Bose–Einstein condensation in satisfiability problems

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.