Abstract
This paper shows that idempotents in finite rings of integers can act as Generalized Boolean Assignments (GBA’s) by providing a completeness theorem. We introduce the notion of a generic Generalized Boolean Assignment. The mere propagation of such an assignment reveals feasibility (existence of a solution) of a formula in propositional logic. Then, we demystify this general concept by formulating the process on the bit-level: It turns out that propagation of a GBA only simulates bitwise (non-communicating) parallel computing. We capitalize on this by modifying the state-of-the-art local search Sat solver UnitWalk accordingly. This modification involves a more complicated parallelism.
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References
Anbulagan, A., et al.: Old Resolution Meets Modern SLS. In: AAAI-05, pp. 354–359 (2005)
Le Berre, D., Simon, L.: The Essentials of the SAT 2003 Competition. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 452–467. Springer, Heidelberg (2004)
Blochinger, W., Sinz, C., Kuchlin, W.: Parallel propositional satisfiability checking with distributed dynamic learning. Parallel Computing 29(7), 969–994 (2003)
Boehm, M., Speckenmeyer, E.: A fast parallel SAT-solver - efficient workload balancing. Ann. Math. Artif. Intell. 17(3-4), 381–400 (2006)
Brown, F.M.: Boolean Reasoning: The Logic of Boolean Equations. Kluwer Academic Publishers, Dordrecht (1990)
Hirsch, E.A., Kojevnikov, A.: UnitWalk: A new SAT solver that uses local search guided by unit clause elimination. Ann. Math. Artif. Intell. 43(1), 91–111 (2005)
Krohm, F., Kuehlmann, A., Mets, A.: The Use of Random Simulation in Formal Verification. In: Proc. of Int’l Conf. on Computer Design, pp. 371–376 (1996)
Selman, B., Kautz, H., Cohen, B.: Local search strategies for satisfiability testing. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, Coloring, and Satisfiability: the Second DIMACS Implementation Challenge, pp. 521–532 (1996)
Zhang, H., Bonacina, M.P., Hsiang, J.: PSATO: A distributed propositional prover and its application to quasigroup problems. Journal of Symbolic Computation 21, 543–560 (1996)
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Heule, M., van Maaren, H. (2007). From Idempotent Generalized Boolean Assignments to Multi-bit Search. In: Marques-Silva, J., Sakallah, K.A. (eds) Theory and Applications of Satisfiability Testing – SAT 2007. SAT 2007. Lecture Notes in Computer Science, vol 4501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72788-0_16
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DOI: https://doi.org/10.1007/978-3-540-72788-0_16
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