Untangling Partial Agreement: Iterated x-consensus Simulations

The basic read/write shared memory model where asynchronous and crash prone processes communicate to solve a task is difficult to analyze. A more structured model is the iterated immediate snapshot model IIS, where processes execute communication closed rounds. In each round, they communicate using read/write registers that cannot be reused in later rounds. It is known that a task is solvable in the IIS model if and only if it is solvable in the basic read/write model. Both models are also equivalent when, in addition to read/write registers, processes also have access to stronger communication objects called 01-tasks. This paper extends further the task computability equivalence presenting a simulation that includes x-consensus objects, which solve consensus among up to x processes. The simulation implies that an iterated model where processes communicate through a sequence consisting only of x-consensus objects is equivalent to the basic shared memory model augmented with x-consensus objects.

[1]  Nancy A. Lynch,et al.  Impossibility of distributed consensus with one faulty process , 1985, JACM.

[2]  Maurice Herlihy,et al.  The decidability of distributed decision tasks (extended abstract) , 1997, STOC '97.

[3]  Maurice Herlihy,et al.  Unifying synchronous and asynchronous message-passing models , 1998, PODC '98.

[4]  Hagit Attiya,et al.  Distributed Computing: Fundamentals, Simulations and Advanced Topics , 1998 .

[5]  Eli Gafni,et al.  Distributed Programming with Tasks , 2010, OPODIS.

[6]  Eli Gafni,et al.  Generalized FLP impossibility result for t-resilient asynchronous computations , 1993, STOC.

[7]  Michel Raynal,et al.  Power and limits of distributed computing shared memory models , 2013, Theor. Comput. Sci..

[8]  Michel Raynal,et al.  Synchrony weakened by message adversaries vs asynchrony restricted by failure detectors , 2013, PODC '13.

[9]  Eli Gafni,et al.  Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony , 1998, PODC '98.

[10]  Maurice Herlihy,et al.  Distributed Computing Through Combinatorial Topology , 2013 .

[11]  Shmuel Zaks,et al.  A Combinatorial Characterization of the Distributed 1-Solvable Tasks , 1990, J. Algorithms.

[12]  Michel Raynal,et al.  The multiplicative power of consensus numbers , 2010, PODC '10.

[13]  Gil Neiger,et al.  Automatically Increasing the Fault-Tolerance of Distributed Algorithms , 1990, J. Algorithms.

[14]  Eli Gafni,et al.  A simple algorithmically reasoned characterization of wait-free computation (extended abstract) , 1997, PODC '97.

[15]  André Schiper,et al.  The Heard-Of model: computing in distributed systems with benign faults , 2009, Distributed Computing.

[16]  Eli Gafni,et al.  Understanding and verifying distributed algorithms using stratified decomposition , 1988, PODC '88.

[17]  Maurice Herlihy,et al.  Linearizability: a correctness condition for concurrent objects , 1990, TOPL.

[18]  Maurice Herlihy,et al.  A classification of wait-free loop agreement tasks , 2003, Theor. Comput. Sci..

[19]  Maurice Herlihy,et al.  Subconsensus Tasks: Renaming Is Weaker Than Set Agreement , 2006, DISC.

[20]  Michel Raynal,et al.  The Distributed Computing Column , 2013 .

[21]  Yehuda Afek,et al.  A completeness theorem for a class of synchronization objects , 1993, PODC '93.

[22]  Maurice Herlihy,et al.  Wait-free synchronization , 1991, TOPL.

[23]  Eli Gafni,et al.  Immediate atomic snapshots and fast renaming , 1993, PODC '93.

[24]  Benny Chor,et al.  Solvability in asynchronous environments , 1989, 30th Annual Symposium on Foundations of Computer Science.

[25]  Nancy A. Lynch,et al.  The BG distributed simulation algorithm , 2001, Distributed Computing.

[26]  Eli Gafni,et al.  Three-Processor Tasks Are Undecidable , 1999, SIAM J. Comput..

[27]  Michel Raynal,et al.  Brief announcement: increasing the power of the iterated immediate snapshot model with failure detectors , 2012, PODC '12.

[28]  Sergio Rajsbaum,et al.  Iterated Shared Memory Models , 2010, LATIN.

[29]  Eli Gafni,et al.  Recursion in Distributed Computing , 2010, SSS.

[30]  Maurice Herlihy,et al.  Simulations and reductions for colorless tasks , 2012, PODC '12.

[31]  Michael E. Saks,et al.  Wait-free k-set agreement is impossible: the topology of public knowledge , 1993, STOC.

[32]  Maurice Herlihy,et al.  Elements of Combinatorial Topology , 2014 .

[33]  Sam Toueg,et al.  Generalized Irreducibility of Consensus and the Equivalence of t-Resilient and Wait-Free Implementations of Consensus , 2004, SIAM J. Comput..

[34]  Sergio Rajsbaum,et al.  The Complexity Gap between Consensus and Safe-Consensus - (Extended Abstract) , 2014, SIROCCO.

[35]  Soma Chaudhuri,et al.  More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems , 1993, Inf. Comput..

[36]  Michel Raynal,et al.  The Iterated Restricted Immediate Snapshot Model , 2008, COCOON.

[37]  Eli Gafni.  The 0-1-Exclusion Families of Tasks , 2008, OPODIS.

[38]  Benny Chor,et al.  Solvability in Asynchronous Environments II: Finite Interactive Tasks , 1999, SIAM J. Comput..

[39]  Soma Chaudhuri,et al.  Understanding the Set Consensus Partial Order Using the Borowsky-Gafni Simulation (Extended Abstract) , 1996, WDAG.

[40]  Nissim Francez,et al.  Decomposition of Distributed Programs into Communication-Closed Layers , 1982, Sci. Comput. Program..

[41]  Petr Kuznetsov,et al.  Strong Equivalence Relations for Iterated Models , 2014, OPODIS.

[42]  Michel Raynal,et al.  An impossibility about failure detectors in the iterated immediate snapshot model , 2008, Inf. Process. Lett..

[43]  Michel Raynal,et al.  Renaming Is Weaker Than Set Agreement But for Perfect Renaming: A Map of Sub-consensus Tasks , 2012, LATIN.

[44]  Maurice Herlihy,et al.  The topological structure of asynchronous computability , 1999, JACM.

[45]  Maurice Herlihy,et al.  The topology of distributed adversaries , 2013, Distributed Computing.

[46]  Maurice Herlihy,et al.  Sporadic Solutions to Zero-One Exclusion Tasks , 2014, ICALP.