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Bose–Einstein condensation in satisfiability problems

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  • Angione, Claudio
  • Occhipinti, Annalisa
  • Stracquadanio, Giovanni
  • Nicosia, Giuseppe

Abstract

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.

Suggested Citation

  • Angione, Claudio & Occhipinti, Annalisa & Stracquadanio, Giovanni & Nicosia, Giuseppe, 2013. "Bose–Einstein condensation in satisfiability problems," European Journal of Operational Research, Elsevier, vol. 227(1), pages 44-54.
    • Handle: RePEc:eee:ejores:v:227:y:2013:i:1:p:44-54
    DOI: 10.1016/j.ejor.2012.11.039
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    References listed on IDEAS

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    3. Mastrolilli, Monaldo & Gambardella, Luca Maria, 2005. "Maximum satisfiability: How good are tabu search and plateau moves in the worst-case?," European Journal of Operational Research, Elsevier, vol. 166(1), pages 63-76, October.
    4. Escoffier, Bruno & Paschos, Vangelis Th., 2007. "Differential approximation of min sat, max sat and related problems," European Journal of Operational Research, Elsevier, vol. 181(2), pages 620-633, September.
    5. Zimmermann, H. J. & Monfroglio, Angelo, 1997. "Linear programs for constraint satisfaction problems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 105-123, February.
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