Bose-Einstein condensation in satisfiability problems

作者：Angione Claudio; Occhipinti Annalisa; Stracquadanio Giovanni; Nicosia Giuseppe^*

来源：European Journal of Operational Research, 2013, 227(1): 44-54.

DOI：10.1016/j.ejor.2012.11.039

• k-SAT
• Complex networks
• Bose-Einstein condensation
• Phase transition
• Performance

This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k-SAT instance, in order to analyze them and show whether a Bose-Einstein condensation occurs. We observe that, analogously to complex networks, the networks of k-SAT instances follow Bose statistics and can undergo Bose-Einstein condensation. In particular, k-SAT instances move from a fit-get-rich network to a winner-takes-all network as the ratio of clauses to variables decreases, and the phase transition of k-SAT approximates the critical temperature for the Bose-Einstein condensation. Finally, we employ the fitness-based classification to enhance SAT solvers (e.g., ChainSAT) and obtain the consistently highest performing SAT solver for CNF formulas, and therefore a new class of efficient hardware and software verification tools.

• 出版日期2013-5-16