A tableau-based decision procedure for a fragment of graph theory involving reachability and acyclicity

Authors:
Domenico Cantone;Calogero G. Zarba
Affiliations:
University of Catania;University of New Mexico
Venue:
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Year:
2005

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Abstract

We study the decision problem for the language DGRA (directed graphs with reachability and acyclicity), a quantifier-free fragment of graph theory involving the notions of reachability and acyclicity. We prove that the language DGRA is decidable, and that its decidability problem is NP-complete. We do so by showing that the language enjoys a small model property: If a formula is satisfiable, then it has a model whose cardinality is polynomial in the size of the formula. Moreover, we show how the small model property can be used in order to devise a tableau-based decision procedure for DGRA.