26 Search Results for "Filiot, Emmanuel"


Document
Regular Transformations (Dagstuhl Seminar 23202)

Authors: Rajeev Alur, Mikołaj Bojańczyk, Emmanuel Filiot, Anca Muscholl, and Sarah Winter

Published in: Dagstuhl Reports, Volume 13, Issue 5 (2023)


Abstract
This report documents the program and the outcomes of the Dagstuhl Seminar 23202 "Regular Transformations". The goal of this seminar was to advance on a list of topics about transducers that have gathered much interest recently, and to explore new connections between the theory of regular transformations and its applications in linguistics.

Cite as

Rajeev Alur, Mikołaj Bojańczyk, Emmanuel Filiot, Anca Muscholl, and Sarah Winter. Regular Transformations (Dagstuhl Seminar 23202). In Dagstuhl Reports, Volume 13, Issue 5, pp. 96-113, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@Article{alur_et_al:DagRep.13.5.96,
  author =	{Alur, Rajeev and Boja\'{n}czyk, Miko{\l}aj and Filiot, Emmanuel and Muscholl, Anca and Winter, Sarah},
  title =	{{Regular Transformations (Dagstuhl Seminar 23202)}},
  pages =	{96--113},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{5},
  editor =	{Alur, Rajeev and Boja\'{n}czyk, Miko{\l}aj and Filiot, Emmanuel and Muscholl, Anca and Winter, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.5.96},
  URN =		{urn:nbn:de:0030-drops-193663},
  doi =		{10.4230/DagRep.13.5.96},
  annote =	{Keywords: transducers; (poly-)regular functions; linguistic transformations}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Deterministic Regular Functions of Infinite Words

Authors: Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.

Cite as

Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic Regular Functions of Infinite Words. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 121:1-121:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{carton_et_al:LIPIcs.ICALP.2023.121,
  author =	{Carton, Olivier and Dou\'{e}neau-Tabot, Ga\"{e}tan and Filiot, Emmanuel and Winter, Sarah},
  title =	{{Deterministic Regular Functions of Infinite Words}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{121:1--121:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.121},
  URN =		{urn:nbn:de:0030-drops-181733},
  doi =		{10.4230/LIPIcs.ICALP.2023.121},
  annote =	{Keywords: infinite words, streaming string transducers, two-way transducers, monadic second-order logic, look-aheads, factorization forests}
}
Document
A Regular and Complete Notion of Delay for Streaming String Transducers

Authors: Emmanuel Filiot, Ismaël Jecker, Christof Löding, and Sarah Winter

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


Abstract
The notion of delay between finite transducers is a core element of numerous fundamental results of transducer theory. The goal of this work is to provide a similar notion for more complex abstract machines: we introduce a new notion of delay tailored to measure the similarity between streaming string transducers (SST). We show that our notion is regular: we design a finite automaton that can check whether the delay between any two SSTs executions is smaller than some given bound. As a consequence, our notion enjoys good decidability properties: in particular, while equivalence between non-deterministic SSTs is undecidable, we show that equivalence up to fixed delay is decidable. Moreover, we show that our notion has good completeness properties: we prove that two SSTs are equivalent if and only if they are equivalent up to some (computable) bounded delay. Together with the regularity of our delay notion, it provides an alternative proof that SSTs equivalence is decidable. Finally, the definition of our delay notion is machine-independent, as it only depends on the origin semantics of SSTs. As a corollary, the completeness result also holds for equivalent machine models such as deterministic two-way transducers, or MSO transducers.

Cite as

Emmanuel Filiot, Ismaël Jecker, Christof Löding, and Sarah Winter. A Regular and Complete Notion of Delay for Streaming String Transducers. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{filiot_et_al:LIPIcs.STACS.2023.32,
  author =	{Filiot, Emmanuel and Jecker, Isma\"{e}l and L\"{o}ding, Christof and Winter, Sarah},
  title =	{{A Regular and Complete Notion of Delay for Streaming String Transducers}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.32},
  URN =		{urn:nbn:de:0030-drops-176843},
  doi =		{10.4230/LIPIcs.STACS.2023.32},
  annote =	{Keywords: Streaming string transducers, Delay, Origin}
}
Document
Two-Player Boundedness Counter Games

Authors: Emmanuel Filiot and Edwin Hamel-de le Court

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)


Abstract
We consider two-player zero-sum games with winning objectives beyond regular languages, expressed as a parity condition in conjunction with a Boolean combination of boundedness conditions on a finite set of counters which can be incremented, reset to 0, but not tested. A boundedness condition requires that a given counter is bounded along the play. Such games are decidable, though with non-optimal complexity, by an encoding into the logic WMSO with the unbounded and path quantifiers, which is known to be decidable over infinite trees. Our objective is to give tight or tighter complexity results for particular classes of counter games with boundedness conditions, and study their strategy complexity. In particular, counter games with conjunction of boundedness conditions are easily seen to be equivalent to Streett games, so, they are CoNP-c. Moreover, finite-memory strategies suffice for Eve and memoryless strategies suffice for Adam. For counter games with a disjunction of boundedness conditions, we prove that they are in solvable in NP∩CoNP, and in PTime if the parity condition is fixed. In that case memoryless strategies suffice for Eve while infinite memory strategies might be necessary for Adam. Finally, we consider an extension of those games with a max operation. In that case, the complexity increases: for conjunctions of boundedness conditions, counter games are EXPTIME-c.

Cite as

Emmanuel Filiot and Edwin Hamel-de le Court. Two-Player Boundedness Counter Games. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{filiot_et_al:LIPIcs.CONCUR.2022.21,
  author =	{Filiot, Emmanuel and Hamel-de le Court, Edwin},
  title =	{{Two-Player Boundedness Counter Games}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir 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.CONCUR.2022.21},
  URN =		{urn:nbn:de:0030-drops-170841},
  doi =		{10.4230/LIPIcs.CONCUR.2022.21},
  annote =	{Keywords: Controller synthesis, Game theory, Counter Games, Boundedness objectives}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
A Generic Solution to Register-Bounded Synthesis with an Application to Discrete Orders

Authors: Léo Exibard, Emmanuel Filiot, and Ayrat Khalimov

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We study synthesis of reactive systems interacting with environments using an infinite data domain. A popular formalism for specifying and modelling such systems is register automata and transducers. They extend finite-state automata by adding registers to store data values and to compare the incoming data values against stored ones. Synthesis from nondeterministic or universal register automata is undecidable in general. However, its register-bounded variant, where additionally a bound on the number of registers in a sought transducer is given, is known to be decidable for universal register automata which can compare data for equality, i.e., for data domain (ℕ, =). This paper extends the decidability border to the domain (ℕ, <) of natural numbers with linear order. Our solution is generic: we define a sufficient condition on data domains (regular approximability) for decidability of register-bounded synthesis. The condition is satisfied by natural data domains like (ℕ, <). It allows one to use simple language-theoretic arguments and avoid technical game-theoretic reasoning. Further, by defining a generic notion of reducibility between data domains, we show the decidability of synthesis in the domain (ℕ^d, <^d) of tuples of numbers equipped with the component-wise partial order and in the domain (Σ^*,≺) of finite strings with the prefix relation.

Cite as

Léo Exibard, Emmanuel Filiot, and Ayrat Khalimov. A Generic Solution to Register-Bounded Synthesis with an Application to Discrete Orders. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 122:1-122:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{exibard_et_al:LIPIcs.ICALP.2022.122,
  author =	{Exibard, L\'{e}o and Filiot, Emmanuel and Khalimov, Ayrat},
  title =	{{A Generic Solution to Register-Bounded Synthesis with an Application to Discrete Orders}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{122:1--122:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.122},
  URN =		{urn:nbn:de:0030-drops-164634},
  doi =		{10.4230/LIPIcs.ICALP.2022.122},
  annote =	{Keywords: Synthesis, Register Automata, Transducers, Ordered Data Domains}
}
Document
Synthesizing Computable Functions from Rational Specifications over Infinite Words

Authors: Emmanuel Filiot and Sarah Winter

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)


Abstract
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing computability notion over infinite inputs. We consider specifications which are rational relations of infinite words, i.e., specifications defined by non-deterministic parity transducers. We prove that the synthesis problem of computable functions from rational specifications is undecidable. We provide an incomplete but sound reduction to some parity game, such that if Eve wins the game, then the rational specification is realizable by a computable function. We prove that this function is even computable by a deterministic two-way transducer. We provide a sufficient condition under which the latter game reduction is complete. This entails the decidability of the synthesis problem of computable functions, which we proved to be ExpTime-complete, for a large subclass of rational specifications, namely deterministic rational specifications. This subclass contains the class of automatic relations over infinite words, a yardstick in reactive synthesis.

Cite as

Emmanuel Filiot and Sarah Winter. Synthesizing Computable Functions from Rational Specifications over Infinite Words. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2021.43,
  author =	{Filiot, Emmanuel and Winter, Sarah},
  title =	{{Synthesizing Computable Functions from Rational Specifications over Infinite Words}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.43},
  URN =		{urn:nbn:de:0030-drops-155541},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.43},
  annote =	{Keywords: uniformization, synthesis, transducers, continuity, computability}
}
Document
Decision Problems for Origin-Close Top-Down Tree Transducers

Authors: Sarah Winter

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to tree transductions, i.e., tagging each output node with the input node it originates from, is a known way to recover decidability for inclusion and equivalence. The origin semantics is rather rigid, in this work, we introduce a similarity measure for transducers with origin semantics and show that we can decide inclusion, equivalence and synthesis problems for origin-close non-deterministic top-down tree transducers.

Cite as

Sarah Winter. Decision Problems for Origin-Close Top-Down Tree Transducers. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 90:1-90:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{winter:LIPIcs.MFCS.2021.90,
  author =	{Winter, Sarah},
  title =	{{Decision Problems for Origin-Close Top-Down Tree Transducers}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{90:1--90:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.90},
  URN =		{urn:nbn:de:0030-drops-145308},
  doi =		{10.4230/LIPIcs.MFCS.2021.90},
  annote =	{Keywords: tree tranducers, equivalence, uniformization, synthesis, origin semantics}
}
Document
Church Synthesis on Register Automata over Linearly Ordered Data Domains

Authors: Léo Exibard, Emmanuel Filiot, and Ayrat Khalimov

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


Abstract
Register automata are finite automata equipped with a finite set of registers in which they can store data, i.e. elements from an unbounded or infinite alphabet. They provide a simple formalism to specify the behaviour of reactive systems operating over data ω-words. We study the synthesis problem for specifications given as register automata over a linearly ordered data domain (e.g. (ℕ, ≤) or (ℚ, ≤)), which allow for comparison of data with regards to the linear order. To that end, we extend the classical Church synthesis game to infinite alphabets: two players, Adam and Eve, alternately play some data, and Eve wins whenever their interaction complies with the specification, which is a language of ω-words over ordered data. Such games are however undecidable, even when the specification is recognised by a deterministic register automaton. This is in contrast with the equality case, where the problem is only undecidable for nondeterministic and universal specifications. Thus, we study one-sided Church games, where Eve instead operates over a finite alphabet, while Adam still manipulates data. We show they are determined, and deciding the existence of a winning strategy is in ExpTime, both for ℚ and ℕ. This follows from a study of constraint sequences, which abstract the behaviour of register automata, and allow us to reduce Church games to ω-regular games. Lastly, we apply these results to the transducer synthesis problem for input-driven register automata, where each output data is restricted to be the content of some register, and show that if there exists an implementation, then there exists one which is a register transducer.

Cite as

Léo Exibard, Emmanuel Filiot, and Ayrat Khalimov. Church Synthesis on Register Automata over Linearly Ordered Data Domains. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{exibard_et_al:LIPIcs.STACS.2021.28,
  author =	{Exibard, L\'{e}o and Filiot, Emmanuel and Khalimov, Ayrat},
  title =	{{Church Synthesis on Register Automata over Linearly Ordered Data Domains}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{28:1--28:16},
  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.2021.28},
  URN =		{urn:nbn:de:0030-drops-136735},
  doi =		{10.4230/LIPIcs.STACS.2021.28},
  annote =	{Keywords: Synthesis, Church Game, Register Automata, Transducers, Ordered Data Words}
}
Document
A Ramsey Theorem for Finite Monoids

Authors: Ismaël Jecker

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


Abstract
Repeated idempotent elements are commonly used to characterise iterable behaviours in abstract models of computation. Therefore, given a monoid M, it is natural to ask how long a sequence of elements of M needs to be to ensure the presence of consecutive idempotent factors. This question is formalised through the notion of the Ramsey function R_M associated to M, obtained by mapping every k ∈ ℕ to the minimal integer R_M(k) such that every word u ∈ M^* of length R_M(k) contains k consecutive non-empty factors that correspond to the same idempotent element of M. In this work, we study the behaviour of the Ramsey function R_M by investigating the regular 𝒟-length of M, defined as the largest size L(M) of a submonoid of M isomorphic to the set of natural numbers {1,2, …, L(M)} equipped with the max operation. We show that the regular 𝒟-length of M determines the degree of R_M, by proving that k^L(M) ≤ R_M(k) ≤ (k|M|⁴)^L(M). To allow applications of this result, we provide the value of the regular 𝒟-length of diverse monoids. In particular, we prove that the full monoid of n × n Boolean matrices, which is used to express transition monoids of non-deterministic automata, has a regular 𝒟-length of (n²+n+2)/2.

Cite as

Ismaël Jecker. A Ramsey Theorem for Finite Monoids. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 44:1-44:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{jecker:LIPIcs.STACS.2021.44,
  author =	{Jecker, Isma\"{e}l},
  title =	{{A Ramsey Theorem for Finite Monoids}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{44:1--44:13},
  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.2021.44},
  URN =		{urn:nbn:de:0030-drops-136890},
  doi =		{10.4230/LIPIcs.STACS.2021.44},
  annote =	{Keywords: Semigroup, monoid, idempotent, automaton}
}
Document
Synthesis from Weighted Specifications with Partial Domains over Finite Words

Authors: Emmanuel Filiot, Christof Löding, and Sarah Winter

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


Abstract
In this paper, we investigate the synthesis problem of terminating reactive systems from quantitative specifications. Such systems are modeled as finite transducers whose executions are represented as finite words in (I × O)^*, where I, O are finite sets of input and output symbols, respectively. A weighted specification S assigns a rational value (or -∞) to words in (I × O)^*, and we consider three kinds of objectives for synthesis, namely threshold objectives where the system’s executions are required to be above some given threshold, best-value and approximate objectives where the system is required to perform as best as it can by providing output symbols that yield the best value and ε-best value respectively w.r.t. S. We establish a landscape of decidability results for these three objectives and weighted specifications with partial domain over finite words given by deterministic weighted automata equipped with sum, discounted-sum and average measures. The resulting objectives are not regular in general and we develop an infinite game framework to solve the corresponding synthesis problems, namely the class of (weighted) critical prefix games.

Cite as

Emmanuel Filiot, Christof Löding, and Sarah Winter. Synthesis from Weighted Specifications with Partial Domains over Finite 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. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2020.46,
  author =	{Filiot, Emmanuel and L\"{o}ding, Christof and Winter, Sarah},
  title =	{{Synthesis from Weighted Specifications with Partial Domains over Finite Words}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{46:1--46:16},
  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.2020.46},
  URN =		{urn:nbn:de:0030-drops-132874},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.46},
  annote =	{Keywords: synthesis, weighted games, weighted automata on finite words}
}
Document
Weighted Transducers for Robustness Verification

Authors: Emmanuel Filiot, Nicolas Mazzocchi, Jean-François Raskin, Sriram Sankaranarayanan, and Ashutosh Trivedi

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)


Abstract
Automata theory provides us with fundamental notions such as languages, membership, emptiness and inclusion that in turn allow us to specify and verify properties of reactive systems in a useful manner. However, these notions all yield "yes"/"no" answers that sometimes fall short of being satisfactory answers when the models being analyzed are imperfect, and the observations made are prone to errors. To address this issue, a common engineering approach is not just to verify that a system satisfies a property, but whether it does so robustly. We present notions of robustness that place a metric on words, thus providing a natural notion of distance between words. Such a metric naturally leads to a topological neighborhood of words and languages, leading to quantitative and robust versions of the membership, emptiness and inclusion problems. More generally, we consider weighted transducers to model the cost of errors. Such a transducer models neighborhoods of words by providing the cost of rewriting a word into another. The main contribution of this work is to study robustness verification problems in the context of weighted transducers. We provide algorithms for solving the robust and quantitative versions of the membership and inclusion problems while providing useful motivating case studies including approximate pattern matching problems to detect clinically relevant events in a large type-1 diabetes dataset.

Cite as

Emmanuel Filiot, Nicolas Mazzocchi, Jean-François Raskin, Sriram Sankaranarayanan, and Ashutosh Trivedi. Weighted Transducers for Robustness Verification. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{filiot_et_al:LIPIcs.CONCUR.2020.17,
  author =	{Filiot, Emmanuel and Mazzocchi, Nicolas and Raskin, Jean-Fran\c{c}ois and Sankaranarayanan, Sriram and Trivedi, Ashutosh},
  title =	{{Weighted Transducers for Robustness Verification}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.17},
  URN =		{urn:nbn:de:0030-drops-128290},
  doi =		{10.4230/LIPIcs.CONCUR.2020.17},
  annote =	{Keywords: Weighted transducers, Quantitative verification, Fault-tolerance}
}
Document
Synthesis of Computable Regular Functions of Infinite Words

Authors: Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, and Nathan Lhote

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)


Abstract
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming ω-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the latter transducers define the class of rational functions. Even though regular functions are robustly characterised by several finite-state devices, even the subclass of rational functions may contain functions which are not computable (by a Turing machine with infinite input). This paper proposes a decision procedure for the following synthesis problem: given a regular function f (equivalently specified by one of the aforementioned transducer model), is f computable and if it is, synthesize a Turing machine computing it. For regular functions, we show that computability is equivalent to continuity, and therefore the problem boils down to deciding continuity. We establish a generic characterisation of continuity for functions preserving regular languages under inverse image (such as regular functions). We exploit this characterisation to show the decidability of continuity (and hence computability) of rational and regular functions. For rational functions, we show that this can be done in NLogSpace (it was already known to be in PTime by Prieur). In a similar fashion, we also effectively characterise uniform continuity of regular functions, and relate it to the notion of uniform computability, which offers stronger efficiency guarantees.

Cite as

Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, and Nathan Lhote. Synthesis of Computable Regular Functions of Infinite Words. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{dave_et_al:LIPIcs.CONCUR.2020.43,
  author =	{Dave, Vrunda and Filiot, Emmanuel and Krishna, Shankara Narayanan and Lhote, Nathan},
  title =	{{Synthesis of Computable Regular Functions of Infinite Words}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.43},
  URN =		{urn:nbn:de:0030-drops-128554},
  doi =		{10.4230/LIPIcs.CONCUR.2020.43},
  annote =	{Keywords: transducers, infinite words, computability, continuity, synthesis}
}
Document
Register Transducers Are Marble Transducers

Authors: Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Paul Gastin

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)


Abstract
Deterministic two-way transducers define the class of regular functions from words to words. Alur and Cerný introduced an equivalent model of transducers with registers called copyless streaming string transducers. In this paper, we drop the "copyless" restriction on these machines and show that they are equivalent to two-way transducers enhanced with the ability to drop marks, named "marbles", on the input. We relate the maximal number of marbles used with the amount of register copies performed by the streaming string transducer. Finally, we show that the class membership problems associated with these models are decidable. Our results can be interpreted in terms of program optimization for simple recursive and iterative programs.

Cite as

Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Paul Gastin. Register Transducers Are Marble Transducers. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{doueneautabot_et_al:LIPIcs.MFCS.2020.29,
  author =	{Dou\'{e}neau-Tabot, Ga\"{e}tan and Filiot, Emmanuel and Gastin, Paul},
  title =	{{Register Transducers Are Marble Transducers}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.29},
  URN =		{urn:nbn:de:0030-drops-126979},
  doi =		{10.4230/LIPIcs.MFCS.2020.29},
  annote =	{Keywords: streaming string transducer, two-way transducer, marbles, pebbles}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Adversarial Stackelberg Value in Quantitative Games

Authors: Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)


Abstract
In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but ε-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems.

Cite as

Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The Adversarial Stackelberg Value in Quantitative Games. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 127:1-127:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{filiot_et_al:LIPIcs.ICALP.2020.127,
  author =	{Filiot, Emmanuel and Gentilini, Raffaella and Raskin, Jean-Fran\c{c}ois},
  title =	{{The Adversarial Stackelberg Value in Quantitative Games}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{127:1--127:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.127},
  URN =		{urn:nbn:de:0030-drops-125348},
  doi =		{10.4230/LIPIcs.ICALP.2020.127},
  annote =	{Keywords: Non-zero sum games, reactive synthesis, adversarial Stackelberg}
}
Document
Two-Way Parikh Automata

Authors: Emmanuel Filiot, Shibashis Guha, and Nicolas Mazzocchi

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)


Abstract
Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer theory, as they enjoy a decidable emptiness problem. In this paper, we study two-way Parikh automata. We show that emptiness becomes undecidable in the non-deterministic case. However, it is PSpace-C when the number of visits to any input position is bounded and the semi-linear set is given as an existential Presburger formula. We also give tight complexity bounds for the inclusion, equivalence and universality problems. Finally, we characterise precisely the complexity of those problems when the semi-linear constraint is given by an arbitrary Presburger formula.

Cite as

Emmanuel Filiot, Shibashis Guha, and Nicolas Mazzocchi. Two-Way Parikh Automata. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 40:1-40:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2019.40,
  author =	{Filiot, Emmanuel and Guha, Shibashis and Mazzocchi, Nicolas},
  title =	{{Two-Way Parikh Automata}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{40:1--40:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.40},
  URN =		{urn:nbn:de:0030-drops-116027},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.40},
  annote =	{Keywords: Parikh automata, two-way automata, Presburger arithmetic}
}
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