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Volume

LIPIcs, Volume 345

50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

MFCS 2025, August 25-29, 2025, Warsaw, Poland

Editors: Paweł Gawrychowski, Filip Mazowiecki, and Michał Skrzypczak

Document

DOI: 10.4230/LIPIcs.LICS.2026.64

Checking History Determinism for Parity Automata Is in NP

Authors: Karoliina Lehtinen, Keya Prakash, and Michał Skrzypczak

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

Abstract

History-deterministic automata, often also called good-for-games, are an intermediate model between deterministic and nondeterministic automata, which are particularly well-suited for applications in verification and reactive synthesis. We show that deciding whether a parity automaton is history-deterministic is in NP. Our result matches an NP-hardness lower bound (Prakash 2024) and builds on insights from a fixed-parameter tractable algorithm (Lehtinen and Prakash 2025). This settles the complexity of the problem, which has been open since 2006.

Cite as

Karoliina Lehtinen, Keya Prakash, and Michał Skrzypczak. Checking History Determinism for Parity Automata Is in NP. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 64:1-64:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lehtinen_et_al:LIPIcs.LICS.2026.64,
  author =	{Lehtinen, Karoliina and Prakash, Keya and Skrzypczak, Micha{\l}},
  title =	{{Checking History Determinism for Parity Automata Is in NP}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{64:1--64:24},
  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.2026.64},
  URN =		{urn:nbn:de:0030-drops-268517},
  doi =		{10.4230/LIPIcs.LICS.2026.64},
  annote =	{Keywords: History-determinism, parity automata, good-for-games}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.13

Totally Unclustered BWT Images of Any Length over Non-Binary Alphabets

Authors: Gabriele Fici, Estéban Gabory, Giuseppe Romana, and Marinella Sciortino

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

We prove that for every integer n > 0 and for every alphabet Σ_k of size k ≥ 3, there exist words of length n whose Burrows-Wheeler Transform (BWT) is totally unclustered, i.e., it consists of exactly n runs with no two consecutive equal symbols. These words represent the worst-case behavior of the clustering effect of the BWT. We also establish a lower bound on their number. This contrasts with the binary case, where the existence of infinitely many totally unclustered BWT images is still an open problem, related to Artin’s conjecture on primitive roots.

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Gabriele Fici, Estéban Gabory, Giuseppe Romana, and Marinella Sciortino. Totally Unclustered BWT Images of Any Length over Non-Binary Alphabets. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fici_et_al:LIPIcs.CPM.2026.13,
  author =	{Fici, Gabriele and Gabory, Est\'{e}ban and Romana, Giuseppe and Sciortino, Marinella},
  title =	{{Totally Unclustered BWT Images of Any Length over Non-Binary Alphabets}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.13},
  URN =		{urn:nbn:de:0030-drops-259399},
  doi =		{10.4230/LIPIcs.CPM.2026.13},
  annote =	{Keywords: Burrows-Wheeler Transform, BWT-runs, Repetitiveness Measure, Clustering Effect, Generalized de Bruijn Words}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.24

On Occurrence-Preserving Morphisms

Authors: Kaisei Kishi, Peaker Guo, Cristian Urbina, and Hideo Bannai

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

A morphism is a mapping that transforms words through letter-wise substitution, where each symbol is consistently replaced by a fixed word. In the field of combinatorics on words, one topic that has attracted considerable attention is the characterization of morphisms that preserve specific properties, such as overlap-freeness, square-freeness, lexicographic order, and primitivity. Continuing this direction, we initiate the study on occurrence-preserving morphisms, which address the following fundamental question: given a morphism ϕ, two words u and v, and k ≥ 1, under what conditions does the number of occurrences of u in v equal the number of occurrences of ϕ^k(u) in ϕ^k(v)? To answer this question, we introduce the notion of interference-free morphisms, examine their properties, and uncover a connection to recognizable morphisms. We then present a precise characterization of occurrence-preserving morphisms in terms of interference-freeness. As applications of our characterization, we first show that there exists a bijection between the starting positions of the occurrences of u in v and those of ϕ^k(u) in ϕ^k(v). We then apply the characterization to the Fibonacci and Thue-Morse words to identify their minimal unique substrings (MUSs). Finally, we exploit the connection between MUSs and net occurrences to simplify existing proofs on net occurrences in these words.

Cite as

Kaisei Kishi, Peaker Guo, Cristian Urbina, and Hideo Bannai. On Occurrence-Preserving Morphisms. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kishi_et_al:LIPIcs.CPM.2026.24,
  author =	{Kishi, Kaisei and Guo, Peaker and Urbina, Cristian and Bannai, Hideo},
  title =	{{On Occurrence-Preserving Morphisms}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.24},
  URN =		{urn:nbn:de:0030-drops-259504},
  doi =		{10.4230/LIPIcs.CPM.2026.24},
  annote =	{Keywords: Property-preserving morphisms, interference-free morphisms, recognizable morphisms, injective morphisms, Fibonacci words, Thue-Morse words, minimal unique substrings (MUSs), net occurrences}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2026.11

Factorised Representations of Join Queries: Tight Bounds and a New Dichotomy

Authors: Christoph Berkholz and Harry Vinall-Smeeth

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract

A common theme in factorised databases and knowledge compilation is the representation of solution sets in a useful yet succinct data structure. In this paper, we study the representation of the result of join queries (or, equivalently, the set of homomorphisms between two relational structures). We focus on the very general format of {∪,×}-circuits - also known as d-representations or DNNF circuits - and aim to find the limits of this approach. In prior work, it has been shown that there always exists a {∪,×}-circuit of size N^O(subw) representing the query result, where N is the size of the database and subw the submodular width of the query. If the arity of all relations is bounded by a constant, then subw is linear in the treewidth tw of the query. In this setting, the authors of this paper proved a lower bound of N^Ω(tw^ε) on the circuit size (ICALP 2023), where ε > 0 depends on the excluded grid theorem. Our first main contribution is to improve this lower bound to N^Ω(tw), which is tight up to a constant factor in the exponent. Our second contribution is a N^Ω(subw^{1/4}) lower bound on the circuit size for join queries over relations of unbounded arity. Both lower bounds are unconditional lower bounds on the circuit size for well-chosen database instances. Their proofs use a combination of structural (hyper)graph theory with communication complexity in a simple yet novel way. While the second lower bound is asymptotically equivalent to Marx’s conditional bound on the decision complexity (JACM 2013), our N^Θ(tw) bound in the bounded arity setting is tight, while the best conditional bound on the decision complexity is N^Ω(tw/log tw). Note that removing this logarithmic factor in the decision setting is a major open problem.

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Christoph Berkholz and Harry Vinall-Smeeth. Factorised Representations of Join Queries: Tight Bounds and a New Dichotomy. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{berkholz_et_al:LIPIcs.ICDT.2026.11,
  author =	{Berkholz, Christoph and Vinall-Smeeth, Harry},
  title =	{{Factorised Representations of Join Queries: Tight Bounds and a New Dichotomy}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.11},
  URN =		{urn:nbn:de:0030-drops-256255},
  doi =		{10.4230/LIPIcs.ICDT.2026.11},
  annote =	{Keywords: join queries, homomorphisms, factorised databases, succinct representation, knowledge compilation, lower bounds}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.25

Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing

Authors: Marek Černý and Tim Seppelt

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

Two graphs G and H are homomorphism indistinguishable over a graph class ℱ if they admit the same number of homomorphisms from every graph F ∈ ℱ. Many graph isomorphism relaxations such as (quantum) isomorphism and cospectrality can be characterised as homomorphism indistinguishability over specific graph classes. Thereby, the problems HomInd(ℱ) of deciding homomorphism indistinguishability over ℱ subsume diverse graph isomorphism relaxations whose complexities range from logspace to undecidable. Establishing the first general result on the complexity of HomInd(ℱ), Seppelt (MFCS 2024) showed that HomInd(ℱ) is in randomised polynomial time for every graph class ℱ of bounded treewidth that can be defined in counting monadic second-order logic CMSO₂. We show that this algorithm is conditionally optimal, i.e. it cannot be derandomised unless polynomial identity testing is in P. For CMSO₂-definable graph classes ℱ of bounded pathwidth, we improve the previous complexity upper bound for HomInd(ℱ) from P to C_ = L and show that this is tight. Secondarily, we establish a connection between homomorphism indistinguishability and multiplicity automata equivalence which allows us to pinpoint the complexity of the latter problem as C_ = L-complete.

Cite as

Marek Černý and Tim Seppelt. Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cerny_et_al:LIPIcs.STACS.2026.25,
  author =	{\v{C}ern\'{y}, Marek and Seppelt, Tim},
  title =	{{Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.25},
  URN =		{urn:nbn:de:0030-drops-255144},
  doi =		{10.4230/LIPIcs.STACS.2026.25},
  annote =	{Keywords: treewidth, Courcelle’s theorem, logspace, multiplicity automata, polynomial identity testing}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.36

Time-Optimal Construction of String Synchronizing Sets

Authors: Jonas Ellert and Tomasz Kociumaka

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

A powerful design principle behind many modern string algorithms is local consistency: breaking the symmetry between string positions based on their small contexts so that matching fragments are handled consistently. Among the most influential instantiations of this principle are string synchronizing sets [Kempa & Kociumaka; STOC 2019]. A τ-synchronizing set of a string of length n is a set of O(n/τ) string positions, chosen using their length-2τ contexts, such that (outside of highly periodic regions) every block of τ consecutive positions contains at least one element of the set. Synchronizing sets have found dozens of applications in diverse settings, from quantum and dynamic algorithms to fully compressed computation. In the classic word RAM model, particularly for strings over small alphabets, they enabled faster solutions to core problems in data compression, text indexing, and string similarity. In this work, we show that any string T ∈ [0 .. σ)ⁿ can be preprocessed in O(n log σ / log n) time so that, for any given integer τ ∈ [1 .. n], a τ-synchronizing set of T can be constructed in O((n log τ)/(τ log n)) time. Both bounds are optimal in the word RAM model with machine word size w = Θ(log n), matching the information-theoretic minimum for the input and output sizes, respectively. Previously, constructing a τ-synchronizing set required O(n/τ) time after an O(n)-time preprocessing [Kociumaka, Radoszewski, Rytter, and Waleń; SICOMP 2024], or, in the restricted regime of τ < 0.2 log_σ n, without any preprocessing needed [Kempa & Kociumaka; STOC 2019]. A simple instantiation of our method outputs the synchronizing set as a sorted list in O(n/τ) time, or as a bitmask in O(n/log n) time. Our optimal construction produces a compact fully indexable dictionary, supporting select queries in O(1) time and rank queries in O(log ((log τ)/(log log n))) time. The latter complexity matches known unconditional cell-probe lower bounds for τ ≤ n^{1-Ω(1)}. To achieve this, we introduce a general framework for efficiently processing sparse integer sequences via a custom variable-length encoding. We also augment the optimal variant of van Emde Boas trees [Pătraşcu & Thorup; STOC 2006] with a deterministic linear-time construction. When the set is represented as a bitmask under our sparse encoding, the same guarantees for select and rank queries hold after preprocessing in time proportional to the size of our encoding (in words).

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Jonas Ellert and Tomasz Kociumaka. Time-Optimal Construction of String Synchronizing Sets. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ellert_et_al:LIPIcs.STACS.2026.36,
  author =	{Ellert, Jonas and Kociumaka, Tomasz},
  title =	{{Time-Optimal Construction of String Synchronizing Sets}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.36},
  URN =		{urn:nbn:de:0030-drops-255258},
  doi =		{10.4230/LIPIcs.STACS.2026.36},
  annote =	{Keywords: synchronizing sets, local consistency, packed strings}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.63

Generalised Quantifiers Based on Rabin-Mostowski Index

Authors: Denis Kuperberg, Damian Niwiński, Paweł Parys, and Michał Skrzypczak

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these quantifiers. We study these problems in the realm of both ω-words and infinite trees. As it turns out, the pictures in these two cases are very different. In the case of ω-words the new quantifiers can be effectively expressed in pure MSO logic. In contrast, in the case of infinite trees, addition of these quantifiers leads to an undecidable formalism. To realise index-quantifier elimination, we consider the extension of MSO by game quantifiers. As a tool, we provide a specific quantifier-elimination procedure for them. Moreover, we introduce a novel construction of transducers realising strategies in ω-regular games with monadic parameters.

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Denis Kuperberg, Damian Niwiński, Paweł Parys, and Michał Skrzypczak. Generalised Quantifiers Based on Rabin-Mostowski Index. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 63:1-63:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kuperberg_et_al:LIPIcs.STACS.2026.63,
  author =	{Kuperberg, Denis and Niwi\'{n}ski, Damian and Parys, Pawe{\l} and Skrzypczak, Micha{\l}},
  title =	{{Generalised Quantifiers Based on Rabin-Mostowski Index}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{63:1--63:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.63},
  URN =		{urn:nbn:de:0030-drops-255526},
  doi =		{10.4230/LIPIcs.STACS.2026.63},
  annote =	{Keywords: monadic quantifiers, decidability, quantifier elimination, parity automata, game quantifier, Rabin-Mostowski index}
}

@InProceedings{kuperberg_et_al:LIPIcs.STACS.2026.63,
  author =	{Kuperberg, Denis and Niwi\'{n}ski, Damian and Parys, Pawe{\l} and Skrzypczak, Micha{\l}},
  title =	{{Generalised Quantifiers Based on Rabin-Mostowski Index}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{63:1--63:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.63},
  URN =		{urn:nbn:de:0030-drops-255526},
  doi =		{10.4230/LIPIcs.STACS.2026.63},
  annote =	{Keywords: monadic quantifiers, decidability, quantifier elimination, parity automata, game quantifier, Rabin-Mostowski index}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.15

Cyclic Proof Theory of Generalised Inductive Definitions

Authors: Gianluca Curzi and Lukas Melgaard

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

We study cyclic proof systems for μPA, an extension of Peano arithmetic by generalised inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic Π^1_2-CA₀ by Möllerfeld. The main result of this paper is that cyclic and inductive μPA have the same proof-theoretic strength. First, we translate cyclic proofs into an annotated variant based on Sprenger and Dam’s systems for first-order μ-calculus, whose stronger validity condition allows for a simpler proof of soundness. We then formalise this argument within Π^1_2-CA₀, leveraging Möllerfeld’s conservativity properties. To this end, we build on prior work by Curzi and Das on the reverse mathematics of the Knaster-Tarski theorem. As a byproduct of our proof methods we show that, despite the stronger validity condition, annotated and "plain" cyclic proofs for μPA prove the same theorems. This work represents a further step in the non-wellfounded proof-theoretic analysis of theories of arithmetic via impredicative fragments of second-order arithmetic, an approach initiated by Simpson’s Cyclic Arithmetic, and continued by Das and Melgaard in the context of arithmetical inductive definitions.

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Gianluca Curzi and Lukas Melgaard. Cyclic Proof Theory of Generalised Inductive Definitions. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{curzi_et_al:LIPIcs.CSL.2026.15,
  author =	{Curzi, Gianluca and Melgaard, Lukas},
  title =	{{Cyclic Proof Theory of Generalised Inductive Definitions}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.15},
  URN =		{urn:nbn:de:0030-drops-254399},
  doi =		{10.4230/LIPIcs.CSL.2026.15},
  annote =	{Keywords: cyclic proofs, positive inductive definitions, arithmetic, fixed points, proof theory, reset proof systems}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.24

Well-Founded Coalgebras Meet Kőnig’s Lemma

Authors: Henning Urbat and Thorsten Wißmann

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

Kőnig’s lemma is a fundamental result about trees with countless applications in mathematics and computer science. In contrapositive form, it states that if a tree is finitely branching and well-founded (i.e. has no infinite paths), then it is finite. We present a coalgebraic version of Kőnig’s lemma featuring two dimensions of generalization: from finitely branching trees to coalgebras for a finitary endofunctor H, and from the base category of sets to a locally finitely presentable category ℂ, such as the category of posets, nominal sets, or convex sets. Our coalgebraic Kőnig’s lemma states that, under mild assumptions on ℂ and H, every well-founded coalgebra for H is the directed join of its well-founded subcoalgebras with finitely generated state space - in particular, the category of well-founded coalgebras is locally presentable. As applications, we derive versions of Kőnig’s lemma for graphs in a topos as well as for nominal and convex transition systems. Additionally, we show that the key construction underlying the proof gives rise to two simple constructions of the initial algebra (equivalently, the final recursive coalgebra) for the functor H: The initial algebra is both the colimit of all well-founded and of all recursive coalgebras with finitely presentable state space. Remarkably, this result holds even in settings where well-founded coalgebras form a proper subclass of recursive ones. The first construction of the initial algebra is entirely new, while for the second one our approach yields a short and transparent new correctness proof.

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Henning Urbat and Thorsten Wißmann. Well-Founded Coalgebras Meet Kőnig’s Lemma. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{urbat_et_al:LIPIcs.CSL.2026.24,
  author =	{Urbat, Henning and Wi{\ss}mann, Thorsten},
  title =	{{Well-Founded Coalgebras Meet K\H{o}nig’s Lemma}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.24},
  URN =		{urn:nbn:de:0030-drops-254485},
  doi =		{10.4230/LIPIcs.CSL.2026.24},
  annote =	{Keywords: K\H{o}nig’s Lemma, Well-Foundedness, Coalgebra}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.29

Parametric Iteration in Resource Theories

Authors: Alessandro Di Giorgio, Pawel Sobocinski, and Niels Voorneveld

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

Many algorithms are specified with respect to a fixed but unknown parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is to capture this phenomenon in a more abstract setting. We focus on resource theories - general calculi of processes with a string diagrammatic syntax - introducing a general parametric iteration construction. By instantiating this construction within the Markov category of probabilistic Boolean circuits and equipping it with a suitable metric, we are able to capture the notion of negligibility via asymptotic equivalence, in a compositional way. This allows us to use diagrammatic reasoning to prove simple cryptographic theorems - for instance, proving that guessing a randomly generated key has negligible success.

Cite as

Alessandro Di Giorgio, Pawel Sobocinski, and Niels Voorneveld. Parametric Iteration in Resource Theories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{digiorgio_et_al:LIPIcs.CSL.2026.29,
  author =	{Di Giorgio, Alessandro and Sobocinski, Pawel and Voorneveld, Niels},
  title =	{{Parametric Iteration in Resource Theories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{29:1--29:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.29},
  URN =		{urn:nbn:de:0030-drops-254541},
  doi =		{10.4230/LIPIcs.CSL.2026.29},
  annote =	{Keywords: Markov categories, Cryptography, String diagrams, Asymptotic equivalence}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.3

Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.

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Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.46

Symmetric Algebraic Circuits and Homomorphism Polynomials

Authors: Anuj Dawar, Benedikt Pago, and Tim Seppelt

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

The central open question of algebraic complexity is whether VP ≠ VNP, which is saying that the permanent cannot be represented by families of polynomial-size algebraic circuits. For symmetric algebraic circuits, this has been confirmed by Dawar and Wilsenach (2020), who showed exponential lower bounds on the size of symmetric circuits for the permanent. In this work, we set out to develop a more general symmetric algebraic complexity theory. Our main result is that a family of symmetric polynomials admits small symmetric circuits if and only if they can be written as a linear combination of homomorphism counting polynomials of graphs of bounded treewidth. We also establish a relationship between the symmetric complexity of subgraph counting polynomials and the vertex cover number of the pattern graph. As a concrete example, we examine the symmetric complexity of immanant families (a generalisation of the determinant and permanent) and show that a known conditional dichotomy due to Curticapean (2021) holds unconditionally in the symmetric setting.

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Anuj Dawar, Benedikt Pago, and Tim Seppelt. Symmetric Algebraic Circuits and Homomorphism Polynomials. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dawar_et_al:LIPIcs.ITCS.2026.46,
  author =	{Dawar, Anuj and Pago, Benedikt and Seppelt, Tim},
  title =	{{Symmetric Algebraic Circuits and Homomorphism Polynomials}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.46},
  URN =		{urn:nbn:de:0030-drops-253330},
  doi =		{10.4230/LIPIcs.ITCS.2026.46},
  annote =	{Keywords: algebraic complexity, finite model theory, symmetric circuits, homomorphism counting, graph homomorphism, treewidth, counting width, first-order logic with counting quantifiers}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2025.2

Unboundedness Problems for Formal Languages (Invited Talk)

Authors: Georg Zetzsche

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract

Informally, unboundedness problems are decision problems that ask about the existence of infinitely many words (satisfying certain properties) in a formal language. For example: Is a given language infinite? Or: Does a given language have super-polynomial growth? These came into focus in recent years because of their connections to downward closure computation and separability problems. Although unboundedness problems may seem difficult at first, it turns out that there are techniques that are at the same time conceptually very simple, but also apply to a surprisingly wide variety of language classes. The talk will survey recent results (and techniques) concerning unboundedness problems.

Cite as

Georg Zetzsche. Unboundedness Problems for Formal Languages (Invited Talk). In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zetzsche:LIPIcs.FSTTCS.2025.2,
  author =	{Zetzsche, Georg},
  title =	{{Unboundedness Problems for Formal Languages}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.2},
  URN =		{urn:nbn:de:0030-drops-250810},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.2},
  annote =	{Keywords: Decidability, formal languages, unifying frameworks, downward closure, separability}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.93

Recognizing and Realizing Temporal Reachability Graphs

Authors: Thomas Erlebach, Othon Michail, and Nils Morawietz

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

A temporal graph 𝒢 = (G,λ) can be represented by an underlying graph G = (V,E) together with a function λ that assigns to each edge e ∈ E the set of time steps during which e is present. The reachability graph of 𝒢 is the directed graph D = (V,A) with (u,v) ∈ A if and only if there is a temporal path from u to v. We study the Reachability Graph Realizability (RGR) problem that asks whether a given directed graph D = (V,A) is the reachability graph of some temporal graph. The question can be asked for undirected or directed temporal graphs, for reachability defined via strict or non-strict temporal paths, and with or without restrictions on λ (simple, proper, or both). Answering an open question posed by Casteigts et al. (TCS 2024), we show that all variants of the problem are NP-complete, except for two variants that become trivial in the directed case. For undirected temporal graphs, we consider the complexity of the problem with respect to the solid graph, that is, the graph containing all edges that could potentially receive a label in any realization. We show that the RGR problem is fixed-parameter tractable for the feedback edge set number of the solid graph. As we show, the latter parameter can presumably not be replaced by smaller parameters like feedback vertex set number or treedepth, since the problem is W[2]-hard for them.

Cite as

Thomas Erlebach, Othon Michail, and Nils Morawietz. Recognizing and Realizing Temporal Reachability Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 93:1-93:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erlebach_et_al:LIPIcs.ESA.2025.93,
  author =	{Erlebach, Thomas and Michail, Othon and Morawietz, Nils},
  title =	{{Recognizing and Realizing Temporal Reachability Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{93:1--93:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.93},
  URN =		{urn:nbn:de:0030-drops-245627},
  doi =		{10.4230/LIPIcs.ESA.2025.93},
  annote =	{Keywords: parameterized complexity, temporal graphs, FPT algorithm, feedback edge set, directed graph recognition}
}

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