7 Search Results for "Villaret, Mateu"

Document
DOI: 10.4230/LIPIcs.FSCD.2025.8
The Unification Type of an Equational Theory May Depend on the Instantiation Preorder

Authors: Franz Baader and Oliver Fernández Gil

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that all variables are considered. It has been known for more than three decades that the unification type of an equational theory may vary, depending on which instantiation preorder is used. More precisely, it was shown in 1991 that the theory ACUI of an associative, commutative, and idempotent binary function symbol with a unit is unitary w.r.t. the restricted instantiation preorder, but not unitary w.r.t. the unrestricted one. In 2016 this result was strengthened by showing that the unrestricted type of this theory also cannot be finitary. Here, we considerably improve on this result by proving that ACUI is infinitary w.r.t. the unrestricted instantiation preorder, thus precluding type zero. We also show that, w.r.t. this preorder, the unification type of ACU (where idempotency is removed from the axioms) and of AC (where additionally the unit is removed) is infinitary, though it is respectively unitary and finitary in the restricted case. In the other direction, we prove (using the example of unification in the description logic EL) that the unification type may actually improve from type zero to infinitary when switching from the restricted instantiation preorder to the unrestricted one. In addition, we establish some general results on the relationship between the two instantiation preorders.
Cite as

Franz Baader and Oliver Fernández Gil. The Unification Type of an Equational Theory May Depend on the Instantiation Preorder. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baader_et_al:LIPIcs.FSCD.2025.8,
  author =	{Baader, Franz and Fern\'{a}ndez Gil, Oliver},
  title =	{{The Unification Type of an Equational Theory May Depend on the Instantiation Preorder}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{8:1--8:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.8},
  URN =		{urn:nbn:de:0030-drops-236230},
  doi =		{10.4230/LIPIcs.FSCD.2025.8},
  annote =	{Keywords: Unification type, Instantiation preorder, Equational theories, Modal and Description Logics}
}
Document
DOI: 10.4230/LIPIcs.CP.2022.22
Plotting: A Planning Problem with Complex Transitions

Authors: Joan Espasa, Ian Miguel, and Mateu Villaret

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract
We focus on a planning problem based on Plotting, a tile-matching puzzle video game published by Taito. The objective of the game is to remove at least a certain number of coloured blocks from a grid by sequentially shooting blocks into the same grid. The interest and difficulty of Plotting is due to the complex transitions after every shot: various blocks are affected directly, while others can be indirectly affected by gravity. We highlight the difficulties and inefficiencies of modelling and solving Plotting using PDDL, the de-facto standard language for AI planners. We also provide two constraint models that are able to capture the inherent complexities of the problem. In addition, we provide a set of benchmark instances, an instance generator and an extensive experimental comparison demonstrating solving performance with SAT, CP, MIP and a state-of-the-art AI planner.
Cite as

Joan Espasa, Ian Miguel, and Mateu Villaret. Plotting: A Planning Problem with Complex Transitions. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{espasa_et_al:LIPIcs.CP.2022.22,
  author =	{Espasa, Joan and Miguel, Ian and Villaret, Mateu},
  title =	{{Plotting: A Planning Problem with Complex Transitions}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.22},
  URN =		{urn:nbn:de:0030-drops-166514},
  doi =		{10.4230/LIPIcs.CP.2022.22},
  annote =	{Keywords: AI Planning, Modelling, Constraint Programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.9
Term-Graph Anti-Unification

Authors: Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
We study anti-unification for possibly cyclic, unranked term-graphs and develop an algorithm, which computes a minimal complete set of generalizations for them. For bisimilar graphs the algorithm computes the join in the lattice generated by a functional bisimulation. These results generalize anti-unification for ranked and unranked terms to the corresponding term-graphs, and solve also anti-unification problems for rational terms and dags. Our results open a way to widen anti-unification based code clone detection techniques from a tree representation to a graph representation of the code.
Cite as

Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. Term-Graph Anti-Unification. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baumgartner_et_al:LIPIcs.FSCD.2018.9,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{Term-Graph Anti-Unification}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.9},
  URN =		{urn:nbn:de:0030-drops-91797},
  doi =		{10.4230/LIPIcs.FSCD.2018.9},
  annote =	{Keywords: Cyclic term-graps, anti-unification, least general generalization}
}
Document
DOI: 10.4230/LIPIcs.RTA.2015.57
Nominal Anti-Unification

Authors: Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

Abstract
We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in generalizations is finite, then there exists a least general generalization which is unique modulo variable renaming and alpha-equivalence. We present an algorithm that computes it. The algorithm relies on a subalgorithm that constructively decides equivariance between two terms-in-context. We prove soundness and completeness properties of both algorithms and analyze their complexity. Nominal anti-unification can be applied to problems where generalization of first-order terms is needed (inductive learning, clone detection, etc.), but bindings are involved.
Cite as

Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. Nominal Anti-Unification. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 57-73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{baumgartner_et_al:LIPIcs.RTA.2015.57,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{Nominal Anti-Unification}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{57--73},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.57},
  URN =		{urn:nbn:de:0030-drops-51895},
  doi =		{10.4230/LIPIcs.RTA.2015.57},
  annote =	{Keywords: Nominal Anti-Unification, Term-in-context, Equivariance}
}
Document
DOI: 10.4230/LIPIcs.RTA.2013.113
A Variant of Higher-Order Anti-Unification

Authors: Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret

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

Abstract
We present a rule-based Huet's style anti-unification algorithm for simply-typed lambda-terms in eta-long beta-normal form, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo alpha-equivalence and variable renaming. The algorithm computes it in cubic time within linear space. It has been implemented and the code is freely available.
Cite as

Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. A Variant of Higher-Order Anti-Unification. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 113-127, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{baumgartner_et_al:LIPIcs.RTA.2013.113,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{A Variant of Higher-Order Anti-Unification}},
  booktitle =	{24th International Conference on Rewriting Techniques and Applications (RTA 2013)},
  pages =	{113--127},
  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.2013.113},
  URN =		{urn:nbn:de:0030-drops-40579},
  doi =		{10.4230/LIPIcs.RTA.2013.113},
  annote =	{Keywords: higher-order anti-unification, higher-order patterns}
}
Document
DOI: 10.4230/LIPIcs.RTA.2011.219
Anti-Unification for Unranked Terms and Hedges

Authors: Temur Kutsia, Jordi Levy, and Mateu Villaret

Published in: LIPIcs, Volume 10, 22nd International Conference on Rewriting Techniques and Applications (RTA'11) (2011)

Abstract
We study anti-unification for unranked terms and hedges that may contain term and hedge variables. The anti-unification problem of two hedges ~s_1 and ~s_2 is concerned with finding their generalization, a hedge ~q such that both ~s_1 and ~s_2 are instances of ~q under some substitutions. Hedge variables help to fill in gaps in generalizations, while term variables abstract single (sub)terms with different top function symbols. First, we design a complete and minimal algorithm to compute least general generalizations. Then, we improve the efficiency of the algorithm by restricting possible alternatives permitted in the generalizations. The restrictions are imposed with the help of a rigidity function that is a parameter in the improved algorithm and selects certain common subsequences from the hedges to be generalized. Finally, we indicate a possible application of the algorithm in software engineering.
Cite as

Temur Kutsia, Jordi Levy, and Mateu Villaret. Anti-Unification for Unranked Terms and Hedges. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 219-234, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{kutsia_et_al:LIPIcs.RTA.2011.219,
  author =	{Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{Anti-Unification for Unranked Terms and Hedges}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{219--234},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-30-9},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{10},
  editor =	{Schmidt-Schauss, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2011.219},
  URN =		{urn:nbn:de:0030-drops-31181},
  doi =		{10.4230/LIPIcs.RTA.2011.219},
  annote =	{Keywords: Anti-unification, generalization, unranked terms, hedges, software clones.}
}
Document
DOI: 10.4230/LIPIcs.RTA.2010.209
An Efficient Nominal Unification Algorithm

Authors: Jordi Levy and Mateu Villaret

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)

Abstract
Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo alpha-equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadratic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently.
Cite as

Jordi Levy and Mateu Villaret. An Efficient Nominal Unification Algorithm. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 209-226, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{levy_et_al:LIPIcs.RTA.2010.209,
  author =	{Levy, Jordi and Villaret, Mateu},
  title =	{{An Efficient Nominal Unification Algorithm}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{209--226},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.209},
  URN =		{urn:nbn:de:0030-drops-26544},
  doi =		{10.4230/LIPIcs.RTA.2010.209},
  annote =	{Keywords: Nominal logic, unification}
}
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