14 Search Results for "Ryzhikov, Andrew"

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DOI: 10.4230/TGDK.4.1.2
Temporal Modelling in Cultural Heritage Knowledge Graphs: Use Cases, Requirements, Evaluation, and Decision Support

Authors: Oleksandra Bruns, Jörg Waitelonis, Jeff Z. Pan, and Harald Sack

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract
Our culture, history and world are in constant motion, continuously shaped by the flow of time, evolving narratives, and shifting relationships. Capturing this temporal complexity within cultural heritage (CH) knowledge graphs is essential for preserving the dynamic nature of human heritage. However, standard RDF predicates fail to effectively model the temporal aspects of cultural data, such as changing facts, evolving relationships, and temporal concepts. Over the past two decades, a variety of RDF-based approaches have been proposed to address this limitation, yet guidance is missing on which method best suits specific CH contexts. This paper presents a systematic evaluation of temporal RDF modelling approaches from a CH perspective. Based on an analysis of real-world CH use cases, core temporal requirements are identified that reflect both modelling expressivity and practical concerns. Six prominent approaches - RDF*, tRDF, Named Graphs, Singleton Property, N-ary Relations, and 4D Fluents - are assessed across these requirements. Our findings reveal that no single solution fits all scenarios, but suitable approaches can be selected based on project-specific priorities. To support practitioners, a decision-support tool is introduced to guide them in selecting the most suitable extension for their specific needs. This work provides practical guidance for CH modelling and contributes to the broader development of temporally aware Linked Data.
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Oleksandra Bruns, Jörg Waitelonis, Jeff Z. Pan, and Harald Sack. Temporal Modelling in Cultural Heritage Knowledge Graphs: Use Cases, Requirements, Evaluation, and Decision Support. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 2:1-2:46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{bruns_et_al:TGDK.4.1.2,
  author =	{Bruns, Oleksandra and Waitelonis, J\"{o}rg and Pan, Jeff Z. and Sack, Harald},
  title =	{{Temporal Modelling in Cultural Heritage Knowledge Graphs: Use Cases, Requirements, Evaluation, and Decision Support}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:46},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.2},
  URN =		{urn:nbn:de:0030-drops-256871},
  doi =		{10.4230/TGDK.4.1.2},
  annote =	{Keywords: Temporal Data Representation, RDF Extensions, Cultural Heritage, Knowledge Graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.60
The Asymptotic Size of Finite Irreducible Semigroups of Rational Matrices

Authors: Stefan Kiefer and Andrew Ryzhikov

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

Abstract
We study finite semigroups of n × n matrices with rational entries. Such semigroups provide a rich generalization of transition monoids of unambiguous (and, in particular, deterministic) finite automata. In this paper we determine the maximum size of finite semigroups of rational n × n matrices, with the goal of shedding more light on the structure of such matrix semigroups. While in general such semigroups can be arbitrarily large in terms of n, a classical result of Schützenberger from 1962 implies an upper bound of 2^{𝒪(n² log n)} for irreducible semigroups, i.e., the only subspaces of ℚⁿ that are invariant for all matrices in the semigroup are ℚⁿ and the subspace consisting only of the zero vector. Irreducible matrix semigroups can be viewed as the building blocks of general matrix semigroups, and as such play an important role in mathematics and computer science. From the point of view of automata theory, they generalize strongly connected automata. Using a very different technique from that of Schützenberger, we improve the upper bound on the cardinality to 3^{n²}. This is the main result of the paper. The bound is in some sense tight, as we show that there exists, for every n, a finite irreducible semigroup with 3^{⌊ n²/4 ⌋} rational matrices. Our main result also leads to an improvement of a bound, due to Almeida and Steinberg, on the mortality threshold. The mortality threshold is a number 𝓁 such that if the zero matrix is in the semigroup, then the zero matrix can be written as a product of at most 𝓁 matrices from any subset that generates the semigroup.
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Stefan Kiefer and Andrew Ryzhikov. The Asymptotic Size of Finite Irreducible Semigroups of Rational Matrices. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 60:1-60:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kiefer_et_al:LIPIcs.STACS.2026.60,
  author =	{Kiefer, Stefan and Ryzhikov, Andrew},
  title =	{{The Asymptotic Size of Finite Irreducible Semigroups of Rational Matrices}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{60:1--60:20},
  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.2026.60},
  URN =		{urn:nbn:de:0030-drops-255496},
  doi =		{10.4230/LIPIcs.STACS.2026.60},
  annote =	{Keywords: finite matrix semigroups, irreducible matrix semigroups, matrix mortality, aperiodic semigroups, unambiguous automata, transition monoids}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.24
A Note on the Parameterised Complexity of Coverability in Vector Addition Systems

Authors: Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks

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

Abstract
We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): V ⊆ ℤ^d, an initial configuration s ∈ ℕ^d, and a target configuration t ∈ ℕ^d, decide whether starting from s, one can iteratively add vectors from V to ultimately arrive at a configuration that is larger than or equal to t on every coordinate, while not observing any negative value on any coordinate along the way. We consider two natural parameters for the problem: the dimension d and the size of V, defined as the total bitsize of its encoding. We present several results charting the complexity of those two parameterisations, among which the highlight is that coverability for VAS parameterised by the dimension and with all the numbers in the input encoded in unary is complete for the class XNL under PL-reductions. We also discuss open problems in the topic, most notably the question about fixed-parameter tractability for the parameterisation by the size of V.
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Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks. A Note on the Parameterised Complexity of Coverability in Vector Addition Systems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pilipczuk_et_al:LIPIcs.IPEC.2025.24,
  author =	{Pilipczuk, Micha{\l} and Schmitz, Sylvain and Sinclair-Banks, Henry},
  title =	{{A Note on the Parameterised Complexity of Coverability in Vector Addition Systems}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{24:1--24:19},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-251563},
  doi =		{10.4230/LIPIcs.IPEC.2025.24},
  annote =	{Keywords: vector addition system, Petri net, parameterised complexity, coverability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.62
The Complexity of Reachability Problems in Strongly Connected Finite Automata

Authors: Stefan Kiefer and Andrew Ryzhikov

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

Abstract
Several reachability problems in finite automata, such as completeness of NFAs and synchronisation of total DFAs, correspond to fundamental properties of sets of nonnegative matrices. In particular, the two mentioned properties correspond to matrix mortality and ergodicity, which ask whether there exists a product of the input matrices that is equal to, respectively, the zero matrix and a matrix with a column of strictly positive entries only. The case where the input automaton is strongly connected (that is, the corresponding set of nonnegative matrices is irreducible) frequently appears in applications and often admits better properties than the general case. In this paper, we address the existence of such properties from the computational complexity point of view, and develop a versatile technique to show that several NL-complete problems remain NL-complete in the strongly connected case. In particular, we show that deciding if a binary total DFA is synchronising is NL-complete even if it is promised to be strongly connected, and that deciding completeness of a binary unambiguous NFA with very limited nondeterminism is NL-complete under the same promise.
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Stefan Kiefer and Andrew Ryzhikov. The Complexity of Reachability Problems in Strongly Connected Finite Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 62:1-62:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kiefer_et_al:LIPIcs.MFCS.2025.62,
  author =	{Kiefer, Stefan and Ryzhikov, Andrew},
  title =	{{The Complexity of Reachability Problems in Strongly Connected Finite Automata}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{62:1--62:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.62},
  URN =		{urn:nbn:de:0030-drops-241690},
  doi =		{10.4230/LIPIcs.MFCS.2025.62},
  annote =	{Keywords: unambiguous automata, nonnegative matrices, irreducible matrix sets, strongly connected automata, matrix monoids, mortality, completeness, synchronisation, ergodicity}
}
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.
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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.2025.19
The Complexity of Learning LTL, CTL and ATL Formulas

Authors: Benjamin Bordais, Daniel Neider, and Rajarshi Roy

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

Abstract
We consider the problem of learning temporal logic formulas from examples of system behavior. Learning temporal properties has crystallized as an effective means to explain complex temporal behaviors. Several efficient algorithms have been designed for learning temporal formulas. However, the theoretical understanding of the complexity of the learning decision problems remains largely unexplored. To address this, we study the complexity of the passive learning problems of three prominent temporal logics, Linear Temporal Logic (LTL), Computation Tree Logic (CTL) and Alternating-time Temporal Logic (ATL) and several of their fragments. We show that learning formulas with unbounded occurrences of binary operators is NP-complete for all of these logics. On the other hand, when investigating the complexity of learning formulas with bounded occurrences of binary operators, we exhibit discrepancies between the complexity of learning LTL, CTL and ATL formulas (with a varying number of agents).
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Benjamin Bordais, Daniel Neider, and Rajarshi Roy. The Complexity of Learning LTL, CTL and ATL Formulas. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bordais_et_al:LIPIcs.STACS.2025.19,
  author =	{Bordais, Benjamin and Neider, Daniel and Roy, Rajarshi},
  title =	{{The Complexity of Learning LTL, CTL and ATL Formulas}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{19:1--19:20},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-228441},
  doi =		{10.4230/LIPIcs.STACS.2025.19},
  annote =	{Keywords: Temporal logic, passive learning, complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.61
Efficiently Computing the Minimum Rank of a Matrix in a Monoid of Zero-One Matrices

Authors: Stefan Kiefer and Andrew Ryzhikov

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

Abstract
A zero-one matrix is a matrix with entries from {0, 1}. We study monoids containing only such matrices. A finite set of zero-one matrices generating such a monoid can be seen as the matrix representation of an unambiguous finite automaton, an important generalisation of deterministic finite automata which shares many of their good properties. Let 𝒜 be a finite set of n×n zero-one matrices generating a monoid of zero-one matrices, and m be the cardinality of 𝒜. We study the computational complexity of computing the minimum rank of a matrix in the monoid generated by 𝒜. By using linear-algebraic techniques, we show that this problem is in NC and can be solved in 𝒪(mn⁴) time. We also provide a combinatorial algorithm finding a matrix of minimum rank in 𝒪(n^{2 + ω} + mn⁴) time, where 2 ≤ ω ≤ 2.4 is the matrix multiplication exponent. As a byproduct, we show a very weak version of a generalisation of the Černý conjecture: there always exists a straight line program of size 𝒪(n²) describing a product resulting in a matrix of minimum rank. For the special case corresponding to complete DFAs (that is, for the case where all matrices have exactly one 1 in each row), the minimum rank is the size of the smallest image of the set of states under the action of a word. Our combinatorial algorithm finds a matrix of minimum rank in time 𝒪(n³ + mn²) in this case.
Cite as

Stefan Kiefer and Andrew Ryzhikov. Efficiently Computing the Minimum Rank of a Matrix in a Monoid of Zero-One Matrices. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 61:1-61:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kiefer_et_al:LIPIcs.STACS.2025.61,
  author =	{Kiefer, Stefan and Ryzhikov, Andrew},
  title =	{{Efficiently Computing the Minimum Rank of a Matrix in a Monoid of Zero-One Matrices}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{61:1--61:22},
  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.2025.61},
  URN =		{urn:nbn:de:0030-drops-228867},
  doi =		{10.4230/LIPIcs.STACS.2025.61},
  annote =	{Keywords: matrix monoids, minimum rank, unambiguous automata}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.20
Boundedness of Cost Register Automata over the Integer Min-Plus Semiring

Authors: Andrei Draghici, Radosław Piórkowski, and Andrew Ryzhikov

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

Abstract
Cost register automata (CRAs) are deterministic automata with registers taking values from a fixed semiring. A CRA computes a function from words to values from this semiring. CRAs are tightly related to well-studied weighted automata. Given a CRA, the boundedness problem asks if there exists a natural number N such that for every word, the value of the CRA on this word does not exceed N. This problem is known to be undecidable for the class of linear CRAs over the integer min-plus semiring (ℤ∪{+∞}, min, +), but very little is known about its subclasses. In this paper, we study boundedness of copyless linear CRAs with resets over the integer min-plus semiring. We show that it is decidable for such CRAs with at most two registers. More specifically, we show that it is, respectively, NL-complete and in coNP if the numbers in the input are presented in unary and binary. We also provide complexity results for two classes with an arbitrary number of registers. Namely, we show that for CRAs that use the minimum operation only in the output function, boundedness is PSPACE-complete if transferring values to other registers is allowed, and is coNP-complete otherwise. Finally, for each f_i in the hierarchy of fast-growing functions, we provide a stateless CRA with i registers whose output exceeds N only on runs longer than f_i(N). Our construction yields a non-elementary lower bound already for four registers.
Cite as

Andrei Draghici, Radosław Piórkowski, and Andrew Ryzhikov. Boundedness of Cost Register Automata over the Integer Min-Plus Semiring. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{draghici_et_al:LIPIcs.CSL.2025.20,
  author =	{Draghici, Andrei and Pi\'{o}rkowski, Rados{\l}aw and Ryzhikov, Andrew},
  title =	{{Boundedness of Cost Register Automata over the Integer Min-Plus Semiring}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.20},
  URN =		{urn:nbn:de:0030-drops-227775},
  doi =		{10.4230/LIPIcs.CSL.2025.20},
  annote =	{Keywords: cost register automata, boundedness, decidability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.81
Monoids of Upper Triangular Matrices over the Boolean Semiring

Authors: Andrew Ryzhikov and Petra Wolf

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Given a finite set 𝒜 of square matrices and a square matrix B, all of the same dimension, the membership problem asks if B belongs to the monoid ℳ(𝒜) generated by 𝒜. The rank one problem asks if there is a matrix of rank one in ℳ(𝒜). We study the membership and the rank one problems in the case where all matrices are upper triangular matrices over the Boolean semiring. We characterize the computational complexity of these problems, and identify their PSPACE-complete and NP-complete special cases. We then consider, for a set 𝒜 of matrices from the same class, the problem of finding in ℳ(𝒜) a matrix of minimum rank with no zero rows. We show that the minimum rank of such matrix can be computed in linear time.We also characterize the space complexity of this problem depending on the size of 𝒜, and apply all these results to the ergodicity problem asking if ℳ(𝒜) contains a matrix with a column consisting of all ones. Finally, we show that our results give better upper bounds for the case where each row of every matrix in 𝒜 contains at most one non-zero entry than for the general case.
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Andrew Ryzhikov and Petra Wolf. Monoids of Upper Triangular Matrices over the Boolean Semiring. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 81:1-81:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ryzhikov_et_al:LIPIcs.MFCS.2024.81,
  author =	{Ryzhikov, Andrew and Wolf, Petra},
  title =	{{Monoids of Upper Triangular Matrices over the Boolean Semiring}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{81:1--81:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.81},
  URN =		{urn:nbn:de:0030-drops-206377},
  doi =		{10.4230/LIPIcs.MFCS.2024.81},
  annote =	{Keywords: matrix monoids, membership, rank, ergodicity, partially ordered automata}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.40
Universality and Forall-Exactness of Cost Register Automata with Few Registers

Authors: Laure Daviaud and Andrew Ryzhikov

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
The universality problem asks whether a given finite state automaton accepts all the input words. For quantitative models of automata, where input words are mapped to real values, this is naturally extended to ask whether all the words are mapped to values above (or below) a given threshold. This is known to be undecidable for commonly studied examples such as weighted automata over the positive rational (plus-times) or the integer tropical (min-plus) semirings, or equivalently cost register automata (CRAs) over these semirings. In this paper, we prove that when restricted to CRAs with only three registers, the universality problem is still undecidable, even with additional restrictions for the CRAs to be copyless linear with resets. In contrast, we show that, assuming the unary encoding of updates, the ∀-exact problem (does the CRA output zero on all the words?) for integer min-plus linear CRAs can be decided in polynomial time if the number of registers is constant. Without the restriction on the number of registers this problem is known to be PSPACE-complete.
Cite as

Laure Daviaud and Andrew Ryzhikov. Universality and Forall-Exactness of Cost Register Automata with Few Registers. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{daviaud_et_al:LIPIcs.MFCS.2023.40,
  author =	{Daviaud, Laure and Ryzhikov, Andrew},
  title =	{{Universality and Forall-Exactness of Cost Register Automata with Few Registers}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.40},
  URN =		{urn:nbn:de:0030-drops-185744},
  doi =		{10.4230/LIPIcs.MFCS.2023.40},
  annote =	{Keywords: cost register automata, universality, forall-exact problem, decidability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.12
Synchronizing Strongly Connected Partial DFAs

Authors: Mikhail V. Berlinkov, Robert Ferens, Andrew Ryzhikov, and Marek Szykuła

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We study synchronizing partial DFAs, which extend the classical concept of synchronizing complete DFAs and are a special case of synchronizing unambiguous NFAs. A partial DFA is called synchronizing if it has a word (called a reset word) whose action brings a non-empty subset of states to a unique state and is undefined for all other states. While in the general case the problem of checking whether a partial DFA is synchronizing is PSPACE-complete, we show that in the strongly connected case this problem can be efficiently reduced to the same problem for a complete DFA. Using combinatorial, algebraic, and formal languages methods, we develop techniques that relate main synchronization problems for strongly connected partial DFAs with the same problems for complete DFAs. In particular, this includes the Černý and the rank conjectures, the problem of finding a reset word, and upper bounds on the length of the shortest reset words of literal automata of finite prefix codes. We conclude that solving fundamental synchronization problems is equally hard in both models, as an essential improvement of the results for one model implies an improvement for the other.
Cite as

Mikhail V. Berlinkov, Robert Ferens, Andrew Ryzhikov, and Marek Szykuła. Synchronizing Strongly Connected Partial DFAs. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{berlinkov_et_al:LIPIcs.STACS.2021.12,
  author =	{Berlinkov, Mikhail V. and Ferens, Robert and Ryzhikov, Andrew and Szyku{\l}a, Marek},
  title =	{{Synchronizing Strongly Connected Partial DFAs}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.12},
  URN =		{urn:nbn:de:0030-drops-136579},
  doi =		{10.4230/LIPIcs.STACS.2021.12},
  annote =	{Keywords: \v{C}ern\'{y} conjecture, literal automaton, partial automaton, prefix code, rank conjecture, reset threshold, reset word, synchronizing automaton, synchronizing word}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.54
The Degree of a Finite Set of Words

Authors: Dominique Perrin and Andrew Ryzhikov

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
We generalize the notions of the degree and composition from uniquely decipherable codes to arbitrary finite sets of words. We prove that if X = Y∘Z is a composition of finite sets of words with Y complete, then d(X) = d(Y) ⋅ d(Z), where d(T) is the degree of T. We also show that a finite set is synchronizing if and only if its degree equals one. This is done by considering, for an arbitrary finite set X of words, the transition monoid of an automaton recognizing X^* with multiplicities. We prove a number of results for such monoids, which generalize corresponding results for unambiguous monoids of relations.
Cite as

Dominique Perrin and Andrew Ryzhikov. The Degree of a Finite Set of Words. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{perrin_et_al:LIPIcs.FSTTCS.2020.54,
  author =	{Perrin, Dominique and Ryzhikov, Andrew},
  title =	{{The Degree of a Finite Set of Words}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.54},
  URN =		{urn:nbn:de:0030-drops-132952},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.54},
  annote =	{Keywords: synchronizing set, degree of a set, group of a set, monoid of relations}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.57
Long Alternating Paths Exist

Authors: Wolfgang Mulzer and Pavel Valtr

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
Let P be a set of 2n points in convex position, such that n points are colored red and n points are colored blue. A non-crossing alternating path on P of length 𝓁 is a sequence p₁, … , p_𝓁 of 𝓁 points from P so that (i) all points are pairwise distinct; (ii) any two consecutive points p_i, p_{i+1} have different colors; and (iii) any two segments p_i p_{i+1} and p_j p_{j+1} have disjoint relative interiors, for i ≠ j. We show that there is an absolute constant ε > 0, independent of n and of the coloring, such that P always admits a non-crossing alternating path of length at least (1 + ε)n. The result is obtained through a slightly stronger statement: there always exists a non-crossing bichromatic separated matching on at least (1 + ε)n points of P. This is a properly colored matching whose segments are pairwise disjoint and intersected by common line. For both versions, this is the first improvement of the easily obtained lower bound of n by an additive term linear in n. The best known published upper bounds are asymptotically of order 4n/3+o(n).
Cite as

Wolfgang Mulzer and Pavel Valtr. Long Alternating Paths Exist. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mulzer_et_al:LIPIcs.SoCG.2020.57,
  author =	{Mulzer, Wolfgang and Valtr, Pavel},
  title =	{{Long Alternating Paths Exist}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.57},
  URN =		{urn:nbn:de:0030-drops-122152},
  doi =		{10.4230/LIPIcs.SoCG.2020.57},
  annote =	{Keywords: Non-crossing path, bichromatic point sets}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.21
Finding Short Synchronizing Words for Prefix Codes

Authors: Andrew Ryzhikov and Marek Szykula

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is defined by its literal decoder (whose size is polynomially equivalent to the total length of all words in the code). For the first case for every epsilon > 0 we prove n^(1 - epsilon)-inapproximability for recognizable binary maximal prefix codes, Theta(log n)-inapproximability for finite binary maximal prefix codes and n^(1/2 - epsilon)-inapproximability for finite binary prefix codes. By c-inapproximability here we mean the non-existence of a c-approximation polynomial time algorithm under the assumption P != NP, and by n the number of states of the decoder in the input. For the second case, we propose approximation and exact algorithms and conjecture that for finite maximal prefix codes the problem can be solved in polynomial time. We also study the related problems of finding a shortest mortal and a shortest avoiding word.
Cite as

Andrew Ryzhikov and Marek Szykula. Finding Short Synchronizing Words for Prefix Codes. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ryzhikov_et_al:LIPIcs.MFCS.2018.21,
  author =	{Ryzhikov, Andrew and Szykula, Marek},
  title =	{{Finding Short Synchronizing Words for Prefix Codes}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.21},
  URN =		{urn:nbn:de:0030-drops-96037},
  doi =		{10.4230/LIPIcs.MFCS.2018.21},
  annote =	{Keywords: synchronizing word, mortal word, avoiding word, Huffman decoder, inapproximability}
}
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