3 Search Results for "Widdershoven, Cas"

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.CONCUR.2021.6
Linear-Time Model Checking Branching Processes

Authors: Stefan Kiefer, Pavel Semukhin, and Cas Widdershoven

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
(Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov chains (but not generally Markov decision processes). We study the complexity of model checking branching processes against linear-time omega-regular specifications: is it the case almost surely that every branch of a tree randomly generated by the branching process satisfies the omega-regular specification? The main result is that for LTL specifications this problem is in PSPACE, subsuming classical results for transition systems and Markov chains, respectively. The underlying general model-checking algorithm is based on the automata-theoretic approach, using unambiguous Büchi automata.
Cite as

Stefan Kiefer, Pavel Semukhin, and Cas Widdershoven. Linear-Time Model Checking Branching Processes. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kiefer_et_al:LIPIcs.CONCUR.2021.6,
  author =	{Kiefer, Stefan and Semukhin, Pavel and Widdershoven, Cas},
  title =	{{Linear-Time Model Checking Branching Processes}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.6},
  URN =		{urn:nbn:de:0030-drops-143834},
  doi =		{10.4230/LIPIcs.CONCUR.2021.6},
  annote =	{Keywords: model checking, Markov chains, branching processes, automata, computational complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.82
Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques

Authors: Stefan Kiefer and Cas Widdershoven

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We introduce a novel technique to analyse unambiguous Büchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant spectral radius. This method can replace a combinatorial procedure that dominates the computational complexity of the existing procedure by Baier et al. We analyse the complexity in detail, showing that, in terms of the set Q of states of the automaton, the new algorithm runs in time O(|Q|^4), improving on an efficient implementation of the combinatorial algorithm by a factor of |Q|.
Cite as

Stefan Kiefer and Cas Widdershoven. Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 82:1-82:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kiefer_et_al:LIPIcs.MFCS.2019.82,
  author =	{Kiefer, Stefan and Widdershoven, Cas},
  title =	{{Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{82:1--82:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar 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.MFCS.2019.82},
  URN =		{urn:nbn:de:0030-drops-110269},
  doi =		{10.4230/LIPIcs.MFCS.2019.82},
  annote =	{Keywords: Algorithms, Automata, Markov Chains, Matrix Semigroups}
}
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