Synchronous counting and computational algorithm design

Autor: Keijo Heljanko, Christoph Lenzen, Jukka Suomela, Matti Järvisalo, Joel Rybicki, Danny Dolev, Siert Wieringa, Janne H. Korhonen
Jazyk: angličtina
Rok vydání: 2016
Předmět:
FOS: Computer and information sciences
Theoretical computer science
Computational complexity theory
Computer Networks and Communications
Deterministic algorithm
Computer science
Boolean circuit
Self-stabilisation
02 engineering and technology
Computational Complexity (cs.CC)
Theoretical Computer Science
Byzantine fault tolerance
Synthesis
Consensus
020204 information systems
Computer Science - Data Structures and Algorithms
0202 electrical engineering
electronic engineering
information engineering
Data Structures and Algorithms (cs.DS)
ta518
ta515
ta113
ta112
ta213
Applied Mathematics
Formal methods
Data structure
Satisfiability
Distributed computing
Computer Science - Computational Complexity
Computational Theory and Mathematics
Computer Science - Distributed
Parallel
and Cluster Computing
ta5141
020201 artificial intelligence & image processing
Node (circuits)
SAT
Distributed
Parallel
and Cluster Computing (cs.DC)
Algorithm
Zdroj: JOURNAL OF COMPUTER AND SYSTEM SCIENCES. 82(2):310-332
ISSN: 0022-0000
Popis: Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates $f$ Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states. This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of $f = 1$. While no algorithm exists for $n < 4$, we show that as few as 3 states per node are sufficient for all values $n \ge 4$. Moreover, the problem cannot be solved with only 2 states per node for $n = 4$, but there is a 2-state solution for all values $n \ge 6$. In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SAT-solvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.
35 pages, extended and revised version
Databáze: OpenAIRE
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