34 Search Results for "Abramsky, Samson"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.89
Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification

Authors: Georg Schindling

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph classes, two structures agree on all homomorphism counts from the class if and only if they satisfy the same sentences in a corresponding logic. This perspective often reveals connections between the combinatorial properties of graph classes and the syntactic structure of logical fragments. In this work, we extend this perspective to logics with restricted requantification, refining the stratification of logical resources in finite-variable counting logics. Specifically, we generalize Lovász-type theorems for these logics with either restricted conjunction or bounded quantifier-rank and present new combinatorial proofs of existing results. To this end, we introduce novel path and tree decompositions that incorporate the concept of reusability and develop characterizations based on pursuit-evasion games. Leveraging this framework, we establish that classes of bounded pathwidth and treewidth with reusability constraints are homomorphism distinguishing closed. Finally, we develop a comonadic perspective on requantification by constructing new comonads that encapsulate restricted-reusability pebble games. We show a tight correspondence between their coalgebras and path/tree decompositions, yielding categorical characterizations of reusability in graph decompositions. This unifies logical, combinatorial, and categorical perspectives on the notion of reusability.
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Georg Schindling. Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 89:1-89:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schindling:LIPIcs.MFCS.2025.89,
  author =	{Schindling, Georg},
  title =	{{Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{89:1--89:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.89},
  URN =		{urn:nbn:de:0030-drops-241962},
  doi =		{10.4230/LIPIcs.MFCS.2025.89},
  annote =	{Keywords: homomorphism indistinguishability, game comonads, finite variable counting logic, restricted conjunction, restricted requantification, tree decomposition, path decomposition}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.86
Probabilistic Finite Automaton Emptiness Is Undecidable for a Fixed Automaton

Authors: Günter Rote

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We construct a probabilistic finite automaton (PFA) with 7 states and an input alphabet of 5 symbols for which the PFA Emptiness Problem is undecidable. The only input for the decision problem is the starting distribution. For the proof, we use reductions from special instances of the Post Correspondence Problem. We also consider some variations: The input alphabet of the PFA can be restricted to a binary alphabet at the expense of a larger number of states. If we allow a rational output value for each state instead of a yes-no acceptance decision, the number of states can even be reduced to 6.
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Günter Rote. Probabilistic Finite Automaton Emptiness Is Undecidable for a Fixed Automaton. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 86:1-86:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rote:LIPIcs.MFCS.2025.86,
  author =	{Rote, G\"{u}nter},
  title =	{{Probabilistic Finite Automaton Emptiness Is Undecidable for a Fixed Automaton}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{86:1--86:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.86},
  URN =		{urn:nbn:de:0030-drops-241930},
  doi =		{10.4230/LIPIcs.MFCS.2025.86},
  annote =	{Keywords: Probabilistic finite automaton, Undecidability, Post Correspondence Problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.61
Quantum Relaxations of CSP and Structure Isomorphism

Authors: Amin Karamlou

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We investigate quantum relaxations of two key decision problems in computer science: the constraint satisfaction problem (CSP) and the structure isomorphism problem. CSP asks whether a homomorphism exists between two relational structures, while structure isomorphism seeks an isomorphism between them. In recent years, it has become increasingly apparent that many special cases of CSP can be reformulated in terms of the existence of perfect classical strategies in non-local games, a key topic of study in quantum information theory. These games have allowed us to study quantum advantage in relation to many important decision problems, such as the k-colouring problem, and the problem of solving binary constraint systems. Abramsky et al. (2017) have shown that all of these games can be seen as special instances of a non-local CSP game. Moreover, they show that perfect quantum strategies in this CSP game can be viewed as Kleisli morphisms of a graded monad on the category of relational structures, which they dub the quantum monad. In this way, the quantum monad provides a categorical characterisation of quantum advantage for the non-local CSP game. In this work we solidify and expand the results of Abramsky et al., answering several of their open questions. Firstly, we compare the definition of quantum graph homomorphisms arising from this work with an earlier definition of the concept due to Mančinska and Roberson and show that there are graphs which exhibit quantum advantage under one definition but not the other. Our second contribution is to extend the results of Abramsky et al. which only hold in the tensor product framework of quantum mechanics to the commuting operator framework. Next, we study a non-local structure isomorphism game, which generalises the well-studied graph isomorphism game. We show how the construction of the quantum monad can be refined to provide categorical semantics for quantum strategies in this game. This results in a category where morphisms coincide with quantum homomorphisms and isomorphisms coincide with quantum isomorphisms.
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Amin Karamlou. Quantum Relaxations of CSP and Structure Isomorphism. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karamlou:LIPIcs.MFCS.2025.61,
  author =	{Karamlou, Amin},
  title =	{{Quantum Relaxations of CSP and Structure Isomorphism}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{61:1--61:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.61},
  URN =		{urn:nbn:de:0030-drops-241686},
  doi =		{10.4230/LIPIcs.MFCS.2025.61},
  annote =	{Keywords: CSP, graph isomorphism, quantum information, non-local game, quantum graph homomorphism, monad}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.23
First-Order Store and Visibility in Name-Passing Calculi

Authors: Daniel Hirschkoff, Iwan Quémerais, and Davide Sangiorgi

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
The π-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how π-calculus processes can be controlled so that computations can only involve storage of first-order values. The discipline is enforced by a type system that is based on the notion of visibility, coming from game semantics. We discuss the impact of visibility on the behavioural theory. We propose characterisations of may-testing and barbed equivalence, based on (variants of) trace equivalence and labelled bisimilarity, in the case where computation is sequential, and in the case where computation is well-bracketed.
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Daniel Hirschkoff, Iwan Quémerais, and Davide Sangiorgi. First-Order Store and Visibility in Name-Passing Calculi. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirschkoff_et_al:LIPIcs.CONCUR.2025.23,
  author =	{Hirschkoff, Daniel and Qu\'{e}merais, Iwan and Sangiorgi, Davide},
  title =	{{First-Order Store and Visibility in Name-Passing Calculi}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.23},
  URN =		{urn:nbn:de:0030-drops-239737},
  doi =		{10.4230/LIPIcs.CONCUR.2025.23},
  annote =	{Keywords: process calculi, behavioural equivalence, type system}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.14
Pareto Fronts for Compositionally Solving String Diagrams of Parity Games

Authors: Kazuki Watanabe

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game with a given compositional structure and solve it efficiently as a divide-and-conquer algorithm by exploiting its compositional structure. Building on our recent progress in open Markov decision processes, we introduce Pareto fronts of open parity games, offering a framework for multi-objective solutions. We establish the positional determinacy of open parity games with respect to their Pareto fronts through a novel translation method. Our translation converts an open parity game into a parity game tailored to a given single-objective. Furthermore, we present a simple algorithm for solving open parity games, derived from this translation that allows the application of existing efficient algorithms for parity games. Expanding on this foundation, we develop a compositional algorithm for string diagrams of parity games.
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Kazuki Watanabe. Pareto Fronts for Compositionally Solving String Diagrams of Parity Games. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{watanabe:LIPIcs.CALCO.2025.14,
  author =	{Watanabe, Kazuki},
  title =	{{Pareto Fronts for Compositionally Solving String Diagrams of Parity Games}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.14},
  URN =		{urn:nbn:de:0030-drops-235734},
  doi =		{10.4230/LIPIcs.CALCO.2025.14},
  annote =	{Keywords: parity game, compositionality, string diagram}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.7
A Coinductive Representation of Computable Functions

Authors: Alvin Tang and Dirk Pattinson

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
We investigate a representation of computable functions as total functions over 2^∞, the set of finite and infinite sequences over {0,1}. In this model, infinite sequences are interpreted as non-terminating computations whilst finite sequences represent the sum of their digits. We introduce a new definition principle, function space corecursion, that simultaneously generalises minimisation and primitive recursion. This defines the class of computable corecursive functions that is closed under composition and function space corecursion. We prove computable corecursive functions represent all partial recursive functions, and show that all computable corecursive functions are indeed computable by translation into the untyped λ-calculus.
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Alvin Tang and Dirk Pattinson. A Coinductive Representation of Computable Functions. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tang_et_al:LIPIcs.CALCO.2025.7,
  author =	{Tang, Alvin and Pattinson, Dirk},
  title =	{{A Coinductive Representation of Computable Functions}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.7},
  URN =		{urn:nbn:de:0030-drops-235662},
  doi =		{10.4230/LIPIcs.CALCO.2025.7},
  annote =	{Keywords: Computability, Coinduction}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.6
Weighted Rewriting: Semiring Semantics for Abstract Reduction Systems

Authors: Emma Ahrens, Jan-Christoph Kassing, Jürgen Giesl, and Joost-Pieter Katoen

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

Abstract
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory and logic, we obtain a formalism that can be used for provenance analysis of arbitrary ARSs. Our semantics handle (possibly unbounded) non-determinism and possibly infinite reductions. Moreover, we develop several techniques to prove upper and lower bounds on the weights resulting from our semantics, and show that in this way one obtains a uniform approach to analyze several different properties like termination, derivational complexity, space complexity, safety, as well as combinations of these properties.
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Emma Ahrens, Jan-Christoph Kassing, Jürgen Giesl, and Joost-Pieter Katoen. Weighted Rewriting: Semiring Semantics for Abstract Reduction Systems. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ahrens_et_al:LIPIcs.FSCD.2025.6,
  author =	{Ahrens, Emma and Kassing, Jan-Christoph and Giesl, J\"{u}rgen and Katoen, Joost-Pieter},
  title =	{{Weighted Rewriting: Semiring Semantics for Abstract Reduction Systems}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{6:1--6:21},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-236215},
  doi =		{10.4230/LIPIcs.FSCD.2025.6},
  annote =	{Keywords: Rewriting, Semirings, Semantics, Termination, Verification}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.13
Unifying Boolean and Algebraic Descriptive Complexity

Authors: Baptiste Chanus, Damiano Mazza, and Morgan Rogers

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

Abstract
We introduce ultrarings, which simultaneously generalize commutative rings and Boolean lextensive categories. As such, they allow to blend together standard algebraic notions (from commutative algebra) and logical notions (from categorical logic), providing a unifying descriptive framework in which complexity classes over arbitrary rings (as in the Blum, Schub, Smale model) and usual, Boolean complexity classes may be captured in a uniform way.
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Baptiste Chanus, Damiano Mazza, and Morgan Rogers. Unifying Boolean and Algebraic Descriptive Complexity. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chanus_et_al:LIPIcs.FSCD.2025.13,
  author =	{Chanus, Baptiste and Mazza, Damiano and Rogers, Morgan},
  title =	{{Unifying Boolean and Algebraic Descriptive Complexity}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{13:1--13:22},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-236286},
  doi =		{10.4230/LIPIcs.FSCD.2025.13},
  annote =	{Keywords: Descriptive complexity theory, Categorical logic, Blum-Shub-Smale complexity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.3
Unsolvable Terms in Filter Models (Invited Talk)

Authors: Mariangiola Dezani-Ciancaglini, Paola Giannini, and Furio Honsell

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

Abstract
Intersection type theories (itt’s) and filter models, i.e. λ-calculus models generated by itt’s, are reviewed in full generality. In this framework, which subsumes most λ-calculus models in the literature based on Scott-continuous functions, we discuss the interpretation of unsolvable terms. We give a necessary, but not sufficient, condition on an itt for the interpretation of some unsolvable term to be non-trivial in the filter model it generates. This result is obtained building on a type theoretic characterisation of the fine structure of unsolvables.
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Mariangiola Dezani-Ciancaglini, Paola Giannini, and Furio Honsell. Unsolvable Terms in Filter Models (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 3:1-3:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dezaniciancaglini_et_al:LIPIcs.FSCD.2025.3,
  author =	{Dezani-Ciancaglini, Mariangiola and Giannini, Paola and Honsell, Furio},
  title =	{{Unsolvable Terms in Filter Models}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{3:1--3:24},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-236181},
  doi =		{10.4230/LIPIcs.FSCD.2025.3},
  annote =	{Keywords: \lambda-calculus, Intersection Types, Unsolvable Terms, Filter Models}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.31
Higher-Dimensional Automata: Extension to Infinite Tracks

Authors: Luc Passemard, Amazigh Amrane, and Uli Fahrenberg

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

Abstract
We introduce higher-dimensional automata for infinite interval ipomsets (ω-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by ω-HDAs under Büchi and Muller semantics. We show that Muller acceptance is more expressive than Büchi acceptance and, in contrast to the finite case, both semantics do not yield languages closed under subsumption. Then, we adapt the original rational operations to deal with ω-HDAs and show that while languages of ω-HDAs are ω-rational, not all ω-rational languages can be expressed by ω-HDAs.
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Luc Passemard, Amazigh Amrane, and Uli Fahrenberg. Higher-Dimensional Automata: Extension to Infinite Tracks. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{passemard_et_al:LIPIcs.FSCD.2025.31,
  author =	{Passemard, Luc and Amrane, Amazigh and Fahrenberg, Uli},
  title =	{{Higher-Dimensional Automata: Extension to Infinite Tracks}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{31:1--31:23},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-236466},
  doi =		{10.4230/LIPIcs.FSCD.2025.31},
  annote =	{Keywords: Higher-dimensional automata, concurrency theory, omega pomsets, B\"{u}chi acceptance, Muller acceptance, interval pomsets, pomsets with interfaces}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.23
∞-Categorical Models of Linear Logic

Authors: Eliès Harington and Samuel Mimram

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

Abstract
The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the earlier notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as weak forms of models of linear logic. The goal of this article is to formally introduce them and study their relationships. We show that ∞-linear-non-linear adjunctions still play the role of a unifying notion of model in this setting. Moreover, we provide a sufficient condition for a symmetric monoidal ∞-category to be Lafont. Finally, we illustrate our constructions by providing models: we construct linear-non-linear adjunctions that generalize well-known models in relations (and variants based on profunctors or spans), domains and vector spaces. In particular, we introduce a model based on spectra, a homotopical variant of abelian groups.
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Eliès Harington and Samuel Mimram. ∞-Categorical Models of Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harington_et_al:LIPIcs.FSCD.2025.23,
  author =	{Harington, Eli\`{e}s and Mimram, Samuel},
  title =	{{∞-Categorical Models of Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{23:1--23:20},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-236381},
  doi =		{10.4230/LIPIcs.FSCD.2025.23},
  annote =	{Keywords: linear logic, linear-non-linear adjunction, ∞-category, spectrum}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.22
Branch Sequentialization in Quantum Polytime

Authors: Emmanuel Hainry, Romain Péchoux, and Mário Silva

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

Abstract
Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes. Current compilation strategies for quantum control flow involve compiling the branches of a quantum conditional, either in-depth or in-width, which in general leads to circuits of exponential size. This problem is coined as the branch sequentialization problem. We introduce and study a compilation technique for avoiding branch sequentialization on a language that is sound and complete for quantum polynomial time, thus, improving on existing polynomial-size-preserving compilation techniques.
Cite as

Emmanuel Hainry, Romain Péchoux, and Mário Silva. Branch Sequentialization in Quantum Polytime. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hainry_et_al:LIPIcs.FSCD.2025.22,
  author =	{Hainry, Emmanuel and P\'{e}choux, Romain and Silva, M\'{a}rio},
  title =	{{Branch Sequentialization in Quantum Polytime}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{22:1--22:22},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-236373},
  doi =		{10.4230/LIPIcs.FSCD.2025.22},
  annote =	{Keywords: Quantum Programs, Implicit Computational Complexity, Quantum Circuits}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.14
Algorithms for the Diverse-k-SAT Problem: The Geometry of Satisfying Assignments

Authors: Per Austrin, Ioana O. Bercea, Mayank Goswami, Nutan Limaye, and Adarsh Srinivasan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Given a k-CNF formula and an integer s ≥ 2, we study algorithms that obtain s solutions to the formula that are as dispersed as possible. For s = 2, this problem of computing the diameter of a k-CNF formula was initiated by Creszenzi and Rossi, who showed strong hardness results even for k = 2. The current best upper bound [Angelsmark and Thapper '04] goes to 4ⁿ as k → ∞. As our first result, we show that this quadratic blow up is not necessary by utilizing the Fast-Fourier transform (FFT) to give a O^*(2ⁿ) time exact algorithm for computing the diameter of any k-CNF formula. For s > 2, the problem was raised in the SAT community (Nadel '11) and several heuristics have been proposed for it, but no algorithms with theoretical guarantees are known. We give exact algorithms using FFT and clique-finding that run in O^*(2^{(s-1)n}) and O^*(s² |Ω_{𝐅}|^{ω ⌈ s/3 ⌉}) respectively, where |Ω_{𝐅}| is the size of the solutions space of the formula 𝐅 and ω is the matrix multiplication exponent. However, current SAT algorithms for finding one solution run in time O^*(2^{ε_{k}n}) for ε_{k} ≈ 1-Θ(1/k), which is much faster than all above run times. As our main result, we analyze two popular SAT algorithms - PPZ (Paturi, Pudlák, Zane '97) and Schöning’s ('02) algorithms, and show that in time poly(s)O^*(2^{ε_{k}n}), they can be used to approximate diameter as well as the dispersion (s > 2) problem. While we need to modify Schöning’s original algorithm for technical reasons, we show that the PPZ algorithm, without any modification, samples solutions in a geometric sense. We believe this geometric sampling property of PPZ may be of independent interest. Finally, we focus on diverse solutions to NP-complete optimization problems, and give bi-approximations running in time poly(s)O^*(2^{ε n}) with ε < 1 for several problems such as Maximum Independent Set, Minimum Vertex Cover, Minimum Hitting Set, Feedback Vertex Set, Multicut on Trees and Interval Vertex Deletion. For all of these problems, all existing exact methods for finding optimal diverse solutions have a runtime with at least an exponential dependence on the number of solutions s. Our methods show that by relaxing to bi-approximations, this dependence on s can be made polynomial.
Cite as

Per Austrin, Ioana O. Bercea, Mayank Goswami, Nutan Limaye, and Adarsh Srinivasan. Algorithms for the Diverse-k-SAT Problem: The Geometry of Satisfying Assignments. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{austrin_et_al:LIPIcs.ICALP.2025.14,
  author =	{Austrin, Per and Bercea, Ioana O. and Goswami, Mayank and Limaye, Nutan and Srinivasan, Adarsh},
  title =	{{Algorithms for the Diverse-k-SAT Problem: The Geometry of Satisfying Assignments}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.14},
  URN =		{urn:nbn:de:0030-drops-233916},
  doi =		{10.4230/LIPIcs.ICALP.2025.14},
  annote =	{Keywords: Exponential time algorithms, Satisfiability, k-SAT, PPZ, Sch\"{o}ning, Dispersion, Diversity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.105
NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability

Authors: Prem Nigam Kar, David E. Roberson, Tim Seppelt, and Peter Zeman

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Mančinska and Roberson [FOCS'20] showed that two graphs are quantum isomorphic if and only if they are homomorphism indistinguishable over the class of planar graphs. Atserias et al. [JCTB'19] proved that quantum isomorphism is undecidable in general. The NPA hierarchy gives a sequence of semidefinite programming relaxations of quantum isomorphism. Recently, Roberson and Seppelt [ICALP'23] obtained a homomorphism indistinguishability characterization of the feasibility of each level of the Lasserre hierarchy of semidefinite programming relaxations of graph isomorphism. We prove a quantum analogue of this result by showing that each level of the NPA hierarchy of SDP relaxations for quantum isomorphism of graphs is equivalent to homomorphism indistinguishability over an appropriate class of planar graphs. By combining the convergence of the NPA hierarchy with the fact that the union of these graph classes is the set of all planar graphs, we are able to give a new proof of the result of Mančinska and Roberson [FOCS'20] that avoids the use of the theory of quantum groups. This homomorphism indistinguishability characterization also allows us to give a randomized polynomial-time algorithm deciding exact feasibility of each fixed level of the NPA hierarchy of SDP relaxations for quantum isomorphism.
Cite as

Prem Nigam Kar, David E. Roberson, Tim Seppelt, and Peter Zeman. NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 105:1-105:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kar_et_al:LIPIcs.ICALP.2025.105,
  author =	{Kar, Prem Nigam and Roberson, David E. and Seppelt, Tim and Zeman, Peter},
  title =	{{NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{105:1--105:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.105},
  URN =		{urn:nbn:de:0030-drops-234828},
  doi =		{10.4230/LIPIcs.ICALP.2025.105},
  annote =	{Keywords: Quantum isomorphism, NPA hierarchy, homomorphism indistinguishability}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.136
The Converse of the Real Orthogonal Holant Theorem

Authors: Ben Young

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The Holant theorem is a powerful tool for studying the computational complexity of counting problems. Due to the great expressiveness of the Holant framework, a converse to the Holant theorem would itself be a very powerful counting indistinguishability theorem. The most general converse does not hold, but we prove the following, still highly general, version: if any two sets of real-valued signatures are Holant-indistinguishable, then they are equivalent up to an orthogonal transformation. This resolves a partially open conjecture of Xia (2010). Consequences of this theorem include the well-known result that homomorphism counts from all graphs determine a graph up to isomorphism, the classical sufficient condition for simultaneous orthogonal similarity of sets of real matrices, and a combinatorial characterization of sets of simultaneosly orthogonally decomposable (odeco) symmetric tensors.
Cite as

Ben Young. The Converse of the Real Orthogonal Holant Theorem. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 136:1-136:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{young:LIPIcs.ICALP.2025.136,
  author =	{Young, Ben},
  title =	{{The Converse of the Real Orthogonal Holant Theorem}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{136:1--136:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.136},
  URN =		{urn:nbn:de:0030-drops-235138},
  doi =		{10.4230/LIPIcs.ICALP.2025.136},
  annote =	{Keywords: Holant, Counting Indistinguishability, Odeco}
}
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