Discrete Optimization Bose–Einstein condensation in satisfiability problems

0377-2217/$ see front matter 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.ejor.2012.11.039 ⇑ Corresponding author. Tel.: +39 095 738 3048; fa E-mail addresses: [email protected] ( unict.it (A. Occhipinti), [email protected] (G. S unict.it (G. Nicosia). 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. 2012 Elsevier B.V. All rights reserved.