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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: a.reuss@in.tum.de, seidl@in.tum.de
HELMUT SEIDL
Affiliation:
Institut für Informatik I2, Technische Universität München, Boltzmannstraße 3, D-85748 Garching, Germany Emails: a.reuss@in.tum.de, seidl@in.tum.de
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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).

References

Baskar, A., Ramanujam, R. and Suresh, S.P. (2007). Knowledge-based modelling of voting protocols. In: TARK, Presses universitaires de Louvain, 62–71, ISBN 978-2-87463-077-4.Google Scholar
Blanchet, B. (2001). An efficient cryptographic protocol verifier based on prolog rules. In: CSFW, IEEE Computer Society, 82–96. ISBN 0-7695-1146-5.Google Scholar
Comon, H. and Jacquemard, F. (1994). Ground reducibility and automata with disequality constraints. In: STACS, Lecture Notes in Computer Science, vol. 775, Springer, 151–162.Google Scholar
Creus, C., Gascón, A., Godoy, G. and Ramos, L. (2012). The hom problem is exptime-complete. In: LICS, IEEE, 255–264. ISBN ISBN 978-1-4673-2263-8.Google Scholar
Frühwirth, T.W., Shapiro, E.Y., Vardi, M.Y. and Yardeni, E. (1991). Logic programs as types for logic programs. In: LICS, IEEE Computer Society, 314–328. ISBN 0-8186-2230-X.Google Scholar
Fujioka, A., Okamoto, T. and Ohta, K. (1993). A practical secret voting scheme for large scale elections. In: AUSCRYPT, Lecture Notes in Computer Science, vol. 718, Springer, 244–251.Google Scholar
Godoy, G., Giménez, O., Ramos, L. and Àlvarez, C. (2010). The hom problem is decidable. In: STOC, ACM, 485–494. ISBN 978-1-4503-0050-6.Google Scholar
Goubault-Larrecq, J. (2005). Deciding H1 by resolution. Information Processing Letters 95 (3) 401–408.Google Scholar
Goubault-Larrecq, J. and Parrennes, F. (2005). Cryptographic protocol analysis on real C code. In: VMCAI, Lecture Notes in Computer Science, vol. 3385, Springer, 363–379.Google Scholar
Müller-Olm, M., Rüthing, O. and Seidl, H. (2005) Checking Herbrand equalities and beyond. In: VMCAI, Lecture Notes in Computer Science, vol. 3385, Springer, 79–96.Google Scholar
Nielson, F., Nielson, H.R. and Seidl, H. (2002). Normalizable horn clauses, strongly recognizable relations, and Spi. In: SAS, Lecture Notes in Computer Science, vol. 2477, Springer, 20–35.Google Scholar
Reuß, A. and Seidl, H. (2010). Bottom-up tree automata with term constraints. In: LPAR-17, Lecture Notes in Computer Science, vol. 6397, Springer, 581–593.Google Scholar
Reuß, A. and Seidl, H. (2012). Crossing the syntactic barrier: Hom-disequalities for H1-clauses. In: CIAA, Lecture Notes in Computer Science, vol. 7381, Springer, 301–312.Google Scholar
Seidl, H. and Neumann, A. (1999). On guarding nested fixpoints. In: CSL, Lecture Notes in Computer Science, vol. 1683, Springer, 484–498.Google Scholar
Seidl, H. and Reuß, A. (2011). Extending H1-clauses with disequalities. Information Processing Letters 111 (20) 1007–1013.Google Scholar
Seidl, H. and Reuß, A. (2012). Extending H1-clauses with path disequalities. In: FoSSaCS, Lecture Notes in Computer Science, vol. 7213, Springer, 165–179.Google Scholar
Weidenbach, C. (1999). Towards an automatic analysis of security protocols in first-order logic. In: CADE, Lecture Notes in Computer Science, vol. 1632, Springer, 314–328.Google Scholar