From idempotent generalized boolean assignments to multi-bit search

Authors:
Marijn Heule;Hans Van Maaren
Affiliations:
Department of Software Technology, Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology;Department of Software Technology, Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology
Venue:
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Year:
2007

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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.