3 Search Results for "Kuijer, Louwe B."

Document
DOI: 10.4230/LIPIcs.LICS.2026.26
The Size of Interpolants in Modal Logics

Authors: Balder ten Cate, Louwe B. Kuijer, and Frank Wolter

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest implicates can be reduced in polynomial time to uniform interpolant computation in classical propositional logic. Hence they are of polynomial dag-size iff NP is included in P/poly. The reduction also holds for Craig interpolants if the tabular modal logic has the Craig interpolation property. Our main lower bound shows an unconditional exponential lower bound on the size of Craig interpolants and strongest implicates covering almost all non-tabular standard normal modal logics. For normal modal logics contained in or containing S4 or GL we obtain the following dichotomy: tabular logics have "propositionally sized" interpolants while for non-tabular logics an unconditional exponential lower bound holds.
Cite as

Balder ten Cate, Louwe B. Kuijer, and Frank Wolter. The Size of Interpolants in Modal Logics. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 26:1-26:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{tencate_et_al:LIPIcs.LICS.2026.26,
  author =	{ten Cate, Balder and Kuijer, Louwe B. and Wolter, Frank},
  title =	{{The Size of Interpolants in Modal Logics}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{26:1--26:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.26},
  URN =		{urn:nbn:de:0030-drops-268132},
  doi =		{10.4230/LIPIcs.LICS.2026.26},
  annote =	{Keywords: Modal logic, strongest implicates, uniform interpolants, Craig interpolants}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.10
The Complexity of Second-Order HyperLTL

Authors: Hadar Frenkel and Martin Zimmermann

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that have been introduced with the aim to facilitate effective model-checking by restricting the sets one can quantify over. The first one restricts second-order quantification to smallest/largest sets that satisfy a guard while the second one restricts second-order quantification further to least fixed points of (first-order) HyperLTL definable functions. All three problems for the first fragment are still equivalent to truth in third-order arithmetic while satisfiability for the second fragment is Σ₁¹-complete, i.e., only as hard as for (first-order) HyperLTL and therefore much less complex. Finally, finite-state satisfiability and model-checking are in Σ₂² and are Σ₁¹-hard, and thus also less complex than for full second-order HyperLTL.
Cite as

Hadar Frenkel and Martin Zimmermann. The Complexity of Second-Order HyperLTL. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{frenkel_et_al:LIPIcs.CSL.2025.10,
  author =	{Frenkel, Hadar and Zimmermann, Martin},
  title =	{{The Complexity of Second-Order HyperLTL}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.10},
  URN =		{urn:nbn:de:0030-drops-227679},
  doi =		{10.4230/LIPIcs.CSL.2025.10},
  annote =	{Keywords: HyperLTL, Satisfiability, Model-checking}
}
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.
Cite as

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}
}
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