The first order theory of primal grammars is decidable

Authors:
Nicolas Peltier
Affiliations:
Centre National de la Recherche Scientifique, Laboratoire LEIBNIZ-IMAG, 46, Avenue Félix Viallet 38031 Grenoble Cedex, France
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

The formalism of primal grammars is one of the most powerful term schematization languages (Theoret. Comput. Sci. 176(1-2) (1997) 111). In this paper, we describe an algorithm to check the satisfiability of first-order formulae in the theory of primal grammars. The correctness, completeness and termination of the algorithm are proven. The core of the procedure is the universal quantifier elimination method, which is based on a new explosion rule especially devoted to handle primal terms.