A Simplifier for Propositional Formulas with Many Binary Clauses

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Abstract

Deciding whether a prepositional formula in conjunctive normal form is satisfiable (SAT) is an NP-complete problem. The problem becomes linear when the formula contains binary clauses only. Interestingly, the reduction to SAT of a number of well-known and important problems - such as classical AI planning and automatic test pattern generation for circuits - yields formulas containing many binary clauses. In this paper we introduce and experiment with 2-SIMPLIFY, a formula simplifier targeted at such problems. 2-SIMPLIFY constructs the transitive closure of the implication graph corresponding to the binary clauses in the formula and uses this graph to deduce new unit literals. The deduced literals are used to simplify the formula and update the graph, and so on, until stabilization. Finally, we use the graph to construct an equivalent, simpler set of binary clauses. Experimental evaluation of this simplifier on a number of bench-mark formulas produced by encoding AI planning problems prove 2-SIMPLIFY to be a useful tool in many circumstances.

Original languageEnglish
Pages (from-to)52-59
Number of pages8
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume34
Issue number1
DOIs
StatePublished - 1 Feb 2004

Keywords

  • 2-SIMPLIFY
  • AI
  • Automatic test pattern generation
  • Formula simplifier
  • NP-complete problem
  • SAT
  • Unit literals

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