survey

A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems. A variety of new results are given, as well as a history of the field and an extensive bibliography. Distributed consensus is of current relevance in a new generation of blockchain-related systems.

[1]  David Griffeath,et al.  Multicomponent Random Systems , 1980 .

[2]  Marcos K. Aguilera,et al.  The correctness proof of Ben-Or’s randomized consensus algorithm , 2012, Distributed Computing.

[3]  Lawrence Gray,et al.  A Reader's Guide to Gacs's “Positive Rates” Paper , 2001 .

[5]  Luca Trevisan,et al.  Stabilizing Consensus with Many Opinions , 2015, SODA.

[6]  M Mitchell,et al.  The evolution of emergent computation. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[7]  James P. Crutchfield,et al.  Evolving Globally Synchronized Cellular Automata , 1995, ICGA.

[8]  Peter Gacs,et al.  A new version of Toom's proof , 1995, ArXiv.

[9]  Zhancang Wang.  MOCA: A Scalable Consensus Algorithm Based on Cellular Automata , 2018, 2018 IEEE 9th International Conference on Software Engineering and Service Science (ICSESS).

[10]  Roelof Kuik,et al.  From PCA's to equilibrium systems and back , 1989 .

[11]  A. Toom,et al.  Chapter 4 CELLULAR AUTOMATA WITH ERRORS: PROBLEMS for STUDENTS of PROBABILITY , 2005 .

[12]  Ilkka Törmä,et al.  Stable Multi-Level Monotonic Eroders , 2018, ArXiv.

[13]  J. Lebowitz,et al.  Statistical mechanics of probabilistic cellular automata , 1990 .

[14]  Elchanan Mossel,et al.  Majority dynamics and aggregation of information in social networks , 2012, Autonomous Agents and Multi-Agent Systems.

[15]  H. Fuks.  Nondeterministic density classification with diffusive probabilistic cellular automata. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Abhishek Mathur,et al.  Efficient system-wide coordination in noisy environments. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Colin Cooper,et al.  The Power of Two Choices in Distributed Voting , 2014, ICALP.

[18]  Abhishek Bhatia,et al.  On the role of evangelism in consensus formation: a simulation approach , 2016, Complex Adapt. Syst. Model..

[19]  Eric Goles Ch.,et al.  Dynamics of Positive Automata Networks , 1985, Theor. Comput. Sci..

[20]  Aaron D. Wyner,et al.  Reliable Circuits Using Less Reliable Relays , 1993 .

[21]  Pedro P. B. de Oliveira.  On Density Determination With Cellular Automata: Results, Constructions and Directions , 2014, J. Cell. Autom..

[22]  Hidenosuke Nishio,et al.  Fault Tolerant Cellular Spaces , 1975, J. Comput. Syst. Sci..

[23]  Constantino Tsallis,et al.  A majority-rule model : real-space renormalization-group solution and finite size scaling , 1982 .

[24]  Predrag T. Tosic.  Cellular automata for distributed computing: models of agent interaction and their implications , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[25]  R. Durrett.  Lecture notes on particle systems and percolation , 1988 .

[26]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[27]  J. von Neumann,et al.  Probabilistic Logic and the Synthesis of Reliable Organisms from Unreliable Components , 1956 .

[28]  Nazim Fatès,et al.  Stochastic Cellular Automata Solutions to the Density Classification Problem , 2012, Theory of Computing Systems.

[29]  Cristopher Moore.  Majority-Vote Cellular Automata, Ising Dynamics, and P-Completeness , 1997 .

[30]  Melanie Mitchell,et al.  Evolving cellular automata to perform computations: mechanisms and impediments , 1994 .

[31]  J. T. Cox,et al.  Diffusive Clustering in the Two Dimensional Voter Model , 1986 .

[32]  Senya Shlosman,et al.  Ergodicity of probabilistic cellular automata: A constructive criterion , 1991 .

[33]  Nicholas Pippenger.  Symmetry in Self-Correcting Cellular Automata , 1994, J. Comput. Syst. Sci..

[34]  Capcarrere,et al.  Two-state, r=1 Cellular Automaton that Classifies Density. , 1996, Physical review letters.

[35]  Klaus Sutner,et al.  Additive Automata On Graphs , 1988, Complex Syst..

[36]  Federico Bergenti,et al.  A Stochastic Model of Self-Stabilizing Cellular Automata for Consensus Formation , 2014, WOA.

[37]  James P. Crutchfield,et al.  G 1 . 15 : Computer Science Application : Evolving Cellular Automata to Perform Computations , 2001 .

[38]  Christian Bettstetter,et al.  Distributed Binary Consensus in Networks with Disturbances , 2015, ACM Trans. Auton. Adapt. Syst..

[39]  Yuval Peres,et al.  Communication cost of consensus for nodes with limited memory , 2020, Proceedings of the National Academy of Sciences.

[40]  Stephen Wolfram,et al.  Approaches to complexity engineering , 1986 .

[41]  T. E. Harris.  Contact Interactions on a Lattice , 1974 .

[42]  Exponential convergence of Toom's probabilistic cellular automata , 1993 .

[43]  Mieko Tanaka-Yamawaki,et al.  Consensus formation and the cellular automata , 1996, Robotics Auton. Syst..

[44]  Péter Gács,et al.  A Simple Three-Dimensional Real-Time Reliable Cellular Array , 1988, J. Comput. Syst. Sci..

[45]  Gina Maira Barbosa de Oliveira,et al.  Some Investigations About Synchronization and Density Classification Tasks in One-dimensional and Two-dimensional Cellular Automata Rule Spaces , 2009, Electron. Notes Theor. Comput. Sci..

[46]  Eric Goles Ch.,et al.  On the complexity of two-dimensional signed majority cellular automata , 2018, J. Comput. Syst. Sci..

[47]  David Griffin,et al.  The Consensus Problem, Cellular Automata, and Self-Replicating Structures , 2016 .

[48]  Bennett,et al.  Role of irreversibility in stabilizing complex and nonergodic behavior in locally interacting discrete systems. , 1985, Physical review letters.

[49]  Ayalvadi Ganesh,et al.  Probabilistic consensus via polling and majority rules , 2013, Queueing Syst. Theory Appl..

[50]  Péter Gács,et al.  Reliable computation with cellular automata , 1983, J. Comput. Syst. Sci..

[51]  R. Dobrushin,et al.  Locally Interacting Systems and Their Application in Biology , 1978 .

[52]  Land,et al.  No perfect two-state cellular automata for density classification exists. , 1995, Physical review letters.

[53]  C. Tsallis,et al.  Do the simple and 2/3 majority models belong to the same universality class?: A monte carlo approach , 1991 .

[54]  F. H. Bennett,et al.  Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem , 1996 .

[55]  Nancy A. Lynch,et al.  Impossibility of distributed consensus with one faulty process , 1983, PODS '83.

[56]  Péter Gács.  Reliable Cellular Automata with Self-Organization , 1997, FOCS 1997.

[57]  C. Marr,et al.  Outer-totalistic cellular automata on graphs , 2008, 0812.2408.

[58]  James P. Crutchfield,et al.  The Evolutionary Design of Collective Computation in Cellular Automata , 1998, adap-org/9809001.

[59]  Albert Y. Zomaya,et al.  Cellular automata based models of wireless sensor networks , 2009, MobiWAC '09.

[60]  Kihong Park,et al.  Ergodicity and mixing rate of one-dimensional cellular automata , 1997 .

[61]  Henryk Fukś,et al.  Explorations of Ternary Cellular Automata and Ternary Density Classification Problems , 2020, Acta Physica Polonica B Proceedings Supplement.

[62]  E. Speert,et al.  Dynamics of an anchored Toom interface , 2022 .

[63]  Soummya Kar,et al.  Distributed Average Consensus in Sensor Networks with Random Link Failures and Communication Channel Noise , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[64]  Colin Cooper,et al.  Fast Consensus for Voting on General Expander Graphs , 2015, DISC.

[65]  Predrag T. Tosic.  Phase Transitions in Possible Dynamics of Cellular and Graph Automata Models of Sparsely Interconnected Multi-Agent Systems , 2017, AAMAS.

[66]  Nicholas Pippenger,et al.  Fault tolerance in cellular automata at low fault rates , 2013, J. Comput. Syst. Sci..