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Documents authored by Gascón, Adrià

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Gascón, Adrià

Document
DOI: 10.4230/LIPIcs.CSL.2015.405
Two-Restricted One Context Unification is in Polynomial Time

Authors: Adrià Gascón, Manfred Schmidt-Schauß, and Ashish Tiwari

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
One Context Unification (1CU) extends first-order unification by introducing a single context variable. This problem was recently shown to be in NP, but it is not known to be solvable in polynomial time. We show that the case of 1CU where the context variable occurs at most twice in the input (1CU2r) is solvable in polynomial time. Moreover, a polynomial representation of all solutions can also be computed in polynomial time. The 1CU2r problem is important as it is used as a subroutine in polynomial time algorithms for several more-general classes of 1CU problem. Our algorithm can be seen as an extension of the usual rules of first-order unification and can be used to solve related problems in polynomial time, such as first-order unification of two terms that tolerates one clash. All our results assume that the input terms are represented as Directed Acyclic Graphs.
Cite as

Adrià Gascón, Manfred Schmidt-Schauß, and Ashish Tiwari. Two-Restricted One Context Unification is in Polynomial Time. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 405-422, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{gascon_et_al:LIPIcs.CSL.2015.405,
  author =	{Gasc\'{o}n, Adri\`{a} and Schmidt-Schau{\ss}, Manfred and Tiwari, Ashish},
  title =	{{Two-Restricted One Context Unification is in Polynomial Time}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{405--422},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.405},
  URN =		{urn:nbn:de:0030-drops-54289},
  doi =		{10.4230/LIPIcs.CSL.2015.405},
  annote =	{Keywords: context unification, first-order unification, deduction, type checking}
}
Document
DOI: 10.4230/LIPIcs.RTA.2012.149
One-context Unification with STG-Compressed Terms is in NP

Authors: Carles Creus, Adria Gascon, and Guillem Godoy

Published in: LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (2012)

Abstract
One-context unification is an extension of first-order term unification in which a variable of arity one standing for a context may occur in the input terms. This problem arises in areas like program analysis, term rewriting and XML processing and is known to be solvable in nondeterministic polynomial time. We prove that this problem can be solved in nondeterministic polynomial time also when the input is compressed using Singleton Tree Grammars (STG's). STG's are a grammar-based compression method for terms that generalizes the directed acyclic graph representation. They have been recently considered as an efficient in-memory representation for large terms, since several operations on terms can be performed efficiently on their STG representation without a prior decompression.
Cite as

Carles Creus, Adria Gascon, and Guillem Godoy. One-context Unification with STG-Compressed Terms is in NP. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 149-164, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{creus_et_al:LIPIcs.RTA.2012.149,
  author =	{Creus, Carles and Gascon, Adria and Godoy, Guillem},
  title =	{{One-context Unification with STG-Compressed Terms is in NP}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12)},
  pages =	{149--164},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Tiwari, Ashish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.149},
  URN =		{urn:nbn:de:0030-drops-34902},
  doi =		{10.4230/LIPIcs.RTA.2012.149},
  annote =	{Keywords: Term Unification, Compression, Grammars}
}
Document
DOI: 10.4230/LIPIcs.RTA.2011.51
First-Order Unification on Compressed Terms

Authors: Adrià Gascón, Sebastian Maneth, and Lander Ramos

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

Abstract
Singleton Tree Grammars (STGs) have recently drawn considerable attention. They generalize the sharing of subtrees known from DAGs to sharing of connected subgraphs. This allows to obtain smaller in-memory representations of trees than with DAGs. In the past years some important tree algorithms were proved to perform efficiently (without decompression) over STGs; e.g., type checking, equivalence checking, and unification. We present a tool that implements an extension of the unification algorithm for STGs. This algorithm makes extensive use of equivalence checking. For the latter we implemented two variants, the classical exact one and a recent randomized one. Our experiments show that the randomized algorithm performs better. The running times are also compared to those of unification over uncompressed trees.
Cite as

Adrià Gascón, Sebastian Maneth, and Lander Ramos. First-Order Unification on Compressed Terms. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 51-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

Copy BibTex To Clipboard

@InProceedings{gascon_et_al:LIPIcs.RTA.2011.51,
  author =	{Gasc\'{o}n, Adri\`{a} and Maneth, Sebastian and Ramos, Lander},
  title =	{{First-Order Unification on Compressed Terms}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{51--60},
  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.2011.51},
  URN =		{urn:nbn:de:0030-drops-31263},
  doi =		{10.4230/LIPIcs.RTA.2011.51},
  annote =	{Keywords: unification, matching, grammars, compression, STG, system C++}
}

Gascon, Adria

Document
DOI: 10.4230/LIPIcs.CSL.2015.405
Two-Restricted One Context Unification is in Polynomial Time

Authors: Adrià Gascón, Manfred Schmidt-Schauß, and Ashish Tiwari

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
One Context Unification (1CU) extends first-order unification by introducing a single context variable. This problem was recently shown to be in NP, but it is not known to be solvable in polynomial time. We show that the case of 1CU where the context variable occurs at most twice in the input (1CU2r) is solvable in polynomial time. Moreover, a polynomial representation of all solutions can also be computed in polynomial time. The 1CU2r problem is important as it is used as a subroutine in polynomial time algorithms for several more-general classes of 1CU problem. Our algorithm can be seen as an extension of the usual rules of first-order unification and can be used to solve related problems in polynomial time, such as first-order unification of two terms that tolerates one clash. All our results assume that the input terms are represented as Directed Acyclic Graphs.
Cite as

Adrià Gascón, Manfred Schmidt-Schauß, and Ashish Tiwari. Two-Restricted One Context Unification is in Polynomial Time. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 405-422, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{gascon_et_al:LIPIcs.CSL.2015.405,
  author =	{Gasc\'{o}n, Adri\`{a} and Schmidt-Schau{\ss}, Manfred and Tiwari, Ashish},
  title =	{{Two-Restricted One Context Unification is in Polynomial Time}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{405--422},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.405},
  URN =		{urn:nbn:de:0030-drops-54289},
  doi =		{10.4230/LIPIcs.CSL.2015.405},
  annote =	{Keywords: context unification, first-order unification, deduction, type checking}
}
Document
DOI: 10.4230/LIPIcs.RTA.2012.149
One-context Unification with STG-Compressed Terms is in NP

Authors: Carles Creus, Adria Gascon, and Guillem Godoy

Published in: LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (2012)

Abstract
One-context unification is an extension of first-order term unification in which a variable of arity one standing for a context may occur in the input terms. This problem arises in areas like program analysis, term rewriting and XML processing and is known to be solvable in nondeterministic polynomial time. We prove that this problem can be solved in nondeterministic polynomial time also when the input is compressed using Singleton Tree Grammars (STG's). STG's are a grammar-based compression method for terms that generalizes the directed acyclic graph representation. They have been recently considered as an efficient in-memory representation for large terms, since several operations on terms can be performed efficiently on their STG representation without a prior decompression.
Cite as

Carles Creus, Adria Gascon, and Guillem Godoy. One-context Unification with STG-Compressed Terms is in NP. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 149-164, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

Copy BibTex To Clipboard

@InProceedings{creus_et_al:LIPIcs.RTA.2012.149,
  author =	{Creus, Carles and Gascon, Adria and Godoy, Guillem},
  title =	{{One-context Unification with STG-Compressed Terms is in NP}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12)},
  pages =	{149--164},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Tiwari, Ashish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.149},
  URN =		{urn:nbn:de:0030-drops-34902},
  doi =		{10.4230/LIPIcs.RTA.2012.149},
  annote =	{Keywords: Term Unification, Compression, Grammars}
}
Document
DOI: 10.4230/LIPIcs.RTA.2011.51
First-Order Unification on Compressed Terms

Authors: Adrià Gascón, Sebastian Maneth, and Lander Ramos

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

Abstract
Singleton Tree Grammars (STGs) have recently drawn considerable attention. They generalize the sharing of subtrees known from DAGs to sharing of connected subgraphs. This allows to obtain smaller in-memory representations of trees than with DAGs. In the past years some important tree algorithms were proved to perform efficiently (without decompression) over STGs; e.g., type checking, equivalence checking, and unification. We present a tool that implements an extension of the unification algorithm for STGs. This algorithm makes extensive use of equivalence checking. For the latter we implemented two variants, the classical exact one and a recent randomized one. Our experiments show that the randomized algorithm performs better. The running times are also compared to those of unification over uncompressed trees.
Cite as

Adrià Gascón, Sebastian Maneth, and Lander Ramos. First-Order Unification on Compressed Terms. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 51-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

Copy BibTex To Clipboard

@InProceedings{gascon_et_al:LIPIcs.RTA.2011.51,
  author =	{Gasc\'{o}n, Adri\`{a} and Maneth, Sebastian and Ramos, Lander},
  title =	{{First-Order Unification on Compressed Terms}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{51--60},
  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.2011.51},
  URN =		{urn:nbn:de:0030-drops-31263},
  doi =		{10.4230/LIPIcs.RTA.2011.51},
  annote =	{Keywords: unification, matching, grammars, compression, STG, system C++}
}
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