24 Search Results for "Pin, Jean-Éric"

Document
DOI: 10.4230/OASIcs.ATMOS.2024.13
A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance

Authors: Felix Prause and Ralf Borndörfer

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

Abstract
We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach.
Cite as

Felix Prause and Ralf Borndörfer. A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{prause_et_al:OASIcs.ATMOS.2024.13,
  author =	{Prause, Felix and Bornd\"{o}rfer, Ralf},
  title =	{{A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{13:1--13:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.13},
  URN =		{urn:nbn:de:0030-drops-212013},
  doi =		{10.4230/OASIcs.ATMOS.2024.13},
  annote =	{Keywords: Rolling stock rotation planning, Predictive maintenance, Rolling horizon approach, Bayesian inference, Local neighborhood search}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.18
Weighted Basic Parallel Processes and Combinatorial Enumeration

Authors: Lorenzo Clemente

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study weighted basic parallel processes (WBPP), a nonlinear recursive generalisation of weighted finite automata inspired from process algebra and Petri net theory. Our main result is an algorithm of 2-EXPSPACE complexity for the WBPP equivalence problem. While (unweighted) BPP language equivalence is undecidable, we can use this algorithm to decide multiplicity equivalence of BPP and language equivalence of unambiguous BPP, with the same complexity. These are long-standing open problems for the related model of weighted context-free grammars. Our second contribution is a connection between WBPP, power series solutions of systems of polynomial differential equations, and combinatorial enumeration. To this end we consider constructible differentially finite power series (CDF), a class of multivariate differentially algebraic series introduced by Bergeron and Reutenauer in order to provide a combinatorial interpretation to differential equations. CDF series generalise rational, algebraic, and a large class of D-finite (holonomic) series, for which no complexity upper bound for equivalence was known. We show that CDF series correspond to commutative WBPP series. As a consequence of our result on WBPP and commutativity, we show that equivalence of CDF power series can be decided with 2-EXPTIME complexity. In order to showcase the CDF equivalence algorithm, we show that CDF power series naturally arise from combinatorial enumeration, namely as the exponential generating series of constructible species of structures. Examples of such species include sequences, binary trees, ordered trees, Cayley trees, set partitions, series-parallel graphs, and many others. As a consequence of this connection, we obtain an algorithm to decide multiplicity equivalence of constructible species, decidability of which was not known before. The complexity analysis is based on effective bounds from algebraic geometry, namely on the length of chains of polynomial ideals constructed by repeated application of finitely many, not necessarily commuting derivations of a multivariate polynomial ring. This is obtained by generalising a result of Novikov and Yakovenko in the case of a single derivation, which is noteworthy since generic bounds on ideal chains are non-primitive recursive in general. On the way, we develop the theory of WBPP series and CDF power series, exposing several of their appealing properties.
Cite as

Lorenzo Clemente. Weighted Basic Parallel Processes and Combinatorial Enumeration. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{clemente:LIPIcs.CONCUR.2024.18,
  author =	{Clemente, Lorenzo},
  title =	{{Weighted Basic Parallel Processes and Combinatorial Enumeration}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.18},
  URN =		{urn:nbn:de:0030-drops-207903},
  doi =		{10.4230/LIPIcs.CONCUR.2024.18},
  annote =	{Keywords: weighted automata, combinatorial enumeration, shuffle, algebraic differential equations, process algebra, basic parallel processes, species of structures}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.21
Reversible Transducers over Infinite Words

Authors: Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to synthesis, where transformation specifications are converted into equivalent transducers. These specifications are presented in a modular way, and composing the resultant machines simulates the full specification. An important result by Dartois et al. [Luc Dartois et al., 2017] shows that composition of two-way transducers enjoy a polynomial composition when the underlying transducer is reversible, that is, if they are both deterministic and co-deterministic. This is a major improvement over general deterministic two-way transducers, for which composition causes a doubly exponential blow-up in the size of the inputs in general. Moreover, they show that reversible two-way transducers have the same expressiveness as deterministic two-way transducers. However, the notion of reversible two-way transducers over infinite words as well as the question of their expressiveness were not studied yet. In this article, we introduce the class of reversible two-way transducers over infinite words and show that they enjoy the same expressive power as deterministic two-way transducers over infinite words. This is done through a non-trivial, effective construction inducing a single exponential blow-up in the set of states. Further, we also prove that composing two reversible two-way transducers over infinite words incurs only a polynomial complexity, thereby providing an efficient procedure for composition of transducers over infinite words.
Cite as

Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna. Reversible Transducers over Infinite Words. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dartois_et_al:LIPIcs.CONCUR.2024.21,
  author =	{Dartois, Luc and Gastin, Paul and Germerie Guizouarn, Lo\"{i}c and Govind, R. and Krishna, Shankaranarayanan},
  title =	{{Reversible Transducers over Infinite Words}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.21},
  URN =		{urn:nbn:de:0030-drops-207932},
  doi =		{10.4230/LIPIcs.CONCUR.2024.21},
  annote =	{Keywords: Transducers, Regular functions, Reversibility, Composition, SSTs}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.22
An Automata-Based Approach for Synchronizable Mailbox Communication

Authors: Romain Delpy, Anca Muscholl, and Grégoire Sutre

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We revisit finite-state communicating systems with round-based communication under mailbox semantics. Mailboxes correspond to one FIFO buffer per process (instead of one buffer per pair of processes in peer-to-peer systems). Round-based communication corresponds to sequences of rounds in which processes can first send messages, then only receive (and receives must be in the same round as their sends). A system is called synchronizable if every execution can be re-scheduled into an equivalent execution that is a sequence of rounds. Previous work mostly considered the setting where rounds have fixed size. Our main contribution shows that the problem whether a mailbox communication system complies with the round-based policy, with no size limitation on rounds, is PSPACE-complete. For this we use a novel automata-based approach, that also allows to determine the precise complexity (PSPACE) of several questions considered in previous literature.
Cite as

Romain Delpy, Anca Muscholl, and Grégoire Sutre. An Automata-Based Approach for Synchronizable Mailbox Communication. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{delpy_et_al:LIPIcs.CONCUR.2024.22,
  author =	{Delpy, Romain and Muscholl, Anca and Sutre, Gr\'{e}goire},
  title =	{{An Automata-Based Approach for Synchronizable Mailbox Communication}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.22},
  URN =		{urn:nbn:de:0030-drops-207947},
  doi =		{10.4230/LIPIcs.CONCUR.2024.22},
  annote =	{Keywords: Concurrent programming, Mailbox communication, Verification}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.29
Strategic Dominance: A New Preorder for Nondeterministic Processes

Authors: Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.
Cite as

Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç. Strategic Dominance: A New Preorder for Nondeterministic Processes. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{henzinger_et_al:LIPIcs.CONCUR.2024.29,
  author =	{Henzinger, Thomas A. and Mazzocchi, Nicolas and Sara\c{c}, N. Ege},
  title =	{{Strategic Dominance: A New Preorder for Nondeterministic Processes}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.29},
  URN =		{urn:nbn:de:0030-drops-208011},
  doi =		{10.4230/LIPIcs.CONCUR.2024.29},
  annote =	{Keywords: quantitative automata, refinement relation, resolver, strategy, history-determinism}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.44
The Freeness Problem for Automaton Semigroups

Authors: Daniele D'Angeli, Emanuele Rodaro, and Jan Philipp Wächter

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

Abstract
We present a new technique to encode Post’s Correspondence Problem into automaton semigroups and monoids. The encoding allows us to precisely control whether there exists a relation in the generated semigroup/monoid and thus show that the freeness problems for automaton semigroups and for automaton monoids (listed as open problems by Grigorchuk, Nekrashevych and Sushchanskĭi) are undecidable. The construction seems to be quite versatile and we obtain the undecidability of further problems: Is a given automaton semigroup (monoid) (left) cancellative? Is it equidivisible (which - together with the existence of a (proper) length function - characterizes free semigroups and monoids)? Does a given map extend into a homomorphism between given automaton semigroups? Finally, our construction can be adapted to show that it is undecidable whether a given automaton generates a free monoid whose basis is given by the states (but where we allow one state to act as the identity). In the semigroup case, we show a weaker version of this.
Cite as

Daniele D'Angeli, Emanuele Rodaro, and Jan Philipp Wächter. The Freeness Problem for Automaton Semigroups. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dangeli_et_al:LIPIcs.MFCS.2024.44,
  author =	{D'Angeli, Daniele and Rodaro, Emanuele and W\"{a}chter, Jan Philipp},
  title =	{{The Freeness Problem for Automaton Semigroups}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{44:1--44:18},
  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.2024.44},
  URN =		{urn:nbn:de:0030-drops-206002},
  doi =		{10.4230/LIPIcs.MFCS.2024.44},
  annote =	{Keywords: Automaton Monoid, Automaton Semigroup, Freeness Problem, Free Presentation}
}
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.
Cite as

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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.134
Functional Closure Properties of Finite ℕ-Weighted Automata

Authors: Julian Dörfler and Christian Ikenmeyer

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We determine all functional closure properties of finite ℕ-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting, and all multivariate closure properties under certain assumptions on the promise, in particular we determine all multivariate closure properties where the output vector lies on a monotone algebraic graph variety.
Cite as

Julian Dörfler and Christian Ikenmeyer. Functional Closure Properties of Finite ℕ-Weighted Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 134:1-134:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dorfler_et_al:LIPIcs.ICALP.2024.134,
  author =	{D\"{o}rfler, Julian and Ikenmeyer, Christian},
  title =	{{Functional Closure Properties of Finite \mathbb{N}-Weighted Automata}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{134:1--134:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.134},
  URN =		{urn:nbn:de:0030-drops-202777},
  doi =		{10.4230/LIPIcs.ICALP.2024.134},
  annote =	{Keywords: Finite automata, weighted automata, counting, closure properties, algebraic varieties}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.116
Dynamic Membership for Regular Languages

Authors: Antoine Amarilli, Louis Jachiet, and Charles Paperman

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We consider this problem on the unit cost RAM model with logarithmic word length, where the problem always has a solution in O(log|w| / log log|w|) per operation. We show that the problem is in O(log log|w|) for languages in an algebraically-defined, decidable class QSG, and that it is in O(1) for another such class QLZG. We show that languages not in QSG admit a reduction from the prefix problem for a cyclic group, so that they require Ω(log|w| /log log|w|) operations in the worst case; and that QSG languages not in QLZG admit a reduction from the prefix problem for the multiplicative monoid U₁ = {0, 1}, which we conjecture cannot be maintained in O(1). This yields a conditional trichotomy. We also investigate intermediate cases between O(1) and O(log log|w|). Our results are shown via the dynamic word problem for monoids and semigroups, for which we also give a classification. We thus solve open problems of the paper of Skovbjerg Frandsen, Miltersen, and Skyum [Skovbjerg Frandsen et al., 1997] on the dynamic word problem, and additionally cover regular languages.
Cite as

Antoine Amarilli, Louis Jachiet, and Charles Paperman. Dynamic Membership for Regular Languages. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 116:1-116:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{amarilli_et_al:LIPIcs.ICALP.2021.116,
  author =	{Amarilli, Antoine and Jachiet, Louis and Paperman, Charles},
  title =	{{Dynamic Membership for Regular Languages}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{116:1--116:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela 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.ICALP.2021.116},
  URN =		{urn:nbn:de:0030-drops-141850},
  doi =		{10.4230/LIPIcs.ICALP.2021.116},
  annote =	{Keywords: regular language, membership, RAM model, updates, dynamic}
}
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
SCICO Journal-first
DOI: 10.4230/LIPIcs.ECOOP.2020.32
A Big Step from Finite to Infinite Computations (SCICO Journal-first)

Authors: Davide Ancona, Francesco Dagnino, Jurriaan Rot, and Elena Zucca

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract
The known is finite, the unknown infinite - Thomas Henry Huxley The behaviour of programs can be described by the final results of computations, and/or their interactions with the context, also seen as observations. For instance, a function call can terminate and return a value, as well as have output effects during its execution. Here, we deal with semantic definitions covering both results and observations. Often, such definitions are provided for finite computations only. Notably, in big-step style, infinite computations are simply not modelled, hence diverging and stuck terms are not distinguished. This becomes even more unsatisfactory if we have observations, since a non-terminating program may have significant infinite behaviour. Recently, examples of big-step semantics modeling divergence have been provided [Davide Ancona et al., 2017; Davide Ancona et al., 2018] by means of generalized inference systems [Davide Ancona et al., 2017; Francesco Dagnino, 2019], which allow corules to control coinduction. Indeed, modeling infinite behaviour by a purely coinductive interpretation of big-step rules would lead to spurious results [Xavier Leroy and Hervé Grall, 2009] and undetermined observation, whereas, by adding appropriate corules, we can correctly get divergence (∞) as the only result, and a uniquely determined observation. This approach has been adopted in [Davide Ancona et al., 2017; Davide Ancona et al., 2018] to design big-step definitions including infinite behaviour for lambda-calculus and a simple imperative Java-like language. However, in such works the designer of the semantics is in charge of finding the appropriate corules, and this is a non-trivial task. In this paper, we show a general construction that extends a given big-step semantics, modeling finite computations, to include infinite behaviour as well, notably by generating appropriate corules. The construction consists of two steps: 1) Starting from a monoid O modeling finite observations (e.g., finite traces), we construct an ω-monoid ⟨O, O_∞⟩ also modeling infinite observations (e.g., infinite traces). The latter structure is a variation of the notion of ω-semigroup [Dominique Perrin and Jean-Eric Pin, 2004], including a mixed product composing a finite with a possibly infinite observation, and an infinite product mapping an infinite sequence of finite observations into a single one (possibly infinite). 2) Starting from an inference system defining a big-step judgment c⇒⟨r, o⟩, with c denoting a configuration, r ∈ R a result, and o ∈ O a finite observation, we construct an inference system with corules defining an extended big-step judgment c⇒c ⇒ ⟨r_∞, o_∞⟩ with r_∞ ∈ R_∞ = R+{∞}, and o_∞ ∈ O_∞ a "possibly infinite" observation. The construction generates additional rules for propagating divergence, and corules for introducing divergence in a controlled way. The exact corules added in the construction depend on the type of observations that one starts with. To show the effectiveness of our approach, we provide several instances of the framework, with different kinds of (finite) observations. Finally, we prove a correctness result for the construction. To this end, we assume the original big-step semantics to be equivalent to (finite sequences of steps in) a reference small-step semantics, and we show that, by applying the construction, we obtain an extended big-step semantics which is still equivalent to the small-step semantics, where we consider possibly infinite sequences of steps.} As hypotheses, rather than {just} equivalence in the finite case {(which would be not enough)}, we assume a set of equivalence conditions between individual big-step rules and the small-step relation. This proof of equivalence holds for deterministic semantics; issues arising in the non-deterministic case and a possible solution are sketched in the conclusion of the full paper.
Cite as

Davide Ancona, Francesco Dagnino, Jurriaan Rot, and Elena Zucca. A Big Step from Finite to Infinite Computations (SCICO Journal-first). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 32:1-32:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ancona_et_al:LIPIcs.ECOOP.2020.32,
  author =	{Ancona, Davide and Dagnino, Francesco and Rot, Jurriaan and Zucca, Elena},
  title =	{{A Big Step from Finite to Infinite Computations}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{32:1--32:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.32},
  URN =		{urn:nbn:de:0030-drops-131895},
  doi =		{10.4230/LIPIcs.ECOOP.2020.32},
  annote =	{Keywords: Operational semantics, coinduction, infinite behaviour}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.7
A Trichotomy for Regular Trail Queries

Authors: Wim Martens, Matthias Niewerth, and Tina Trautner

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice.
Cite as

Wim Martens, Matthias Niewerth, and Tina Trautner. A Trichotomy for Regular Trail Queries. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{martens_et_al:LIPIcs.STACS.2020.7,
  author =	{Martens, Wim and Niewerth, Matthias and Trautner, Tina},
  title =	{{A Trichotomy for Regular Trail Queries}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.7},
  URN =		{urn:nbn:de:0030-drops-118681},
  doi =		{10.4230/LIPIcs.STACS.2020.7},
  annote =	{Keywords: Regular languages, query languages, path queries, graph databases, databases, complexity, trails, simple paths}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.125
A Mahler’s Theorem for Word Functions (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Jean-Éric Pin and Christophe Reutenauer

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Let p be a prime number and let G_p be the variety of all languages recognised by a finite p-group. We give a construction process of all G_p-preserving functions from a free monoid to a free group. Our result follows from a new noncommutative generalization of Mahler’s theorem on interpolation series, a celebrated result of p-adic analysis.
Cite as

Jean-Éric Pin and Christophe Reutenauer. A Mahler’s Theorem for Word Functions (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 125:1-125:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{pin_et_al:LIPIcs.ICALP.2019.125,
  author =	{Pin, Jean-\'{E}ric and Reutenauer, Christophe},
  title =	{{A Mahler’s Theorem for Word Functions}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{125:1--125:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.125},
  URN =		{urn:nbn:de:0030-drops-107019},
  doi =		{10.4230/LIPIcs.ICALP.2019.125},
  annote =	{Keywords: group languages, interpolation series, pro-p metric, regularity preserving}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.43
Eilenberg Theorems for Free

Authors: Henning Urbat, Jiri Adámek, Liang-Ting Chen, and Stefan Milius

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Eilenberg-type correspondences, relating varieties of languages (e.g., of finite words, infinite words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic language theory. We show that they all arise from the same recipe: one models languages and the algebras recognizing them by monads on an algebraic category, and applies a Stone-type duality. Our main contribution is a variety theorem that covers e.g. Wilke's and Pin's work on infinity-languages, the variety theorem for cost functions of Daviaud, Kuperberg, and Pin, and unifies the two categorical approaches of Bojanczyk and of Adamek et al. In addition we derive new results, such as an extension of the local variety theorem of Gehrke, Grigorieff, and Pin from finite to infinite words.
Cite as

Henning Urbat, Jiri Adámek, Liang-Ting Chen, and Stefan Milius. Eilenberg Theorems for Free. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{urbat_et_al:LIPIcs.MFCS.2017.43,
  author =	{Urbat, Henning and Ad\'{a}mek, Jiri and Chen, Liang-Ting and Milius, Stefan},
  title =	{{Eilenberg Theorems for Free}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.43},
  URN =		{urn:nbn:de:0030-drops-81032},
  doi =		{10.4230/LIPIcs.MFCS.2017.43},
  annote =	{Keywords: Eilenberg's theorem, variety of languages, pseudovariety, monad, duality}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.30
Varieties of Cost Functions

Authors: Laure Daviaud, Denis Kuperberg, and Jean-Éric Pin

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalising two results on regular languages to cost functions: Eilenberg's varieties theorem and profinite equational characterisations of lattices of regular languages. This opens interesting new perspectives, but the specificities of cost functions introduce difficulties that prevent these generalisations to be straightforward. In contrast, although syntactic algebras can be defined for formal power series over a commutative ring, no such notion is known for series over semirings and in particular over the tropical semiring.
Cite as

Laure Daviaud, Denis Kuperberg, and Jean-Éric Pin. Varieties of Cost Functions. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{daviaud_et_al:LIPIcs.STACS.2016.30,
  author =	{Daviaud, Laure and Kuperberg, Denis and Pin, Jean-\'{E}ric},
  title =	{{Varieties of Cost Functions}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{30:1--30:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.30},
  URN =		{urn:nbn:de:0030-drops-57319},
  doi =		{10.4230/LIPIcs.STACS.2016.30},
  annote =	{Keywords: Cost functions, regular language, varieties, syntactic algebra}
}
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