@MISC{Beckert_anddeduction, author = {Bernhard Beckert and Reiner Hähnle and Neil V. Murray and Anavai Ramesh}, title = {and Deduction Systems}, year = {} }

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Abstract

Manipulation of Boolean functions has important applications in such fields as hardware verification, non-monotonic reasoning, and decision support. Most often, in such applications, the set of prime implicates/implicants of a large formula must be computed. Many algorithms have been proposed to compute the prime implicates of propositionalBoolean formulas, e.g. [4, 5]. Most of them assume that the input is in conjunctive/disjunctive normal form (CNF/DNF). The bottleneck of such algorithms is usually the large number of subsumed (i.e. non-minimal) disjunctive/conjunctive paths through the given formula. Therefore, it is crucial to remove as much redundancy of this kind as possible, before any explicit enumeration of prime implicates/implicants starts. Even if such explicit computation of prime implicates/implicants is not an immediate goal, removing any redundancies due to subsumed disjunctive/conjunctive paths is usually highly desirable. Among the most successful methods used to deal with this task are binary decision diagrams (BDDs) [2, 3]. It is, however, well known that BDD methods do not work well on some classes of formulas, in particular, when they are used to compute prime implicants. Another restriction of BDDs is that they (at least the efficient versions) essentially produce an XOR-AND normal form, but this is not always what is needed.