9 Search Results for "Rigo, Michel"


Document
Linear Time Subsequence and Supersequence Regex Matching

Authors: Antoine Amarilli, Florin Manea, Tina Ringleb, and Markus L. Schmid

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


Abstract
It is well-known that checking whether a given string w matches a given regular expression r can be done in quadratic time O(|w|⋅ |r|) and that this cannot be improved to a truly subquadratic running time of O((|w|⋅ |r|)^{1-ε}) assuming the strong exponential time hypothesis (SETH). We study a different matching paradigm where we ask instead whether w has a subsequence that matches r, and show that regex matching in this sense can be solved in linear time O(|w| + |r|). Further, the same holds if we ask for a supersequence. We show that the quantitative variants where we want to compute a longest or shortest subsequence or supersequence of w that matches r can be solved in O(|w|⋅ |r|), i. e., asymptotically no worse than classical regex matching; and we show that O(|w| + |r|) is conditionally not possible for these problems. We also investigate these questions with respect to other natural string relations like the infix, prefix, left-extension or extension relation instead of the subsequence and supersequence relation. We further study the complexity of the universal problem where we ask if all subsequences (or supersequences, infixes, prefixes, left-extensions or extensions) of an input string satisfy a given regular expression.

Cite as

Antoine Amarilli, Florin Manea, Tina Ringleb, and Markus L. Schmid. Linear Time Subsequence and Supersequence Regex Matching. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{amarilli_et_al:LIPIcs.MFCS.2025.9,
  author =	{Amarilli, Antoine and Manea, Florin and Ringleb, Tina and Schmid, Markus L.},
  title =	{{Linear Time Subsequence and Supersequence Regex Matching}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{9:1--9:19},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-241162},
  doi =		{10.4230/LIPIcs.MFCS.2025.9},
  annote =	{Keywords: subsequence, supersequence, regular language, regular expression, automata}
}
Document
Morphisms and BWT-Run Sensitivity

Authors: Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina

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


Abstract
We study how the application of morphisms affects the number r of equal-letter runs in the Burrows–Wheeler Transform (BWT). This parameter has emerged as a key repetitiveness measure in compressed indexing. We focus on the notion of BWT-run sensitivity after application of morphisms. For binary alphabets, we characterize the class of injective morphisms that preserve the number of BWT-runs up to a bounded additive increase by showing that it coincides with the known class of primitivity-preserving morphisms, which are those that map primitive words to primitive words. We further prove that deciding whether a given binary morphism has bounded BWT-run sensitivity is possible in polynomial time with respect to the total length of the images of the two letters. Additionally, we explore new structural and combinatorial properties of synchronizing and recognizable morphisms. These results establish new connections between BWT-based compressibility, code theory, and symbolic dynamics.

Cite as

Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina. Morphisms and BWT-Run Sensitivity. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 49:1-49:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{fici_et_al:LIPIcs.MFCS.2025.49,
  author =	{Fici, Gabriele and Romana, Giuseppe and Sciortino, Marinella and Urbina, Cristian},
  title =	{{Morphisms and BWT-Run Sensitivity}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{49:1--49:18},
  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.2025.49},
  URN =		{urn:nbn:de:0030-drops-241567},
  doi =		{10.4230/LIPIcs.MFCS.2025.49},
  annote =	{Keywords: Burrows-Wheeler transform, BWT-runs, morphism, pure code, repetitiveness}
}
Document
Games with ω-Automatic Preference Relations

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

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


Abstract
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as ω-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an ω-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of ω-automatic relations and their implications in the existence of equilibria.

Cite as

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. Games with ω-Automatic Preference Relations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{bruyere_et_al:LIPIcs.MFCS.2025.31,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{Games with \omega-Automatic Preference Relations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{31:1--31:19},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-241381},
  doi =		{10.4230/LIPIcs.MFCS.2025.31},
  annote =	{Keywords: Games played on graphs, Nash equilibrium, \omega-automatic relations, \omega-recognizable relations, constrained Nash equilibria existence problem}
}
Document
The Non-Cooperative Rational Synthesis Problem for SPEs and ω-Regular Objectives

Authors: Véronique Bruyère, Jean-François Raskin, Alexis Reynouard, and Marie Van Den Bogaard

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


Abstract
This paper studies the rational synthesis problem for multi-player games played on graphs when rational players are following subgame perfect equilibria. In these games, one player, the system, declares his strategy upfront, and the other players, composing the environment, then rationally respond by playing strategies forming a subgame perfect equilibrium. We study the complexity of the rational synthesis problem when the players have ω-regular objectives encoded as parity objectives. Our algorithm is based on an encoding into a three-player game with imperfect information, showing that the problem is in 2ExpTime. When the number of environment players is fixed, the problem is in ExpTime and is NP- and coNP-hard. Moreover, for a fixed number of players and reachability objectives, we get a polynomial algorithm.

Cite as

Véronique Bruyère, Jean-François Raskin, Alexis Reynouard, and Marie Van Den Bogaard. The Non-Cooperative Rational Synthesis Problem for SPEs and ω-Regular Objectives. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2025.12,
  author =	{Bruy\`{e}re, V\'{e}ronique and Raskin, Jean-Fran\c{c}ois and Reynouard, Alexis and Van Den Bogaard, Marie},
  title =	{{The Non-Cooperative Rational Synthesis Problem for SPEs and \omega-Regular Objectives}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{12:1--12:23},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-239622},
  doi =		{10.4230/LIPIcs.CONCUR.2025.12},
  annote =	{Keywords: non-zero-sum games, subgame perfect equilibria, rational synthesis}
}
Document
BWT and Combinatorics on Words

Authors: Gabriele Fici, Sabrina Mantaci, Antonio Restivo, Giuseppe Romana, Giovanna Rosone, and Marinella Sciortino

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)


Abstract
The Burrows-Wheeler Transform (BWT) is a reversible transformation on words (strings) introduced in 1994 in the context of data compression, which is a permutation of the characters in the word. Its clustering effect, i.e., the remarkable property of grouping identical characters (BWT runs) when they share common contexts, has made it a powerful tool for boosting compression performances and enabling efficient pattern searching in highly repetitive string collections. In this chapter, we analyze the Burrows-Wheeler transform under the combinatorial point of view, and we survey known properties and connections with different aspects of combinatorics on words. In particular, we focus on the properties of words in relation to the number of their BWT runs. The value r, which counts the number of BWT runs, impacts both compression performance and indexing efficiency, and is considered a measure to evaluate the above-mentioned clustering effect and, consequently, the repetitiveness of a word. We give an overview of the results relating r to other combinatorial repetitiveness measures related to the factor complexity. The chapter also explores extremal cases of the clustering effect. Finally, some results on the sensitivity of the measure r are considered, where the effects of combinatorial operations are studied, such as reversal, edits, and the application of morphisms.

Cite as

Gabriele Fici, Sabrina Mantaci, Antonio Restivo, Giuseppe Romana, Giovanna Rosone, and Marinella Sciortino. BWT and Combinatorics on Words. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{fici_et_al:OASIcs.Manzini.1,
  author =	{Fici, Gabriele and Mantaci, Sabrina and Restivo, Antonio and Romana, Giuseppe and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{BWT and Combinatorics on Words}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{1:1--1:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.1},
  URN =		{urn:nbn:de:0030-drops-239090},
  doi =		{10.4230/OASIcs.Manzini.1},
  annote =	{Keywords: Burrows-Wheeler Transform, Combinatorics on Words, Clustering Effect, BWT Runs}
}
Document
Net Occurrences in Fibonacci and Thue-Morse Words

Authors: Peaker Guo and Kaisei Kishi

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)


Abstract
A net occurrence of a repeated string in a text is an occurrence with unique left and right extensions, and the net frequency of the string is the number of its net occurrences in the text. Originally introduced for applications in Natural Language Processing, net frequency has recently gained attention for its algorithmic aspects. Guo et al. [CPM 2024] and Ohlebusch et al. [SPIRE 2024] focus on its computation in the offline setting, while Guo et al. [SPIRE 2024], Inenaga [arXiv 2024], and Mieno and Inenaga [CPM 2025] tackle the online counterpart. Mieno and Inenaga also characterize net occurrences in terms of the minimal unique substrings of the text. Additionally, Guo et al. [CPM 2024] initiate the study of net occurrences in Fibonacci words to establish a lower bound on the asymptotic running time of algorithms. Although there has been notable progress in algorithmic developments and some initial combinatorial insights, the combinatorial aspects of net occurrences have yet to be thoroughly examined. In this work, we make two key contributions. First, we confirm the conjecture that each Fibonacci word contains exactly three net occurrences. Second, we show that each Thue-Morse word contains exactly nine net occurrences. To achieve these results, we introduce the notion of overlapping net occurrence cover, which narrows down the candidate net occurrences in any text. Furthermore, we provide a precise characterization of occurrences of Fibonacci and Thue-Morse words of smaller order, offering structural insights that may have independent interest and potential applications in algorithm analysis and combinatorial properties of these words.

Cite as

Peaker Guo and Kaisei Kishi. Net Occurrences in Fibonacci and Thue-Morse Words. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{guo_et_al:LIPIcs.CPM.2025.16,
  author =	{Guo, Peaker and Kishi, Kaisei},
  title =	{{Net Occurrences in Fibonacci and Thue-Morse Words}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{16:1--16:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.16},
  URN =		{urn:nbn:de:0030-drops-231107},
  doi =		{10.4230/LIPIcs.CPM.2025.16},
  annote =	{Keywords: Fibonacci words, Thue-Morse words, net occurrence, net frequency, factorization}
}
Document
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
On Extended Boundary Sequences of Morphic and Sturmian Words

Authors: Michel Rigo, Manon Stipulanti, and Markus A. Whiteland

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the nth term of the 𝓁-boundary sequence of an infinite word is the finite set of pairs (u,v) of prefixes and suffixes of length 𝓁 appearing in factors uyv of length n+𝓁 (n ≥ 𝓁 ≥ 1). Otherwise stated, for increasing values of n, one looks for all pairs of factors of length 𝓁 separated by n-𝓁 symbols. For the large class of addable numeration systems U, we show that if an infinite word is U-automatic, then the same holds for its 𝓁-boundary sequence. In particular, they are both morphic (or generated by an HD0L system). We also provide examples of numeration systems and U-automatic words with a boundary sequence that is not U-automatic. In the second part of the paper, we study the 𝓁-boundary sequence of a Sturmian word. We show that it is obtained through a sliding block code from the characteristic Sturmian word of the same slope. We also show that it is the image under a morphism of some other characteristic Sturmian word.

Cite as

Michel Rigo, Manon Stipulanti, and Markus A. Whiteland. On Extended Boundary Sequences of Morphic and Sturmian Words. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{rigo_et_al:LIPIcs.MFCS.2022.79,
  author =	{Rigo, Michel and Stipulanti, Manon and Whiteland, Markus A.},
  title =	{{On Extended Boundary Sequences of Morphic and Sturmian Words}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{79:1--79:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.79},
  URN =		{urn:nbn:de:0030-drops-168776},
  doi =		{10.4230/LIPIcs.MFCS.2022.79},
  annote =	{Keywords: Boundary sequences, Sturmian words, Numeration systems, Automata, Graph of addition}
}
Document
An Efficient Algorithm to Decide Periodicity of b-Recognisable Sets Using MSDF Convention

Authors: Bernard Boigelot, Isabelle Mainz, Victor Marsault, and Michel Rigo

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
Given an integer base b>1, a set of integers is represented in base b by a language over {0,1,...,b-1}. The set is said to be b-recognisable if its representation is a regular language. It is known that eventually periodic sets are b-recognisable in every base b, and Cobham's theorem implies the converse: no other set is b-recognisable in every base b. We are interested in deciding whether a b-recognisable set of integers (given as a finite automaton) is eventually periodic. Honkala showed that this problem is decidable in 1986 and recent developments give efficient decision algorithms. However, they only work when the integers are written with the least significant digit first. In this work, we consider the natural order of digits (Most Significant Digit First) and give a quasi-linear algorithm to solve the problem in this case.

Cite as

Bernard Boigelot, Isabelle Mainz, Victor Marsault, and Michel Rigo. An Efficient Algorithm to Decide Periodicity of b-Recognisable Sets Using MSDF Convention. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 118:1-118:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{boigelot_et_al:LIPIcs.ICALP.2017.118,
  author =	{Boigelot, Bernard and Mainz, Isabelle and Marsault, Victor and Rigo, Michel},
  title =	{{An Efficient Algorithm to Decide Periodicity of b-Recognisable Sets Using MSDF Convention}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{118:1--118:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.118},
  URN =		{urn:nbn:de:0030-drops-74317},
  doi =		{10.4230/LIPIcs.ICALP.2017.118},
  annote =	{Keywords: integer-base systems, automata, recognisable sets, periodic sets}
}
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