DROPS

Volume

LIPIcs, Volume 254

40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

STACS 2023, March 7-9, 2023, Hamburg, Germany

Editors: Petra Berenbrink, Patricia Bouyer, Anuj Dawar, and Mamadou Moustapha Kanté

Volume

LIPIcs, Volume 250

42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

FSTTCS 2022, December 18-20, 2022, IIT Madras, Chennai, India

Editors: Anuj Dawar and Venkatesan Guruswami

Volume

LIPIcs, Volume 168

47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference)

Editors: Artur Czumaj, Anuj Dawar, and Emanuela Merelli

Document

DOI: 10.4230/LIPIcs.LICS.2026.37

Complexity of Satisfiability in Kochen-Specker Partial Boolean Algebras

Authors: Anuj Dawar and Nihil Shah

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

Abstract

The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert space. Each partial Boolean algebra provides a semantics for interpreting propositional logic. In this paper, we examine the complexity of propositional satisfiability for various classes of partial Boolean algebras. We first show that the satisfiability problem for the class of non-trivial partial Boolean algebras is NP-complete. Next, we consider the satisfiability problem for the class of partial Boolean algebras arising from projectors on finite dimensional Hilbert spaces. For real Hilbert spaces of dimension greater 2 and any complex Hilbert spaces of dimension greater than 3, we demonstrate that the satisfiability problem is complete for the existential theory of the reals. Interestingly, the proofs of these results make use of Kochen-Specker sets as gadgets. As a corollary, we conclude that deciding quantum homomorphism in these fixed dimensions are also complete for the existential theory of the reals. Finally, we show that the satisfiability problems for the class of all Hilbert spaces and all finite-dimensional Hilbert spaces is undecidable.

Cite as

Anuj Dawar and Nihil Shah. Complexity of Satisfiability in Kochen-Specker Partial Boolean Algebras. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 37:1-37:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dawar_et_al:LIPIcs.LICS.2026.37,
  author =	{Dawar, Anuj and Shah, Nihil},
  title =	{{Complexity of Satisfiability in Kochen-Specker Partial Boolean Algebras}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{37:1--37:25},
  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.2026.37},
  URN =		{urn:nbn:de:0030-drops-268247},
  doi =		{10.4230/LIPIcs.LICS.2026.37},
  annote =	{Keywords: partial Boolean algebra, quantum logic, existential theory of the reals}
}

Document

DOI: 10.4230/LIPIcs.LICS.2026.54

A Categorical Perspective on Constraint Satisfaction: The Wonderland of Adjunctions

Authors: Maximilian Hadek, Tomáš Jakl, and Jakub Opršal

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

Abstract

The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000’s. The core of this approach is the notion of polymorphisms which determine the complexity of the problem (up to log-space reductions). In the past few years, a new, more general version of the CSP emerged, the promise constraint satisfaction problem (PCSP), and the notion of polymorphisms and most of the core theses of the algebraic approach were generalised to the promise setting. Nevertheless, recent work also suggests that insights from other fields are immensely useful in the study of PCSPs including algebraic topology. In this paper, we provide an entry point for category-theorists into the study of complexity of CSPs and PCSPs. We show that many standard CSP notions have clear and well-known categorical counterparts. For example, the algebraic structure of polymorphisms can be described as a set-functor defined as a right Kan extension. We provide purely categorical proofs of core results of the algebraic approach including a proof that the complexity only depends on the polymorphisms. Our new proofs are substantially shorter and, from the categorical perspective, cleaner than previous proofs of the same results. Moreover, as expected, they are applicable more widely. We believe that, in particular in the case of PCSPs, category theory brings insights that can help solve some of the current challenges of the field.

Cite as

Maximilian Hadek, Tomáš Jakl, and Jakub Opršal. A Categorical Perspective on Constraint Satisfaction: The Wonderland of Adjunctions. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 54:1-54:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hadek_et_al:LIPIcs.LICS.2026.54,
  author =	{Hadek, Maximilian and Jakl, Tom\'{a}\v{s} and Opr\v{s}al, Jakub},
  title =	{{A Categorical Perspective on Constraint Satisfaction: The Wonderland of Adjunctions}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{54:1--54:27},
  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.2026.54},
  URN =		{urn:nbn:de:0030-drops-268415},
  doi =		{10.4230/LIPIcs.LICS.2026.54},
  annote =	{Keywords: constraint satisfaction problem, categorical models and logics}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2026.172

Preservation Theorems in Semiring Semantics

Authors: Sophie Brinke, Anuj Dawar, Erich Grädel, and Benedikt Pago

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

We study the status of classical model-theoretic preservation theorems such as the Łoś-Tarski theorem and the homomorphism preservation theorem in the context of semiring semantics. Semiring semantics has its origins in the provenance analysis of database queries but has been extended to a systematic way of evaluating logical statements to values in a commutative semiring. Depending on the underlying semiring, this allows us to track descriptions of the atomic facts that are responsible for the truth of a statement or practical information about the evaluation such as costs or confidence. The systematic development of semiring semantics for first-order logic and other logical systems raises the question to what extent classical model-theoretic results can be generalised to this setting and how such results depend on the underlying semiring. The definitions of semantic properties such as preservation under extensions, substructures, or homomorphisms naturally generalise to the setting of semiring semantics. However, the status of the corresponding preservation theorem strongly depends on the algebraic properties of the particular semirings. We prove that these preservation theorems do indeed hold for all lattice semirings (a quite large class, encompassing practically relevant semirings and in particular all min-max semirings). The proofs combine adaptations of the classical compactness and amalgamation methods with specific reduction methods for logical entailment that have been developed in semiring semantics. On the other side, variants of the existential preservation theorem fail for many other semirings, including the tropical semiring, the Viterbi semiring, the Łukasiewicz semiring, and the natural semirings ℕ and ℕ^∞. Surprisingly, the existential preservation theorem does hold for finite interpretations in a number of semirings, including the three-element min-max semiring, which extends the Boolean by just a single additional truth value. Thus, the situation for these semirings is in sharp contrast to the Boolean case, where the Łoś-Tarski theorem holds in general, but not in the finite.

Cite as

Sophie Brinke, Anuj Dawar, Erich Grädel, and Benedikt Pago. Preservation Theorems in Semiring Semantics. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 172:1-172:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brinke_et_al:LIPIcs.ICALP.2026.172,
  author =	{Brinke, Sophie and Dawar, Anuj and Gr\"{a}del, Erich and Pago, Benedikt},
  title =	{{Preservation Theorems in Semiring Semantics}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{172:1--172:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.172},
  URN =		{urn:nbn:de:0030-drops-265605},
  doi =		{10.4230/LIPIcs.ICALP.2026.172},
  annote =	{Keywords: Semiring semantics, preservation theorems, model theory, algebraic logics}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.15

One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming

Authors: Avinandan Das

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

This paper investigates the semi-streaming complexity of k-partial coloring, a generalization of proper graph coloring. For k ≥ 1, a k-partial coloring requires that each vertex v in an n-node graph is assigned a color such that at least min{k, deg(v)} of its neighbors are assigned colors different from its own. This framework naturally extends classical coloring problems: specifically, k-partial (k+1)-coloring and k-partial k-coloring generalize (Δ+1)-proper coloring and Δ-proper coloring, respectively. Prior works of Assadi, Chen, and Khanna [SODA 2019] and Assadi, Kumar, and Mittal [TheoretiCS 2023] show that both (Δ+1)-proper coloring and Δ-proper coloring admit one-pass randomized semi-streaming algorithms. We explore whether these efficiency gains extend to their partial coloring generalizations and reveal a sharp computational threshold: while k-partial (k+1)-coloring admits a one-pass randomized semi-streaming algorithm, the k-partial k-coloring remains semi-streaming intractable, effectively demonstrating a "dichotomy of one color" in the streaming model.

Cite as

Avinandan Das. One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{das:LIPIcs.SWAT.2026.15,
  author =	{Das, Avinandan},
  title =	{{One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.15},
  URN =		{urn:nbn:de:0030-drops-260515},
  doi =		{10.4230/LIPIcs.SWAT.2026.15},
  annote =	{Keywords: Graph Coloring, Semi-streaming algorithms, Lower bounds}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.27

Exploring the Gap Between LCS and LCStr

Authors: Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom

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

Abstract

The Longest Common Subsequence (LCS) problem and the Longest Common Substring (LCStr) problem are classical string problems with broad theoretical and practical significance. The former has a quadratic conditional lower bound [FOCS, 2015], while the latter admits a linear-time solution. In this paper, we study a natural variation of these problems, the Longest Common Subsequence-Substring (LCSS) problem. The LCSS problem seeks the longest string that is simultaneously a subsequence of one input string and a substring of the other. This variant bridges LCS and LCStr, raising intriguing algorithmic questions: Does the complexity of computing LCSS interpolate between the linear time of LCStr and the quadratic time of LCS? What about approximability? We also examine a natural extension of LCSS to multiple strings, parameterizing the balance between subsequence and substring requirements. Our results reveal several insights. First, under the SETH conjecture, the inherent complexity of LCSS is quadratic, similar to LCS. In contrast, we provide a linear-time approximation for LCSS. Finally, for the multi-string variant, unlike both problems, we design a quadratic-time algorithm, uncovering deeper structural properties of the problem. By studying the complexity of the LCSS problem, we aim to gain some understanding of what influences whether a variant of the LCS problem behaves more like the standard LCS or like LCStr. Our findings suggest that hybrid constraints can create computational "sweet spots," where problems become more tractable than their pure counterparts. This opens a broader research direction in constraint-mediated algorithm design. Beyond LCSS itself, our work highlights unexpected connections between subsequence and substring constraints, advancing the theoretical understanding of string problems and laying the foundation for new algorithmic techniques and complexity-theoretic insights in the rich space between classical string comparison paradigms.

Cite as

Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom. Exploring the Gap Between LCS and LCStr. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{golan_et_al:LIPIcs.CPM.2026.27,
  author =	{Golan, Shay and Kraus, Matan and Porat, Ely and Shalom, B. Riva},
  title =	{{Exploring the Gap Between LCS and LCStr}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{27:1--27:21},
  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.2026.27},
  URN =		{urn:nbn:de:0030-drops-259535},
  doi =		{10.4230/LIPIcs.CPM.2026.27},
  annote =	{Keywords: Longest Common Subsequence, Longest Common Substring, Conditional Lower Bound}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.10

Packing Compact Subgraphs with Applications to Districting

Authors: Ho-Lin Chen, Po-Yu Chou, Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and that satisfy additional composition requirements, such as a minimum population/weight threshold or balanced weight types (e.g., political affiliations). We aim to maximize coverage by disjoint districts that meet these requirements. In this work, we present new results that substantially improve the previously known bounds on balanced star districts for planar and minor-free graphs [Prathamesh Dharangutte et al., 2025]. In particular, we improve the approximation factor from O(log n) to O(1) for packing balanced star districts using the exact same algorithm, but with a refined analysis. We also extend the results beyond planar graphs to minor-free graphs and an even broader family of graphs of bounded expansion. Additionally, we obtain an O(1) approximation for packing radius-k districts (with a constant k) in planar and apex-minor-free graphs. In order to get a (1+ε) approximation on the max coverage, we show that this can be achieved if we allow a slight relaxation of the balancedness parameters (by a factor that can be made arbitrarily close to 1), for bounded radius-k districts on planar and apex-minor-free graphs. We show that all of these results can also be obtained if we enforce a minimum weight threshold for each district as the composition requirement, rather than balancedness. We present various results on hardness and hardness of approximation for this variant, by graph and district types.

Cite as

Ho-Lin Chen, Po-Yu Chou, Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu. Packing Compact Subgraphs with Applications to Districting. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 10:1-10:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.FORC.2026.10,
  author =	{Chen, Ho-Lin and Chou, Po-Yu and Dharangutte, Prathamesh and Gao, Jie and Huang, Shang-En and Yu, Fang-Yi},
  title =	{{Packing Compact Subgraphs with Applications to Districting}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{10:1--10:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.10},
  URN =		{urn:nbn:de:0030-drops-259820},
  doi =		{10.4230/LIPIcs.FORC.2026.10},
  annote =	{Keywords: Approximation algorithms, algorithmic fairness}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.9

Intersection Patterns of Set Systems on Manifolds with Slowly Growing Homological Shatter Functions

Authors: Sergey Avvakumov, Marguerite Bin, and Xavier Goaoc

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

A theorem of Matoušek asserts that for any k ≥ 2, any set system whose shatter function is o(n^k) enjoys a fractional Helly theorem of order k: in the k-wise intersection hypergraph, positive density implies a linear-size clique. Kalai and Meshulam conjectured a generalization of that phenomenon to homological shatter functions. It was verified for set systems with bounded homological shatter functions and whose ground set has a forbidden homological minor (which includes ℝ^d by a homological analogue of the van Kampen-Flores theorem). We present two contributions to this line of research: - We study homological minors in certain manifolds (possibly with boundary), for which we prove analogues of the van Kampen-Flores theorem and of the Hanani-Tutte theorem. - We introduce graded analogues of the Radon and Helly numbers of set systems and relate their growth rate to the original parameters. This allows to extend the verification of the Kalai-Meshulam conjecture to sufficiently slowly growing homological shatter functions.

Cite as

Sergey Avvakumov, Marguerite Bin, and Xavier Goaoc. Intersection Patterns of Set Systems on Manifolds with Slowly Growing Homological Shatter Functions. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{avvakumov_et_al:LIPIcs.SoCG.2026.9,
  author =	{Avvakumov, Sergey and Bin, Marguerite and Goaoc, Xavier},
  title =	{{Intersection Patterns of Set Systems on Manifolds with Slowly Growing Homological Shatter Functions}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.9},
  URN =		{urn:nbn:de:0030-drops-258152},
  doi =		{10.4230/LIPIcs.SoCG.2026.9},
  annote =	{Keywords: Fractional Helly theorem, homological minor, combinatorial convexity}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.42

Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

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

Abstract

Twin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes. Despite its algorithmic importance, computing twin-width remains poorly understood: even recognizing graphs of twin-width at most four is NP-hard, and no fixed-parameter approximations parameterized by twin-width itself are known. A recent approach towards breaking this barrier focuses on first developing fixed-parameter algorithms for computing or approximating twin-width under parameterizations distinct from twin-width. Our first result establishes that approximating twin-width is fixed-parameter tractable when parameterized by treedepth, thereby breaking the long-standing barrier that all previous tractable parameterizations were based on deletion distance. The proof proceeds via oriented twin-width, yielding the first constructive evidence that this variant may be easier to handle algorithmically. As our second main result, we show that computing twin-width exactly is fixed-parameter tractable with respect to vertex integrity. This constitutes the first non-trivial parameterized algorithm for computing optimal contraction sequences.

Cite as

Robert Ganian and Mathis Rocton. Computing Twin-Width via Treedepth and Vertex Integrity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  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.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}

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.2026.64

One-Clock Synthesis Problems

Authors: Sławomir Lasota, Mathieu Lehaut, Julie Parreaux, and Radosław Piórkowski

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

Abstract

We study a generalisation of Büchi-Landweber games to the timed setting. The winning condition is specified by a non-deterministic timed automaton, and one of the players can elapse time. We perform a systematic study of synthesis problems in all variants of timed games, depending on which player’s winning condition is specified, and which player’s strategy (or controller, a finite-memory strategy) is sought. As our main result we prove ubiquitous undecidability in all the variants, both for strategy and controller synthesis, already for winning conditions specified by one-clock automata. This strengthens and generalises previously known undecidability results. We also fully characterise those cases where finite memory is sufficient to win, namely existence of a strategy implies existence of a controller. All our results are stated in the timed setting, while analogous results hold in the data setting where one-clock automata are replaced by one-register ones.

Cite as

Sławomir Lasota, Mathieu Lehaut, Julie Parreaux, and Radosław Piórkowski. One-Clock Synthesis Problems. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 64:1-64:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lasota_et_al:LIPIcs.STACS.2026.64,
  author =	{Lasota, S{\l}awomir and Lehaut, Mathieu and Parreaux, Julie and Pi\'{o}rkowski, Rados{\l}aw},
  title =	{{One-Clock Synthesis Problems}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{64:1--64:21},
  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.2026.64},
  URN =		{urn:nbn:de:0030-drops-255533},
  doi =		{10.4230/LIPIcs.STACS.2026.64},
  annote =	{Keywords: timed automata, register automata, B\"{u}chi-Landweber games, Church synthesis problem, reactive synthesis problem}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.68

Dynamic Pattern Matching with Wildcards

Authors: Arshia Ataee Naeini, Amir-Parsa Mobed, Masoud Seddighin, and Saeed Seddighin

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

Abstract

We study the fully dynamic pattern matching problem where the pattern may contain up to k wildcard symbols, each matching any symbol of the alphabet. Both the text and the pattern are subject to updates (insert, delete, change). We design an algorithm with 𝒪(n log² n) preprocessing and update/query time 𝒪̃(kn^{k/{k+1}} + k² log n). The bound is truly sublinear for a constant k, and sublinear when k = o(log n). We further complement our results with a conditional lower bound: assuming subquadratic preprocessing time, achieving truly sublinear update time for the case k = Ω(log n) would contradict the Strong Exponential Time Hypothesis (SETH). Finally, we develop sublinear algorithms for two special cases: - If the pattern contains w non-wildcard symbols, we give an algorithm with preprocessing time 𝒪(nw) and update time 𝒪(w + log n), which is truly sublinear whenever w is truly sublinear. - Using FFT technique combined with block decomposition, we design a deterministic truly sublinear algorithm with preprocessing time 𝒪(n^{1.8}) and update time 𝒪(n^{0.8} log n) for the case that there are at most two non-wildcards.

Cite as

Arshia Ataee Naeini, Amir-Parsa Mobed, Masoud Seddighin, and Saeed Seddighin. Dynamic Pattern Matching with Wildcards. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{naeini_et_al:LIPIcs.STACS.2026.68,
  author =	{Naeini, Arshia Ataee and Mobed, Amir-Parsa and Seddighin, Masoud and Seddighin, Saeed},
  title =	{{Dynamic Pattern Matching with Wildcards}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{68:1--68:20},
  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.2026.68},
  URN =		{urn:nbn:de:0030-drops-255579},
  doi =		{10.4230/LIPIcs.STACS.2026.68},
  annote =	{Keywords: pattern matching, wildcards, dynamic algorithms, string algorithms, data structures}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.53

Maximum Reachability Orientation of Mixed Graphs

Authors: Florian Hörsch

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

Abstract

We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph D, we use P(D) for the set of ordered pairs of distinct vertices in V(D) and we define κ_D:P(D) → {0,1} by κ_D(u,v) = 1 if v is reachable from u in D, and κ_D(u,v) = 0, otherwise. We use R(D) = ∑_{(u,v) ∈ P(D)}κ_D(u,v). Now, given a mixed graph G, we aim to find an orientation x⃑{G} of G that maximizes R(x⃑{G}). Hakimi, Schmeichel, and Young proved that the problem can be solved in polynomial time when restricted to undirected inputs. They inquired about the complexity in mixed graphs. We answer this question by showing that this problem is NP-hard, and, moreover, APX-hard. We then develop a finer understanding of how quickly the problem becomes difficult when going from undirected to mixed graphs. To this end, we consider the parameterized complexity of the problem with respect to the number k of preoriented arcs of G, a poorly studied form of parameterization. We show that the problem can be solved in time n^{O(k)} and that a (1-ε)-approximation can be computed in time f(k,ε)n^{O(1)} for any ε > 0.

Cite as

Florian Hörsch. Maximum Reachability Orientation of Mixed Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 53:1-53:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{horsch:LIPIcs.STACS.2026.53,
  author =	{H\"{o}rsch, Florian},
  title =	{{Maximum Reachability Orientation of Mixed Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{53:1--53:17},
  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.2026.53},
  URN =		{urn:nbn:de:0030-drops-255421},
  doi =		{10.4230/LIPIcs.STACS.2026.53},
  annote =	{Keywords: orientations, mixed graphs, reachability, parameterized complexity, approximation}
}

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