Document

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

A regular data language is a language over an infinite alphabet recognized by a deterministic register automaton (DRA), as defined by Benedikt, Ley and Puppis. The later model, which is expressively equivalent to the deterministic finite-memory automata introduced earlier by Francez and Kaminsky, enjoys unique minimal automata (up to isomorphism), based on a Myhill-Nerode theorem.
In this paper, we introduce a polynomial time passive learning algorithm for regular data languages from positive and negative samples. Following Gold’s model for learning languages, we prove that our algorithm can identify in the limit any regular data language L, i.e. it returns a minimal DRA recognizing L if a characteristic sample set for L is provided as input. We prove that there exist characteristic sample sets of polynomial size with respect to the size of the minimal DRA recognizing L. To the best of our knowledge, it is the first passive learning algorithm for data languages, and the first learning algorithm which is fully polynomial, both with respect to time complexity and size of the characteristic sample set.

Mrudula Balachander, Emmanuel Filiot, and Raffaella Gentilini. Passive Learning of Regular Data Languages in Polynomial Time and Data. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balachander_et_al:LIPIcs.CONCUR.2024.10, author = {Balachander, Mrudula and Filiot, Emmanuel and Gentilini, Raffaella}, title = {{Passive Learning of Regular Data Languages in Polynomial Time and Data}}, booktitle = {35th International Conference on Concurrency Theory (CONCUR 2024)}, pages = {10:1--10:21}, 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.2024.10}, URN = {urn:nbn:de:0030-drops-207829}, doi = {10.4230/LIPIcs.CONCUR.2024.10}, annote = {Keywords: Register automata, passive learning, automata over infinite alphabets} }

Document

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

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.

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

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

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.

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

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

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.

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

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

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.

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} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

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

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.

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

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

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.

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} }

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

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.

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} }

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

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.

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} }

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

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.

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} }

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

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.

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} }

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

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.

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} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

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

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.

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} }

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

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.

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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**Published in:** LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata over infinite sequences of signals (omega-words), while implementations are represented as transducers. In the classical setting, the set of signals is assumed to be finite. In this paper, we consider data omega-words instead, i.e., words over an infinite alphabet. In this context, we study specifications and implementations respectively given as automata and transducers extended with a finite set of registers. We consider different instances, depending on whether the specification is nondeterministic, universal or deterministic, and depending on whether the number of registers of the implementation is given or not.
In the unbounded setting, we show undecidability for both universal and non-deterministic specifications, while decidability is recovered in the deterministic case. In the bounded setting, undecidability still holds for non-deterministic specifications, but can be recovered by disallowing tests over input data. The generic technique we use to show the latter result allows us to reprove some known result, namely decidability of bounded synthesis for universal specifications.

Léo Exibard, Emmanuel Filiot, and Pierre-Alain Reynier. Synthesis of Data Word Transducers. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{exibard_et_al:LIPIcs.CONCUR.2019.24, author = {Exibard, L\'{e}o and Filiot, Emmanuel and Reynier, Pierre-Alain}, title = {{Synthesis of Data Word Transducers}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {24:1--24:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-121-4}, ISSN = {1868-8969}, year = {2019}, volume = {140}, editor = {Fokkink, Wan and van Glabbeek, Rob}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.24}, URN = {urn:nbn:de:0030-drops-109269}, doi = {10.4230/LIPIcs.CONCUR.2019.24}, annote = {Keywords: Register Automata, Synthesis, Data words, Transducers} }

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**Published in:** LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

This paper investigates canonical transducers for rational functions over infinite words, i.e., functions of infinite words defined by finite transducers. We first consider sequential functions, defined by finite transducers with a deterministic underlying automaton. We provide a Myhill-Nerode-like characterization, in the vein of Choffrut's result over finite words, from which we derive an algorithm that computes a transducer realizing the function which is minimal and unique (up to the automaton for the domain).
The main contribution of the paper is the notion of a canonical transducer for rational functions over infinite words, extending the notion of canonical bimachine due to Reutenauer and Schützenberger from finite to infinite words. As an application, we show that the canonical transducer is aperiodic whenever the function is definable by some aperiodic transducer, or equivalently, by a first-order transduction. This allows to decide whether a rational function of infinite words is first-order definable.

Emmanuel Filiot, Olivier Gauwin, Nathan Lhote, and Anca Muscholl. On Canonical Models for Rational Functions over Infinite Words. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2018.30, author = {Filiot, Emmanuel and Gauwin, Olivier and Lhote, Nathan and Muscholl, Anca}, title = {{On Canonical Models for Rational Functions over Infinite Words}}, booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, pages = {30:1--30:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-093-4}, ISSN = {1868-8969}, year = {2018}, volume = {122}, editor = {Ganguly, Sumit and Pandya, Paritosh}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.30}, URN = {urn:nbn:de:0030-drops-99295}, doi = {10.4230/LIPIcs.FSTTCS.2018.30}, annote = {Keywords: transducers, infinite words, minimization, aperiodicty, first-order logic} }

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

The transducer synthesis problem on finite words asks, given a specification S subseteq I x O, where I and O are sets of finite words, whether there exists an implementation f: I - > O which (1) fulfils the specification, i.e., (i,f(i))in S for all i in I, and (2) can be defined by some input-deterministic (aka sequential) transducer T_f. If such an implementation f exists, the procedure should also output T_f. The realisability problem is the corresponding decision problem.
For specifications given by synchronous transducers (which read and write alternately one symbol), this is the finite variant of the classical synthesis problem on omega-words, solved by Büchi and Landweber in 1969, and the realisability problem is known to be ExpTime-c in both finite and omega-word settings. For specifications given by asynchronous transducers (which can write a batch of symbols, or none, in a single step), the realisability problem is known to be undecidable.
We consider here the class of multi-sequential specifications, defined as finite unions of sequential transducers over possibly incomparable domains. We provide optimal decision procedures for the realisability problem in both the synchronous and asynchronous setting, showing that it is PSpace-c. Moreover, whenever the specification is realisable, we expose the construction of a sequential transducer that realises it and has a size that is doubly exponential, which we prove to be optimal.

Léo Exibard, Emmanuel Filiot, and Ismaël Jecker. The Complexity of Transducer Synthesis from Multi-Sequential Specifications. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{exibard_et_al:LIPIcs.MFCS.2018.46, author = {Exibard, L\'{e}o and Filiot, Emmanuel and Jecker, Isma\"{e}l}, title = {{The Complexity of Transducer Synthesis from Multi-Sequential Specifications}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {46:1--46:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.46}, URN = {urn:nbn:de:0030-drops-96286}, doi = {10.4230/LIPIcs.MFCS.2018.46}, annote = {Keywords: Transducers, Multi-Sequentiality, Synthesis} }

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**Published in:** Dagstuhl Reports, Volume 7, Issue 4 (2018)

The goal of this Dagstuhl seminar was to gather researchers working on the theory and practice of transformations (also know as transductions) of word and tree structures, which are realised by transducers (automata with outputs). This seminar was motivated by recent advances and breakthrough results, both in the settings of words and trees.

Emmanuel Filiot, Sebastian Maneth, and Helmut Seidl. Formal Methods of Transformations (Dagstuhl Seminar 17142). In Dagstuhl Reports, Volume 7, Issue 4, pp. 23-37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{filiot_et_al:DagRep.7.4.23, author = {Filiot, Emmanuel and Maneth, Sebastian and Seidl, Helmut}, title = {{Formal Methods of Transformations (Dagstuhl Seminar 17142)}}, pages = {23--37}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2017}, volume = {7}, number = {4}, editor = {Filiot, Emmanuel and Maneth, Sebastian and Seidl, Helmut}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.4.23}, URN = {urn:nbn:de:0030-drops-75462}, doi = {10.4230/DagRep.7.4.23}, annote = {Keywords: string transducers, tree transducers, expressiveness, complexity} }

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**Published in:** LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

It is known that a language of finite words is definable in monadic second-order logic - MSO - (resp. first-order logic - FO -) iff it is recognized by some finite automaton (resp. some aperiodic finite automaton). Deciding whether an automaton A is equivalent to an aperiodic one is known to be PSPACE-complete. This problem has an important application in logic: it allows one to decide whether a given MSO formula is equivalent to some FO formula. In this paper, we address the aperiodicity problem for functions from finite words to finite words (transductions), defined by finite transducers, or equivalently by bimachines, a transducer model studied by Schützenberger and Reutenauer. Precisely, we show that the problem of deciding whether a given bimachine is equivalent to some aperiodic one is PSPACE-complete.

Emmanuel Filiot, Olivier Gauwin, and Nathan Lhote. Aperiodicity of Rational Functions Is PSPACE-Complete. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2016.13, author = {Filiot, Emmanuel and Gauwin, Olivier and Lhote, Nathan}, title = {{Aperiodicity of Rational Functions Is PSPACE-Complete}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {13:1--13:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-027-9}, ISSN = {1868-8969}, year = {2016}, volume = {65}, editor = {Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.13}, URN = {urn:nbn:de:0030-drops-68482}, doi = {10.4230/LIPIcs.FSTTCS.2016.13}, annote = {Keywords: Rational word transductions, decision problem, aperiodicity, bimachines} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

We study the computational complexity of the cooperative and non-cooperative rational synthesis problems, as introduced by Kupferman, Vardi and co-authors. We provide tight results for most of the classical omega-regular objectives, and show how to solve those problems optimally.

Rodica Condurache, Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The Complexity of Rational Synthesis. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 121:1-121:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{condurache_et_al:LIPIcs.ICALP.2016.121, author = {Condurache, Rodica and Filiot, Emmanuel and Gentilini, Raffaella and Raskin, Jean-Fran\c{c}ois}, title = {{The Complexity of Rational Synthesis}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {121:1--121:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.121}, URN = {urn:nbn:de:0030-drops-62565}, doi = {10.4230/LIPIcs.ICALP.2016.121}, annote = {Keywords: Non-zero sum games, reactive synthesis, omega-regular objectives} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them.

Emmanuel Filiot, Ismaël Jecker, Christof Löding, and Sarah Winter. On Equivalence and Uniformisation Problems for Finite Transducers. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 125:1-125:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{filiot_et_al:LIPIcs.ICALP.2016.125, author = {Filiot, Emmanuel and Jecker, Isma\"{e}l and L\"{o}ding, Christof and Winter, Sarah}, title = {{On Equivalence and Uniformisation Problems for Finite Transducers}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {125:1--125:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.125}, URN = {urn:nbn:de:0030-drops-62605}, doi = {10.4230/LIPIcs.ICALP.2016.125}, annote = {Keywords: Transducers, Equivalence, Uniformisation} }

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**Published in:** LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defined by k-valued automata, for all parameters k. We consider several measures to associate values with runs: sum, discounted-sum, and more generally values in groups.
We define a general procedure which decides, given a bound k and a WA over a group, whether this automaton is k-valued. We also show that any k-valued WA over a group, under some general conditions, can be decomposed as a union of k unambiguous WA. While inclusion and equivalence are undecidable problems for arbitrary sum-automata, we show, based on this decomposition, that they are decidable for k-valued sum-automata, and k-valued discounted sum-automata over inverted integer discount factors. We finally show that the quantitative Church problem is undecidable for k-valued sum-automata, even given as finite unions of deterministic sum-automata.

Emmanuel Filiot, Raffaella Gentilini, and Jean-Francois Raskin. Finite-Valued Weighted Automata. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 133-145, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2014.133, author = {Filiot, Emmanuel and Gentilini, Raffaella and Raskin, Jean-Francois}, title = {{Finite-Valued Weighted Automata}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {133--145}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.133}, URN = {urn:nbn:de:0030-drops-48388}, doi = {10.4230/LIPIcs.FSTTCS.2014.133}, annote = {Keywords: Nested word, Transducer, Streaming} }

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**Published in:** LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

The connection between languages defined by computational models and logic for languages is well-studied. Monadic second-order logic and finite automata are shown to closely correspond to each-other for the languages of strings, trees, and partial-orders. Similar connections are shown for first-order logic and finite automata with certain aperiodicity restriction. Courcelle in 1994 proposed a way to use logic to define functions over structures where the output structure is defined using logical formulas interpreted over the input structure. Engelfriet and Hoogeboom discovered the corresponding "automata connection" by showing that two-way generalised sequential machines capture the class of monadic-second order definable transformations. Alur and Cerny further refined the result by proposing a one-way deterministic transducer model with string variables - called the streaming string transducers - to capture the same class of transformations. In this paper we establish a transducer-logic correspondence for Courcelle's first-order definable string transformations. We propose a new notion of transition monoid for streaming string transducers that involves structural properties of both underlying input automata and variable dependencies. By putting an aperiodicity restriction on the transition monoids, we define a class of streaming string transducers that captures exactly the class of first-order definable transformations.

Emmanuel Filiot, Shankara Narayanan Krishna, and Ashutosh Trivedi. First-order Definable String Transformations. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 147-159, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2014.147, author = {Filiot, Emmanuel and Krishna, Shankara Narayanan and Trivedi, Ashutosh}, title = {{First-order Definable String Transformations}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {147--159}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.147}, URN = {urn:nbn:de:0030-drops-48393}, doi = {10.4230/LIPIcs.FSTTCS.2014.147}, annote = {Keywords: First-order logic, streaming string transducers} }

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**Published in:** LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Classical analysis of two-player quantitative games involves an adversary (modeling the environment of the system) which is purely antagonistic and asks for strict guarantees while Markov decision processes model systems facing a purely randomized environment: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. We introduce the beyond worst-case synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worst-case while providing an higher expected value against a particular stochastic model of the environment given as input. We consider both the mean-payoff value problem and the shortest path problem. In both cases, we show how to decide the existence of finite-memory strategies satisfying the problem and how to synthesize one if one exists. We establish algorithms and we study complexity bounds and memory requirements.

Véronique Bruyère, Emmanuel Filiot, Mickael Randour, and Jean-François Raskin. Meet Your Expectations With Guarantees: Beyond Worst-Case Synthesis in Quantitative Games. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 199-213, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{bruyere_et_al:LIPIcs.STACS.2014.199, author = {Bruy\`{e}re, V\'{e}ronique and Filiot, Emmanuel and Randour, Mickael and Raskin, Jean-Fran\c{c}ois}, title = {{Meet Your Expectations With Guarantees: Beyond Worst-Case Synthesis in Quantitative Games}}, booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)}, pages = {199--213}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-65-1}, ISSN = {1868-8969}, year = {2014}, volume = {25}, editor = {Mayr, Ernst W. and Portier, Natacha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.199}, URN = {urn:nbn:de:0030-drops-44589}, doi = {10.4230/LIPIcs.STACS.2014.199}, annote = {Keywords: two-player games on graphs, Markov decision processes, quantitative objectives, synthesis, worst-case and expected value, mean-payoff, shortest path} }

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**Published in:** LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

We consider the problem of evaluating in streaming (i.e. in a single left-to-right pass) a nested word transduction with a limited amount of memory. A transduction T is said to be height bounded memory (HBM) if it can be evaluated with a memory that depends only on the size of T and on the height of the input word. We show that it is decidable in coNPTime for a nested word transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In this case, the required amount of memory may depend exponentially on the height of the word. We exhibit a sufficient, decidable condition for a VPT to be evaluated with a memory that depends quadratically on the height of the word. This condition defines a class of transductions that strictly contains all determinizable VPTs.

Emmanuel Filiot, Olivier Gauwin, Pierre-Alain Reynier, and Frédéric Servais. Streamability of Nested Word Transductions. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 312-324, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2011.312, author = {Filiot, Emmanuel and Gauwin, Olivier and Reynier, Pierre-Alain and Servais, Fr\'{e}d\'{e}ric}, title = {{Streamability of Nested Word Transductions}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {312--324}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.312}, URN = {urn:nbn:de:0030-drops-33523}, doi = {10.4230/LIPIcs.FSTTCS.2011.312}, annote = {Keywords: nested word, visibly pushdown transducer, streaming, XML} }

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