# A decision procedure for unquantified formulas of graph theory

Conference paper

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## Abstract

A procedure for deciding the validity of ground formulas in a theory of directed graphs is described. The procedure, which decides equality and containment relations for vertex, edge and graph terms, is based on the method of congruence closure and involves the formation of equivalence classes and their representatives. An interesting aspect of the procedure is its use of maximal, rather than minimal, normal forms as equivalence class representatives. The correctness, efficiency, and limitations of the procedure are discussed.

## Key words and phrases

Directed graph decision procedure congruence closure normal form equivalence class representative## Preview

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© Springer-Verlag Berlin Heidelberg 1988