Simplest random K-satisfiability problem

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 2, 2001, Pages 11-

  Ricci Tersenghi, Federico ^a   Weigt, Martin ^a,b   Zecchina, Riccardo ^a  

^a ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85035298160     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.026702     Document Type: Article

References (33)

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11. In this context, the study of Boolean satisfiability (Formula presented)-SAT) problems has played a major role, allowing for both theoretical and numerical analysis. An instance of random K-SAT consists of a set of (Formula presented) random logical clauses over N Boolean variables. Each clause contains exactly K variables which are connected by logical OR operations and appear negated with probability 1/2. The important computational question is whether there exists an assignment to the variables that simultaneously satisfies all clauses (“constraints”) for a given instance. When (Formula presented) crosses a critical value (Formula presented) and for (Formula presented), the probability of finding solutions vanishes abruptly, i.e., (Formula presented) identifies the so-called satisfiable to unsatifiable (SAT/UNSAT) transition. At the same point and for (Formula presented), hard computational instances cluster, leading to an exponential median search cost for the most efficient known algorithms. The random K-SAT problem therefore provides a good model for the study of the onset of true intractability of “typical” instances of NP-complete problems. Moreover, recents results 7 have pointed out a clear connection between typical-case computational complexity and the type of threshold phenomena taking place at (Formula presented)
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33. Similarly to what happens in Max-(Formula presented)SAT. See, for instance, P. Beame, R. Karp, T. Pitassi, and M. Saks, in Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing (ACM, New York, 1998), p. 561.