From Idempotent Generalized Boolean Assignments to Multi-bit Search

  • Marijn Heule
  • Hans van Maaren
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4501)


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.


Local Search Boolean Function Propositional Logic Unit Propagation Completeness Theorem 
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  1. 1.
    Anbulagan, A., et al.: Old Resolution Meets Modern SLS. In: AAAI-05, pp. 354–359 (2005)Google Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    Blochinger, W., Sinz, C., Kuchlin, W.: Parallel propositional satisfiability checking with distributed dynamic learning. Parallel Computing 29(7), 969–994 (2003)CrossRefGoogle Scholar
  4. 4.
    Boehm, M., Speckenmeyer, E.: A fast parallel SAT-solver - efficient workload balancing. Ann. Math. Artif. Intell. 17(3-4), 381–400 (2006)Google Scholar
  5. 5.
    Brown, F.M.: Boolean Reasoning: The Logic of Boolean Equations. Kluwer Academic Publishers, Dordrecht (1990)zbMATHGoogle Scholar
  6. 6.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marijn Heule
    • 1
  • Hans van Maaren
    • 1
  1. 1.Department of Software Technology, Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology 

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