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Satisfiability checking using Boolean Expression Diagrams

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Abstract

In this paper we present an algorithm for determining satisfiability of general Boolean formulas which are not necessarily in conjunctive normal form. The algorithm extends the well-known Davis–Putnam algorithm to work on Boolean formulas represented using Boolean Expression Diagrams (BEDs). The BED data structure allows the algorithm to take advantage of the built-in reduction rules and the sharing of sub-formulas. Furthermore, it is possible to combine the algorithm with traditional BDD construction (using Bryant’s Apply-procedure). By adjusting a single parameter to the BedSat algorithm, it is possible to control to what extent the algorithm behaves like the Apply-algorithm or like a SAT-solver. Thus, the algorithm can be seen as bridging the gap between standard SAT-solvers and BDDs. We present promising experimental results for 566 non-clausal formulas obtained from the multi-level combinational circuits in the ISCAS’85 benchmark suite and from performing model checking of a shift-and-add multiplier.

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  1. Synopsys, Inc., 377 Simarano Drive, Suite 300, MA 01752, Marlborough, USA

    Poul F. Williams, Henrik R. Andersen & Henrik Hulgaard

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  1. Poul F. Williams
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  2. Henrik R. Andersen
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  3. Henrik Hulgaard
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Correspondence to Poul F. Williams, Henrik R. Andersen or Henrik Hulgaard.

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Williams, P., Andersen, H. & Hulgaard, H. Satisfiability checking using Boolean Expression Diagrams. Int J Softw Tools Technol Transfer 5, 4–14 (2003). https://doi.org/10.1007/s10009-002-0102-5

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