A modular reduction of regular logic to classical logic

Abstract

In this paper we first define a reduction /spl delta/ that transforms an instance /spl Gamma/ of Regular-SAT into a satisfiability equivalent instance /spl Gamma//sup /spl delta// of SAT. The reduction /spl delta/ has interesting properties: (i) the size of /spl Gamma//sup /spl delta// is linear in the size of /spl Gamma/, (ii) /spl delta/ transforms regular Horn formulas into Horn formulas, and (iii) /spl delta/ transforms regular 2-CNF formulas into 2-CNF formulas. Second, we describe a new satisfiability algorithm that determines the satisfiability of a regular 2-CNF formula /spl Gamma/ in time O(|/spl Gamma/|log|/spl Gamma/|); this algorithm is inspired by the reduction /spl delta/. Third, we introduce the concept of renamable-Horn regular CNF formula and define another reduction /spl delta/' that transforms a renamable-Horn instance /spl Gamma/ of Regular-SAT into a renamable-Horn instance /spl Gamma//sup /spl delta/'/ of SAT. We use this reduction to show that both membership and satisfiability of renamable-Horn regular CNF formulas can be decided in time O(|/spl Gamma/|log|/spl Gamma/|).