4 Search Results for "Ringeissen, Christophe"


Document
Termination of Generalized Term Rewriting Systems

Authors: Salvador Lucas

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)


Abstract
We investigate termination of Generalized Term Rewriting Systems (GTRS), which extend Conditional Term Rewriting Systems by considering replacement restrictions on selected arguments of function symbols, as in Context-Sensitive Rewriting, and conditional rewriting rules whose conditional part may include not only a mix of the usual (reachability, joinability,...) conditions, but also atoms defined by a set of definite Horn clauses. GTRS can be used to prove confluence and termination of Generalized Rewrite Theories and Maude programs. We have characterized confluence of terminating GTRS as the joinability of a finite set of conditional pairs. Since termination of GTRS is underexplored to date, this paper introduces a Dependency Pair Framework which is well-suited to automatically (dis)prove termination of GTRS.

Cite as

Salvador Lucas. Termination of Generalized Term Rewriting Systems. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{lucas:LIPIcs.FSCD.2024.32,
  author =	{Lucas, Salvador},
  title =	{{Termination of Generalized Term Rewriting Systems}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.32},
  URN =		{urn:nbn:de:0030-drops-203616},
  doi =		{10.4230/LIPIcs.FSCD.2024.32},
  annote =	{Keywords: Program Analysis, Reduction-Based Systems, Termination}
}
Document
Knowledge Problems in Security Protocols: Going Beyond Subterm Convergent Theories

Authors: Saraid Dwyer Satterfield, Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)


Abstract
We introduce a new form of restricted term rewrite system, the graph-embedded term rewrite system. These systems, and thus the name, are inspired by the graph minor relation and are more flexible extensions of the well-known homeomorphic-embedded property of term rewrite systems. As a motivating application area, we consider the symbolic analysis of security protocols, and more precisely the two knowledge problems defined by the deduction problem and the static equivalence problem. In this field restricted term rewrite systems, such as subterm convergent ones, have proven useful since the knowledge problems are decidable for such systems. However, many of the same decision procedures still work for examples of systems which are "beyond subterm convergent". However, the applicability of the corresponding decision procedures to these examples must often be proven on an individual basis. This is due to the problem that they don't fit into an existing syntactic definition for which the procedures are known to work. Here we show that many of these systems belong to a particular subclass of graph-embedded convergent systems, called contracting convergent systems. On the one hand, we show that the knowledge problems are decidable for the subclass of contracting convergent systems. On the other hand, we show that the knowledge problems are undecidable for the class of graph-embedded systems.

Cite as

Saraid Dwyer Satterfield, Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen. Knowledge Problems in Security Protocols: Going Beyond Subterm Convergent Theories. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dwyersatterfield_et_al:LIPIcs.FSCD.2023.30,
  author =	{Dwyer Satterfield, Saraid and Erbatur, Serdar and Marshall, Andrew M. and Ringeissen, Christophe},
  title =	{{Knowledge Problems in Security Protocols: Going Beyond Subterm Convergent Theories}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.30},
  URN =		{urn:nbn:de:0030-drops-180148},
  doi =		{10.4230/LIPIcs.FSCD.2023.30},
  annote =	{Keywords: Term rewriting, security protocols, verification}
}
Document
Combined Hierarchical Matching: the Regular Case

Authors: Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)


Abstract
Matching algorithms are often central sub-routines in many areas of automated reasoning. They are used in areas such as functional programming, rule-based programming, automated theorem proving, and the symbolic analysis of security protocols. Matching is related to unification but provides a somewhat simplified problem. Thus, in some cases, we can obtain a matching algorithm even if the unification problem is undecidable. In this paper we consider a hierarchical approach to constructing matching algorithms. The hierarchical method has been successful for developing unification algorithms for theories defined over a constructor sub-theory. We show how the approach can be extended to matching problems which allows for the development, in a modular way, of hierarchical matching algorithms. Here we focus on regular theories, where both sides of each equational axiom have the same set of variables. We show that the combination of two hierarchical matching algorithms leads to a hierarchical matching algorithm for the union of regular theories sharing only a common constructor sub-theory.

Cite as

Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen. Combined Hierarchical Matching: the Regular Case. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{erbatur_et_al:LIPIcs.FSCD.2022.6,
  author =	{Erbatur, Serdar and Marshall, Andrew M. and Ringeissen, Christophe},
  title =	{{Combined Hierarchical Matching: the Regular Case}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.6},
  URN =		{urn:nbn:de:0030-drops-162879},
  doi =		{10.4230/LIPIcs.FSCD.2022.6},
  annote =	{Keywords: Matching, combination problem, equational theories}
}
Document
Automatic Decidability: A Schematic Calculus for Theories with Counting Operators

Authors: Elena Tushkanova, Christophe Ringeissen, Alain Giorgetti, and Olga Kouchnarenko

Published in: LIPIcs, Volume 21, 24th International Conference on Rewriting Techniques and Applications (RTA 2013)


Abstract
Many verification problems can be reduced to a satisfiability problem modulo theories. For building satisfiability procedures the rewriting-based approach uses a general calculus for equational reasoning named paramodulation. Schematic paramodulation, in turn, provides means to reason on the derivations computed by paramodulation. Until now, schematic paramodulation was only studied for standard paramodulation. We present a schematic paramodulation calculus modulo a fragment of arithmetics, namely the theory of Integer Offsets. This new schematic calculus is used to prove the decidability of the satisfiability problem for some theories equipped with counting operators. We illustrate our theoretical contribution on theories representing extensions of classical data structures, e.g., lists and records. An implementation within the rewriting-based Maude system constitutes a practical contribution. It enables automatic decidability proofs for theories of practical use.

Cite as

Elena Tushkanova, Christophe Ringeissen, Alain Giorgetti, and Olga Kouchnarenko. Automatic Decidability: A Schematic Calculus for Theories with Counting Operators. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 303-318, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{tushkanova_et_al:LIPIcs.RTA.2013.303,
  author =	{Tushkanova, Elena and Ringeissen, Christophe and Giorgetti, Alain and Kouchnarenko, Olga},
  title =	{{Automatic Decidability: A Schematic Calculus for Theories with Counting Operators}},
  booktitle =	{24th International Conference on Rewriting Techniques and Applications (RTA 2013)},
  pages =	{303--318},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-53-8},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{21},
  editor =	{van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2013.303},
  URN =		{urn:nbn:de:0030-drops-40696},
  doi =		{10.4230/LIPIcs.RTA.2013.303},
  annote =	{Keywords: decision procedures, superposition, schematic saturation}
}
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