16 Search Results for "Straubing, Howard"

Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2026.1
Query Languages for Machine-Learning Models (Invited Talk)

Authors: Martin Grohe

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

Abstract
In my invited talk and this accompanying paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Grädel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.
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Martin Grohe. Query Languages for Machine-Learning Models (Invited Talk). In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grohe:LIPIcs.STACS.2026.1,
  author =	{Grohe, Martin},
  title =	{{Query Languages for Machine-Learning Models}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{1:1--1:18},
  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.2026.1},
  URN =		{urn:nbn:de:0030-drops-254904},
  doi =		{10.4230/LIPIcs.STACS.2026.1},
  annote =	{Keywords: Expressive power of query languages, fixed-point logics, weighted structures, neural networks, explainable AI}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.41
On the Complexity of Computing Strahler Numbers

Authors: Moses Ganardi and Markus Lohrey

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

Abstract
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform NC¹. For several variants, where the binary tree is given by a pointer structure or in a succinct form by a directed acyclic graph or a tree straight-line program, the complexity of computing the Strahler number is determined as well. The problem, whether a given context-free grammar in Chomsky normal form produces a derivation tree (resp., an acyclic derivation tree), whose Strahler number is at least a given number k is shown to be P-complete (resp., PSPACE-complete).
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Moses Ganardi and Markus Lohrey. On the Complexity of Computing Strahler Numbers. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 41:1-41:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2026.41,
  author =	{Ganardi, Moses and Lohrey, Markus},
  title =	{{On the Complexity of Computing Strahler Numbers}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{41:1--41:22},
  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.2026.41},
  URN =		{urn:nbn:de:0030-drops-255301},
  doi =		{10.4230/LIPIcs.STACS.2026.41},
  annote =	{Keywords: Strahler number, circuit complexity classes, context-free grammars}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.9
Algebraic Characterizations of Classes of Regular Languages in DynFO

Authors: Corentin Barloy, Felix Tschirbs, Nils Vortmeier, and Thomas Zeume

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

Abstract
This paper explores the fine-grained structure of classes of regular languages maintainable in fragments of first-order logic within the dynamic descriptive complexity framework of Patnaik and Immerman. A result by Hesse states that the class of regular languages is maintainable by first-order formulas even if only unary auxiliary relations can be used. Another result by Gelade, Marquardt, and Schwentick states that the class of regular languages coincides with the class of languages maintainable by quantifier-free formulas with binary auxiliary relations. We refine Hesse’s result and show that with unary auxiliary data ∃^*∀^*-formulas can maintain all regular languages. We then obtain precise algebraic characterizations of the classes of languages maintainable with quantifier-free formulas and positive ∃^*-formulas in the presence of unary auxiliary relations.
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Corentin Barloy, Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Algebraic Characterizations of Classes of Regular Languages in DynFO. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barloy_et_al:LIPIcs.STACS.2026.9,
  author =	{Barloy, Corentin and Tschirbs, Felix and Vortmeier, Nils and Zeume, Thomas},
  title =	{{Algebraic Characterizations of Classes of Regular Languages in DynFO}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{9:1--9:19},
  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.2026.9},
  URN =		{urn:nbn:de:0030-drops-254986},
  doi =		{10.4230/LIPIcs.STACS.2026.9},
  annote =	{Keywords: Dynamic descriptive complexity, formal languages, monoid theory}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.27
Uniformity Within Parameterized Circuit Classes

Authors: Steef Hegeman, Jan Martens, and Alfons Laarman

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We study uniformity conditions for parameterized Boolean circuit families. Uniformity conditions require that the infinitely many circuits in a circuit family are in some sense easy to construct from one shared description. For shallow circuit families, logtime-uniformity is often desired but quite technical to prove. Despite that, proving it is often left as an exercise for the reader - even for recently introduced classes in parameterized circuit complexity, where uniformity conditions have not yet been explicitly studied. We formally define parameterized versions of linear-uniformity, logtime-uniformity, and FO-uniformity, and prove that these result in equivalent complexity classes when imposed on para-AC⁰ and para-AC^{0↑}. Overall, we provide a convenient way to verify uniformity for shallow parameterized circuit classes, and thereby substantiate claims of uniformity in the literature.
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Steef Hegeman, Jan Martens, and Alfons Laarman. Uniformity Within Parameterized Circuit Classes. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hegeman_et_al:LIPIcs.IPEC.2025.27,
  author =	{Hegeman, Steef and Martens, Jan and Laarman, Alfons},
  title =	{{Uniformity Within Parameterized Circuit Classes}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.27},
  URN =		{urn:nbn:de:0030-drops-251598},
  doi =		{10.4230/LIPIcs.IPEC.2025.27},
  annote =	{Keywords: Parameterized complexity, circuit complexity, uniformity, descriptive complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.26
Characterizing NC¹ with Typed Monoids

Authors: Anuj Dawar and Aidan T. Evans

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

Abstract
Krebs et al. (2007) gave a characterization of the complexity class TC⁰ as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to infinite monoids and hence characterize classes beyond the regular languages. We advance this line of work beyond TC⁰ by giving a characterization of NC¹. This is obtained by first showing that NC¹ can be defined as the languages expressible in an extension of first-order logic using only unary quantifiers over regular languages. The expressibility result is a consequence of a general result showing that finite monoid multiplication quantifiers of higher dimension can be replaced with unary quantifiers in the context of interpretations over strings, which also answers a question of Lautemann et al. (2001). We estblish this collapse result for a much more general class of interpretations using results on interpretations due to Bojańczyk et al. (2019), which may be of independent interest.
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Anuj Dawar and Aidan T. Evans. Characterizing NC¹ with Typed Monoids. 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. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dawar_et_al:LIPIcs.FSTTCS.2025.26,
  author =	{Dawar, Anuj and Evans, Aidan T.},
  title =	{{Characterizing NC¹ with Typed Monoids}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{26:1--26:19},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-251070},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.26},
  annote =	{Keywords: algebraic automata theory, circuit complexity, descriptive complexity, typed monoids, semigroups, generalized quantifiers}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.8
Dynamic Membership for Regular Tree Languages

Authors: Antoine Amarilli, Corentin Barloy, Louis Jachiet, and Charles Paperman

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

Abstract
We study the dynamic membership problem for regular tree languages under relabeling updates: we fix an alphabet Σ and a regular tree language L over Σ (expressed, e.g., as a tree automaton), we are given a tree T with labels in Σ, and we must maintain the information of whether the tree T belongs to L while handling relabeling updates that change the labels of individual nodes in T. Our first contribution is to show that this problem admits an O(log n / log log n) algorithm for any fixed regular tree language, improving over known O(log n) algorithms. This generalizes the known O(log n / log log n) upper bound over words, and it matches the lower bound of Ω(log n / log log n) from dynamic membership to some word languages and from the existential marked ancestor problem. Our second contribution is to introduce a class of regular languages, dubbed almost-commutative tree languages, and show that dynamic membership to such languages under relabeling updates can be decided in constant time per update. Almost-commutative languages generalize both commutative languages and finite languages: they are the analogue for trees of the ZG languages enjoying constant-time dynamic membership over words. Our main technical contribution is to show that this class is conditionally optimal when we assume that the alphabet features a neutral letter, i.e., a letter that has no effect on membership to the language. More precisely, we show that any regular tree language with a neutral letter which is not almost-commutative cannot be maintained in constant time under the assumption that the prefix-U1 problem from [Antoine Amarilli et al., 2021] also does not admit a constant-time algorithm.
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Antoine Amarilli, Corentin Barloy, Louis Jachiet, and Charles Paperman. Dynamic Membership for Regular Tree Languages. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.MFCS.2025.8,
  author =	{Amarilli, Antoine and Barloy, Corentin and Jachiet, Louis and Paperman, Charles},
  title =	{{Dynamic Membership for Regular Tree Languages}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{8:1--8:18},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-241155},
  doi =		{10.4230/LIPIcs.MFCS.2025.8},
  annote =	{Keywords: automaton, dynamic membership, incremental maintenance, forest algebra}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.5
Characterizations of Fragments of Temporal Logic over Mazurkiewicz Traces

Authors: Bharat Adsul, Paul Gastin, and Shantanu Kulkarni

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

Abstract
We study fragments of temporal logics over Mazurkiewicz traces which are well known and established partial-order models of concurrent behaviours. We focus on concurrent versions of "strict past" and "strict future" modalities. Over words, the corresponding fragments have been shown to coincide with natural algebraic conditions on the recognizing monoids. We provide non-trivial generalizations of these classical results to traces. We exploit the local nature of the temporal modalities and obtain modular translations of specifications into asynchronous automata. More specifically, we provide novel characterizations of these fragments via local cascade products of a very simple two-state asynchronous automaton operating on a single process.
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Bharat Adsul, Paul Gastin, and Shantanu Kulkarni. Characterizations of Fragments of Temporal Logic over Mazurkiewicz Traces. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adsul_et_al:LIPIcs.CONCUR.2025.5,
  author =	{Adsul, Bharat and Gastin, Paul and Kulkarni, Shantanu},
  title =	{{Characterizations of Fragments of Temporal Logic over Mazurkiewicz Traces}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{5:1--5:20},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-239551},
  doi =		{10.4230/LIPIcs.CONCUR.2025.5},
  annote =	{Keywords: Mazurkiewicz traces, temporal logics, asynchronous automata, cascade product, Green’s relations, algebraic automata theory}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.161
Nonuniform Deterministic Finite Automata over Finite Algebraic Structures

Authors: Paweł M. Idziak, Piotr Kawałek, and Jacek Krzaczkowski

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

Abstract
Nonuniform deterministic finite automata (NUDFA) over monoids were invented by Barrington in [Barrington, 1985] to study boundaries of nonuniform constant-memory computation. Later, results on these automata helped to identify interesting classes of groups for which equation satisfiability problem (PolSat) is solvable in (probabilistic) polynomial time [Mikael Goldmann and Alexander Russell, 2002; Idziak et al., 2022]. Based on these results, we present a full characterization of groups, for which the identity checking problem (called PolEqv) has a probabilistic polynomial-time algorithm. We also go beyond groups, and propose how to generalise the notion of NUDFA to arbitrary finite algebraic structures. We study satisfiability of these automata in this more general setting. As a consequence, we present a full description of finite algebras from congruence modular varieties for which testing circuit equivalence CEqv can be solved by a probabilistic polynomial-time procedure. In our proofs we use two computational complexity assumptions: randomized Expotential Time Hypothesis and Constant Degree Hypothesis.
Cite as

Paweł M. Idziak, Piotr Kawałek, and Jacek Krzaczkowski. Nonuniform Deterministic Finite Automata over Finite Algebraic Structures. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 161:1-161:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{idziak_et_al:LIPIcs.ICALP.2025.161,
  author =	{Idziak, Pawe{\l} M. and Kawa{\l}ek, Piotr and Krzaczkowski, Jacek},
  title =	{{Nonuniform Deterministic Finite Automata over Finite Algebraic Structures}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{161:1--161:14},
  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.2025.161},
  URN =		{urn:nbn:de:0030-drops-235386},
  doi =		{10.4230/LIPIcs.ICALP.2025.161},
  annote =	{Keywords: program satisfiability, circuit equivalence, identity checking}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.162
Positive and Monotone Fragments of FO and LTL

Authors: Simon Iosti, Denis Kuperberg, and Quentin Moreau

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

Abstract
We study the positive logic FO^+ on finite words, and its fragments, pursuing and refining the work initiated in [Denis Kuperberg, 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO^+ is equivalent to LTL^+, and its two-variable fragment FO^{2+} with (resp. without) successor available is equivalent to UTL^+ with (resp. without) the "next" operator X available. This shows that despite previous negative results, the class of FO^+-definable languages exhibits some form of robustness. We then exhibit an example of an FO-definable monotone language on one predicate, that is not FO^+-definable, refining the example from [Denis Kuperberg, 2023] with 3 predicates. Moreover, we show that such a counter-example cannot be FO²-definable. Finally, we provide a new example distinguishing the positive and monotone versions of FO² without quantifier alternation. This does not rely on a variant of the previously known counter-example, and witnesses a new phenomenon.
Cite as

Simon Iosti, Denis Kuperberg, and Quentin Moreau. Positive and Monotone Fragments of FO and LTL. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 162:1-162:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{iosti_et_al:LIPIcs.ICALP.2025.162,
  author =	{Iosti, Simon and Kuperberg, Denis and Moreau, Quentin},
  title =	{{Positive and Monotone Fragments of FO and LTL}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{162:1--162:17},
  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.2025.162},
  URN =		{urn:nbn:de:0030-drops-235398},
  doi =		{10.4230/LIPIcs.ICALP.2025.162},
  annote =	{Keywords: Positive logic, LTL, separation, first-order, monotone}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.31
On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators

Authors: Alessandro Artale, Anton Gnatenko, Vladislav Ryzhikov, and Michael Zakharyaschev

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Our concern is the data complexity of answering linear monadic datalog queries whose atoms in the rule bodies can be prefixed by operators of linear temporal logic LTL. We first observe that, for data complexity, answering any connected query with operators ○/○- (at the next/previous moment) is either in AC⁰, or in ACC⁰\AC⁰, or NC¹-complete, or L-hard and in NL. Then we show that the problem of deciding L-hardness of answering such queries is PSpace-complete, while checking membership in the classes AC⁰ and ACC⁰ as well as NC¹-completeness can be done in ExpSpace. Finally, we prove that membership in AC⁰ or in ACC⁰, NC¹-completeness, and L-hardness are undecidable for queries with operators ◇/◇- (sometime in the future/past) provided that NC¹ ≠ NL and L ≠ NL.
Cite as

Alessandro Artale, Anton Gnatenko, Vladislav Ryzhikov, and Michael Zakharyaschev. On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{artale_et_al:LIPIcs.ICDT.2025.31,
  author =	{Artale, Alessandro and Gnatenko, Anton and Ryzhikov, Vladislav and Zakharyaschev, Michael},
  title =	{{On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.31},
  URN =		{urn:nbn:de:0030-drops-229723},
  doi =		{10.4230/LIPIcs.ICDT.2025.31},
  annote =	{Keywords: Linear monadic datalog, linear temporal logic, data complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.66
The Hardness of Decision Tree Complexity

Authors: Bruno Loff and Alexey Milovanov

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Let f be a Boolean function given as either a truth table or a circuit. How difficult is it to find the decision tree complexity, also known as deterministic query complexity, of f in both cases? We prove that this problem is NC¹-hard and PSPACE-hard, respectively. The second bound is tight, and the first bound is close to being tight.
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Bruno Loff and Alexey Milovanov. The Hardness of Decision Tree Complexity. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{loff_et_al:LIPIcs.STACS.2025.66,
  author =	{Loff, Bruno and Milovanov, Alexey},
  title =	{{The Hardness of Decision Tree Complexity}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{66:1--66:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.66},
  URN =		{urn:nbn:de:0030-drops-228913},
  doi =		{10.4230/LIPIcs.STACS.2025.66},
  annote =	{Keywords: Decision tree, Log-depth circuits}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.58
Violating Constant Degree Hypothesis Requires Breaking Symmetry

Authors: Piotr Kawałek and Armin Weiß

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
The Constant Degree Hypothesis was introduced by Barrington et. al. [David A. Mix Barrington et al., 1990] to study some extensions of q-groups by nilpotent groups and the power of these groups in a computation model called NuDFA (non-uniform DFA). In its simplest formulation, it establishes exponential lower bounds for MOD_q∘MOD_m∘AND_d circuits computing AND of unbounded arity n (for constant integers d,m and a prime q). While it has been proved in some special cases (including d = 1), it remains wide open in its general form for over 30 years. In this paper we prove that the hypothesis holds when we restrict our attention to symmetric circuits with m being a prime. While we build upon techniques by Grolmusz and Tardos [Vince Grolmusz and Gábor Tardos, 2000], we have to prove a new symmetric version of their Degree Decreasing Lemma and use it to simplify circuits in a symmetry-preserving way. Moreover, to establish the result, we perform a careful analysis of automorphism groups of MOD_m∘AND_d subcircuits and study the periodic behaviour of the computed functions. Our methods also yield lower bounds when d is treated as a function of n. Finally, we present a construction of symmetric MOD_q∘MOD_m∘AND_d circuits that almost matches our lower bound and conclude that a symmetric function f can be computed by symmetric MOD_q∘MOD_p∘AND_d circuits of quasipolynomial size if and only if f has periods of polylogarithmic length of the form p^k q^𝓁.
Cite as

Piotr Kawałek and Armin Weiß. Violating Constant Degree Hypothesis Requires Breaking Symmetry. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 58:1-58:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kawalek_et_al:LIPIcs.STACS.2025.58,
  author =	{Kawa{\l}ek, Piotr and Wei{\ss}, Armin},
  title =	{{Violating Constant Degree Hypothesis Requires Breaking Symmetry}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{58:1--58:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.58},
  URN =		{urn:nbn:de:0030-drops-228837},
  doi =		{10.4230/LIPIcs.STACS.2025.58},
  annote =	{Keywords: Circuit lower bounds, constant degree hypothesis, permutation groups, CC⁰-circuits}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.51
An Algebraic Approach to Vectorial Programs

Authors: Charles Paperman, Sylvain Salvati, and Claire Soyez-Martin

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
Vectorial programming, the combination of SIMD instructions with usual processor instructions, is known to speed-up many standard algorithms. Simple regular languages have benefited from this technology. This paper is a first step towards pushing these benefits further. We take advantage of the inner algebraic structure of regular languages and produce high level representations of efficient vectorial programs that recognize certain classes of regular languages. As a technical ingredient, we establish equivalences between classes of vectorial circuits and logical formalisms, namely unary temporal logic and first order logic. The main result is the construction of compilation procedures that turns syntactic semigroups into vectorial circuits. The circuits we obtain are small in that they improve known upper-bounds on representations of automata within the logical formalisms. The gain is mostly due to a careful sharing of sub-formulas based on algebraic tools.
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Charles Paperman, Sylvain Salvati, and Claire Soyez-Martin. An Algebraic Approach to Vectorial Programs. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 51:1-51:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{paperman_et_al:LIPIcs.STACS.2023.51,
  author =	{Paperman, Charles and Salvati, Sylvain and Soyez-Martin, Claire},
  title =	{{An Algebraic Approach to Vectorial Programs}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{51:1--51:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.51},
  URN =		{urn:nbn:de:0030-drops-177030},
  doi =		{10.4230/LIPIcs.STACS.2023.51},
  annote =	{Keywords: Automata theory, Semigroups, Vectorisation}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.28
An Algebraic Decision Procedure for Two-Variable Logic with a Between Relation

Authors: Andreas Krebs, Kamal Lodaya, Paritosh K. Pandya, and Howard Straubing

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
In earlier work (LICS 2016), the authors introduced two-variable first-order logic supplemented by a binary relation that allows one to say that a letter appears between two positions. We found an effective algebraic criterion that is a necessary condition for definability in this logic, and conjectured that the criterion is also sufficient, although we proved this only in the case of two-letter alphabets. Here we prove the general conjecture. The proof is quite different from the arguments in the earlier work, and required the development of novel techniques concerning factorizations of words. We extend the results to binary relations specifying that a factor appears between two positions.
Cite as

Andreas Krebs, Kamal Lodaya, Paritosh K. Pandya, and Howard Straubing. An Algebraic Decision Procedure for Two-Variable Logic with a Between Relation. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{krebs_et_al:LIPIcs.CSL.2018.28,
  author =	{Krebs, Andreas and Lodaya, Kamal and Pandya, Paritosh K. and Straubing, Howard},
  title =	{{An Algebraic Decision Procedure for Two-Variable Logic with a Between Relation}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.28},
  URN =		{urn:nbn:de:0030-drops-96953},
  doi =		{10.4230/LIPIcs.CSL.2018.28},
  annote =	{Keywords: two-variable logic, finite model theory, algebraic automata theory}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.86
An effective characterization of the alternation hierarchy in two-variable logic

Authors: Andreas Krebs and Howard Straubing

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that two-sided semidirect products with J as the right-hand factor preserve decidability.
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Andreas Krebs and Howard Straubing. An effective characterization of the alternation hierarchy in two-variable logic. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 86-98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{krebs_et_al:LIPIcs.FSTTCS.2012.86,
  author =	{Krebs, Andreas and Straubing, Howard},
  title =	{{An effective characterization of the alternation hierarchy in two-variable logic}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{86--98},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.86},
  URN =		{urn:nbn:de:0030-drops-38501},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.86},
  annote =	{Keywords: FO\underline2, Quantifier Alternation, J, Pseudovarities, Identities}
}
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