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Paths, tree homomorphisms and disequalities for -clauses

Published online by Cambridge University Press:  06 December 2017

ANDREAS REUß  and
HELMUT SEIDL
ANDREAS REUß
Affiliation:
Institut für Informatik I2, Technische Universität München, Boltzmannstraße 3, D-85748 Garching, Germany Emails: [email protected], [email protected]
HELMUT SEIDL
Affiliation:
Institut für Informatik I2, Technische Universität München, Boltzmannstraße 3, D-85748 Garching, Germany Emails: [email protected], [email protected]
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Abstract

It is well known that satisfiability is decidable for Horn clauses of the class . Since arbitrary Horn clauses can naturally be approximated by -clauses, can be used for realizing any program analysis which can be specified by means of Horn clauses. Recently, we have shown that decidability for Horn clauses from is retained if the clauses are either extended with tests for disequality between subterms identified by paths or for disequality between homomorphic images of terms. These two results refer to orthogonal extensions of -clauses. Here, we provide a generalization of both results. For that, we introduce hom-path disequalities and show that for each finite set of -clauses extended with such tests an equivalent tree automaton with hom-path disequalities can be constructed. Since emptiness for that class of automata has been shown decidable by Godoy et al. in 2010, we conclude that satisfiability is decidable for -clauses with hom-path disequalities.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 10 , November 2018 , pp. 1786 - 1846
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

*

This work was partly supported by the DFG Graduiertenkolleg 1480 (PUMA).

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