2 Search Results for "Perez, Thomas"


Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Compositionality of Planar Perfect Matchings: A Universal and Complete Fragment of ZW-Calculus

Authors: Titouan Carette, Etienne Moutot, Thomas Perez, and Renaud Vilmart

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
We exhibit a strong connection between the matchgate formalism introduced by Valiant and the ZW-calculus of Coecke and Kissinger. This connection provides a natural compositional framework for matchgate theory as well as a direct combinatorial interpretation of the diagrams of ZW-calculus through the perfect matchings of their underlying graphs. We identify a precise fragment of ZW-calculus, the planar W-calculus, that we prove to be complete and universal for matchgates, that are linear maps satisfying the matchgate identities. Computing scalars of the planar W-calculus corresponds to counting perfect matchings of planar graphs, and so can be carried in polynomial time using the FKT algorithm, making the planar W-calculus an efficiently simulable fragment of the ZW-calculus, in a similar way that the Clifford fragment is for ZX-calculus. This work opens new directions for the investigation of the combinatorial properties of ZW-calculus as well as the study of perfect matching counting through compositional diagrammatical technics.

Cite as

Titouan Carette, Etienne Moutot, Thomas Perez, and Renaud Vilmart. Compositionality of Planar Perfect Matchings: A Universal and Complete Fragment of ZW-Calculus. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 120:1-120:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{carette_et_al:LIPIcs.ICALP.2023.120,
  author =	{Carette, Titouan and Moutot, Etienne and Perez, Thomas and Vilmart, Renaud},
  title =	{{Compositionality of Planar Perfect Matchings: A Universal and Complete Fragment of ZW-Calculus}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{120:1--120:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.120},
  URN =		{urn:nbn:de:0030-drops-181726},
  doi =		{10.4230/LIPIcs.ICALP.2023.120},
  annote =	{Keywords: Perfect Matchings Counting, Quantum Computing, Matchgates, ZW-Calculus, String Diagrams, Completeness}
}
Document
Quantitative Games under Failures

Authors: Thomas Brihaye, Gilles Geeraerts, Axel Haddad, Benjamin Monmege, Guillermo A. Pérez, and Gabriel Renault

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)


Abstract
We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an extension of the sabotage games in which the first player (Runner) traverses an arena with dynamic weights determined by the second player (Saboteur). In our model of quantitative sabotage games, Saboteur is now given a budget that he can distribute amongst the edges of the graph, whilst Runner attempts to minimise the quantity of budget witnessed while completing his task. We show that, on the one hand, for most of the classical cost functions considered in the literature, the problem of determining if Runner has a strategy to ensure a cost below some threshold is EXPTIME-complete. On the other hand, if the budget of Saboteur is fixed a priori, then the problem is in PTIME for most cost functions. Finally, we show that restricting the dynamics of the game also leads to better complexity.

Cite as

Thomas Brihaye, Gilles Geeraerts, Axel Haddad, Benjamin Monmege, Guillermo A. Pérez, and Gabriel Renault. Quantitative Games under Failures. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 293-306, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Copy BibTex To Clipboard

@InProceedings{brihaye_et_al:LIPIcs.FSTTCS.2015.293,
  author =	{Brihaye, Thomas and Geeraerts, Gilles and Haddad, Axel and Monmege, Benjamin and P\'{e}rez, Guillermo A. and Renault, Gabriel},
  title =	{{Quantitative Games under Failures}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{293--306},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.293},
  URN =		{urn:nbn:de:0030-drops-56229},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.293},
  annote =	{Keywords: Quantitative games, verification, synthesis, game theory}
}
  • Refine by Author
  • 1 Brihaye, Thomas
  • 1 Carette, Titouan
  • 1 Geeraerts, Gilles
  • 1 Haddad, Axel
  • 1 Monmege, Benjamin
  • Show More...

  • Refine by Classification
  • 1 Mathematics of computing → Matchings and factors
  • 1 Theory of computation → Equational logic and rewriting
  • 1 Theory of computation → Quantum computation theory

  • Refine by Keyword
  • 1 Completeness
  • 1 Matchgates
  • 1 Perfect Matchings Counting
  • 1 Quantitative games
  • 1 Quantum Computing
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2015
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail