Experiments with a Tautology Checking Algorithm

نویسندگان

  • Martin Richards
  • Randy Bryant
چکیده

This paper presents various versions of a tautology checking algorithm that is related both to St̊almarck’s algorithm and the mechanism described by Kunz and Stoffel in Reasoning in Boolean Networks[KS97]. The algorithm uses as its central data structure the conjunction of a set of terms, with each term being a relation over a small number of variables. In St̊almarck’s algorithm the relation is limited to Boolean operators with up to two operand variables and one result variable. This representation has been generalised to allow arbitrary relations on three boolean variables, and then further extended to allow relations over as many as eight boolean variables. Another extension is to increase the richness of the variable mapping information obtained from the inference rule applications. In St̊almarck’s algorithm the mapping information is a set of equalities/inequalities between pairs of variables. This has been extended to arbitrary relations over boolean pairs. The paper includes test results showing the effect these various extensions have depth of recursion needed and the number of terms required at each level.

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تاریخ انتشار 2005