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Documents authored by Fortin, Marie

Document
DOI: 10.4230/LIPIcs.MFCS.2021.47
HyperLTL Satisfiability Is Σ₁¹-Complete, HyperCTL* Satisfiability Is Σ₁²-Complete

Authors: Marie Fortin, Louwe B. Kuijer, Patrick Totzke, and Martin Zimmermann

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by trace quantification. It is known that this expressiveness comes at a price, i.e. satisfiability is undecidable for both logics. In this paper we settle the exact complexity of these problems, showing that both are in fact highly undecidable: we prove that HyperLTL satisfiability is Σ₁¹-complete and HyperCTL* satisfiability is Σ₁²-complete. These are significant increases over the previously known lower bounds and the first upper bounds. To prove Σ₁²-membership for HyperCTL*, we prove that every satisfiable HyperCTL* sentence has a model that is equinumerous to the continuum, the first upper bound of this kind. We prove this bound to be tight. Finally, we show that the membership problem for every level of the HyperLTL quantifier alternation hierarchy is Π₁¹-complete.
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Marie Fortin, Louwe B. Kuijer, Patrick Totzke, and Martin Zimmermann. HyperLTL Satisfiability Is Σ₁¹-Complete, HyperCTL* Satisfiability Is Σ₁²-Complete. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 47:1-47:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{fortin_et_al:LIPIcs.MFCS.2021.47,
  author =	{Fortin, Marie and Kuijer, Louwe B. and Totzke, Patrick and Zimmermann, Martin},
  title =	{{HyperLTL Satisfiability Is \Sigma₁¹-Complete, HyperCTL* Satisfiability Is \Sigma₁²-Complete}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{47:1--47:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.47},
  URN =		{urn:nbn:de:0030-drops-144870},
  doi =		{10.4230/LIPIcs.MFCS.2021.47},
  annote =	{Keywords: HyperLTL, HyperCTL*, Satisfiability, Analytical Hierarchy}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.116
FO = FO^3 for Linear Orders with Monotone Binary Relations (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Marie Fortin

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We show that over the class of linear orders with additional binary relations satisfying some monotonicity conditions, monadic first-order logic has the three-variable property. This generalizes (and gives a new proof of) several known results, including the fact that monadic first-order logic has the three-variable property over linear orders, as well as over (R,<,+1), and answers some open questions mentioned in a paper from Antonopoulos, Hunter, Raza and Worrell [FoSSaCS 2015]. Our proof is based on a translation of monadic first-order logic formulas into formulas of a star-free variant of Propositional Dynamic Logic, which are in turn easily expressible in monadic first-order logic with three variables.
Cite as

Marie Fortin. FO = FO^3 for Linear Orders with Monotone Binary Relations (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 116:1-116:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{fortin:LIPIcs.ICALP.2019.116,
  author =	{Fortin, Marie},
  title =	{{FO = FO^3 for Linear Orders with Monotone Binary Relations}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{116:1--116:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.116},
  URN =		{urn:nbn:de:0030-drops-106923},
  doi =		{10.4230/LIPIcs.ICALP.2019.116},
  annote =	{Keywords: first-order logic, three-variable property, propositional dynamic logic}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2018.7
It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"

Authors: Benedikt Bollig, Marie Fortin, and Paul Gastin

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport's happened-before relation. We introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results state that (i) every first-order sentence can be transformed into an equivalent star-free PDL sentence (and conversely), and (ii) every star-free PDL sentence can be translated into an equivalent CFM. This answers an open question and settles the exact relation between CFMs and fragments of monadic second-order logic. As a byproduct, we show that first-order logic over MSCs has the three-variable property.
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Benedikt Bollig, Marie Fortin, and Paul Gastin. It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before". In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bollig_et_al:LIPIcs.CONCUR.2018.7,
  author =	{Bollig, Benedikt and Fortin, Marie and Gastin, Paul},
  title =	{{It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.7},
  URN =		{urn:nbn:de:0030-drops-95455},
  doi =		{10.4230/LIPIcs.CONCUR.2018.7},
  annote =	{Keywords: communicating finite-state machines, first-order logic, happened-before relation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.17
Communicating Finite-State Machines and Two-Variable Logic

Authors: Benedikt Bollig, Marie Fortin, and Paul Gastin

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
Communicating finite-state machines are a fundamental, well-studied model of finite-state processes that communicate via unbounded first-in first-out channels. We show that they are expressively equivalent to existential MSO logic with two first-order variables and the order relation.
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Benedikt Bollig, Marie Fortin, and Paul Gastin. Communicating Finite-State Machines and Two-Variable Logic. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bollig_et_al:LIPIcs.STACS.2018.17,
  author =	{Bollig, Benedikt and Fortin, Marie and Gastin, Paul},
  title =	{{Communicating Finite-State Machines and Two-Variable Logic}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.17},
  URN =		{urn:nbn:de:0030-drops-85298},
  doi =		{10.4230/LIPIcs.STACS.2018.17},
  annote =	{Keywords: communicating finite-state machines, MSO logic, message sequence charts}
}
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