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

Weighted automata (WA) are an extension of finite automata that define functions from words to values in a given semiring. An alternative deterministic model, called Cost Register Automata (CRA), was introduced by Alur et al. It enriches deterministic finite automata with a finite number of registers, which store values, updated at each transition using the operations of the semiring. It is known that CRA with register updates defined by linear maps have the same expressiveness as WA. Previous works have studied the register minimization problem: given a function computable by a WA and an integer k, is it possible to realize it using a CRA with at most k registers?
In this paper, we solve this problem for CRA over a field with linear register updates, using the notion of linear hull, an algebraic invariant of WA introduced recently by Bell and Smertnig. We then generalise the approach to solve a more challenging problem, that consists in minimizing simultaneously the number of states and that of registers. In addition, we also lift our results to the setting of CRA with affine updates. Last, while the linear hull was recently shown to be computable by Bell and Smertnig, no complexity bounds were given. To fill this gap, we provide two new algorithms to compute invariants of WA. This allows us to show that the register (resp. state-register) minimization problem can be solved in 2-ExpTime (resp. in NExpTime).

Yahia Idriss Benalioua, Nathan Lhote, and Pierre-Alain Reynier. Minimizing Cost Register Automata over a Field. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{benalioua_et_al:LIPIcs.MFCS.2024.23, author = {Benalioua, Yahia Idriss and Lhote, Nathan and Reynier, Pierre-Alain}, title = {{Minimizing Cost Register Automata over a Field}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {23:1--23:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.23}, URN = {urn:nbn:de:0030-drops-205798}, doi = {10.4230/LIPIcs.MFCS.2024.23}, annote = {Keywords: Weighted automata, Cost Register automata, Zariski topology} }

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

Weighted Timed Games (WTGs for short) are widely used to describe real-time controller synthesis problems, but they rely on an unrealistic perfect measure of time elapse. In order to produce strategies tolerant to timing imprecisions, we consider a notion of robustness, expressed as a parametric semantics, first introduced for timed automata. WTGs are two-player zero-sum games played in a weighted timed automaton in which one of the players, that we call Min, wants to reach a target location while minimising the cumulated weight. The opponent player, in addition to controlling some of the locations, can perturb delays chosen by Min. The robust value problem asks, given some threshold, whether there exists a positive perturbation and a strategy for Min ensuring to reach the target, with an accumulated weight below the threshold, whatever the opponent does.
We provide in this article the first decidability result for this robust value problem. More precisely, we show that we can compute the robust value function, in a parametric way, for the class of divergent WTGs (this class has been introduced previously to obtain decidability of the (classical) value problem in WTGs without bounding the number of clocks). To this end, we show that the robust value is the fixpoint of some operators, as is classically done for value iteration algorithms. We then combine in a very careful way two representations: piecewise affine functions introduced in [Alur et al., 2004] to analyse WTGs, and shrunk Difference Bound Matrices (shrunk DBMs for short) considered in [Sankur et al., 2011] to analyse robustness in timed automata. The crux of our result consists in showing that using this representation, the operator of value iteration can be computed for infinitesimally small perturbations. Last, we also study qualitative decision problems and close an open problem on robust reachability, showing it is EXPTIME-complete for general WTGs.

Benjamin Monmege, Julie Parreaux, and Pierre-Alain Reynier. Synthesis of Robust Optimal Real-Time Systems. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 74:1-74:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{monmege_et_al:LIPIcs.MFCS.2024.74, author = {Monmege, Benjamin and Parreaux, Julie and Reynier, Pierre-Alain}, title = {{Synthesis of Robust Optimal Real-Time Systems}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {74:1--74:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.74}, URN = {urn:nbn:de:0030-drops-206304}, doi = {10.4230/LIPIcs.MFCS.2024.74}, annote = {Keywords: Weighted timed games, Algorithmic game theory, Robustness} }

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

Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTG has attracted a lot of attention, especially because they are known to be decidable when only non-negative weights are allowed. However, when arbitrary weights are considered, despite several recent works, their decidability status was still unknown. In this paper, we solve this problem positively and show that the value function can be computed in exponential time (if weights are encoded in unary).

Benjamin Monmege, Julie Parreaux, and Pierre-Alain Reynier. Decidability of One-Clock Weighted Timed Games with Arbitrary Weights. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{monmege_et_al:LIPIcs.CONCUR.2022.15, author = {Monmege, Benjamin and Parreaux, Julie and Reynier, Pierre-Alain}, title = {{Decidability of One-Clock Weighted Timed Games with Arbitrary Weights}}, booktitle = {33rd International Conference on Concurrency Theory (CONCUR 2022)}, pages = {15:1--15:22}, 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.2022.15}, URN = {urn:nbn:de:0030-drops-170786}, doi = {10.4230/LIPIcs.CONCUR.2022.15}, annote = {Keywords: Weighted timed games, Algorithmic game theory, Timed automata} }

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

Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested words, i.e. words enriched with two matchings (a.k.a. 2-visibly pushdown languages), is not as successful: the corresponding model of automata is not closed under determinization. In this work, inspired by homomorphic representations of indexed languages, we identify a subclass of 2-nested words, which we call 2-wave words. This class strictly extends the class of nested words, while preserving its main properties. More precisely, we prove closure under determinization of the corresponding automaton model, we provide a logical characterization of the recognized languages, and show that the corresponding graphs have bounded treewidth. As a consequence, we derive important closure and decidability properties. Last, we show that the word projections of the languages we define belong to the class of linear indexed languages.

Séverine Fratani, Guillaume Maurras, and Pierre-Alain Reynier. A Robust Class of Languages of 2-Nested Words. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fratani_et_al:LIPIcs.MFCS.2022.50, author = {Fratani, S\'{e}verine and Maurras, Guillaume and Reynier, Pierre-Alain}, title = {{A Robust Class of Languages of 2-Nested Words}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {50:1--50:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.50}, URN = {urn:nbn:de:0030-drops-168485}, doi = {10.4230/LIPIcs.MFCS.2022.50}, annote = {Keywords: Nested word, Determinization, Indexed languages} }

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**Published in:** LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature; on one hand, lifting this result to a weighted setting has been widely studied. On the other hand, beyond the free monoid, different monoids can be considered: for instance, two-way automata, and even tree-walking automata, can be described by expressions using the free inverse monoid. In the present work, we aim at combining both research directions and consider weighted extensions of automata and expressions over a class of monoids that we call pre-rational, generalising both the free inverse monoid and graded monoids. The presence of idempotent elements in these pre-rational monoids leads in the weighted setting to consider infinite sums. To handle such sums, we will have to restrict ourselves to rationally additive semirings. Our main result is thus a generalisation of the Kleene theorem for pre-rational monoids and rationally additive semirings. As a corollary, we obtain a class of expressions equivalent to weighted two-way automata, as well as one for tree-walking automata.

Nicolas Baudru, Louis-Marie Dando, Nathan Lhote, Benjamin Monmege, Pierre-Alain Reynier, and Jean-Marc Talbot. Weighted Automata and Expressions over Pre-Rational Monoids. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{baudru_et_al:LIPIcs.CSL.2022.6, author = {Baudru, Nicolas and Dando, Louis-Marie and Lhote, Nathan and Monmege, Benjamin and Reynier, Pierre-Alain and Talbot, Jean-Marc}, title = {{Weighted Automata and Expressions over Pre-Rational Monoids}}, booktitle = {30th EACSL Annual Conference on Computer Science Logic (CSL 2022)}, pages = {6:1--6:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-218-1}, ISSN = {1868-8969}, year = {2022}, volume = {216}, editor = {Manea, Florin and Simpson, Alex}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.6}, URN = {urn:nbn:de:0030-drops-157266}, doi = {10.4230/LIPIcs.CSL.2022.6}, annote = {Keywords: Weighted Automata and Expressions, Inverse Monoids, Two-Way Automata} }

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

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

Weighted timed games are two-player zero-sum games played in a timed automaton equipped with integer weights. We consider optimal reachability objectives, in which one of the players, that we call Min, wants to reach a target location while minimising the cumulated weight. While knowing if Min has a strategy to guarantee a value lower than a given threshold is known to be undecidable (with two or more clocks), several conditions, one of them being the divergence, have been given to recover decidability. In such weighted timed games (like in untimed weighted games in the presence of negative weights), Min may need finite memory to play (close to) optimally. This is thus tempting to try to emulate this finite memory with other strategic capabilities. In this work, we allow the players to use stochastic decisions, both in the choice of transitions and of timing delays. We give for the first time a definition of the expected value in weighted timed games, overcoming several theoretical challenges. We then show that, in divergent weighted timed games, the stochastic value is indeed equal to the classical (deterministic) value, thus proving that Min can guarantee the same value while only using stochastic choices, and no memory.

Benjamin Monmege, Julie Parreaux, and Pierre-Alain Reynier. Playing Stochastically in Weighted Timed Games to Emulate Memory. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 137:1-137:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{monmege_et_al:LIPIcs.ICALP.2021.137, author = {Monmege, Benjamin and Parreaux, Julie and Reynier, Pierre-Alain}, title = {{Playing Stochastically in Weighted Timed Games to Emulate Memory}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {137:1--137:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.137}, URN = {urn:nbn:de:0030-drops-142066}, doi = {10.4230/LIPIcs.ICALP.2021.137}, annote = {Keywords: Weighted timed games, Algorithmic game theory, Randomisation} }

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

Shortest-path games are two-player zero-sum games played on a graph equipped with integer weights. One player, that we call Min, wants to reach a target set of states while minimising the total weight, and the other one has an antagonistic objective. This combination of a qualitative reachability objective and a quantitative total-payoff objective is one of the simplest settings where Min needs memory (pseudo-polynomial in the weights) to play optimally. In this article, we aim at studying a tradeoff allowing Min to play at random, but using no memory. We show that Min can achieve the same optimal value in both cases. In particular, we compute a randomised memoryless ε-optimal strategy when it exists, where probabilities are parametrised by ε. We also show that for some games, no optimal randomised strategies exist. We then characterise, and decide in polynomial time, the class of games admitting an optimal randomised memoryless strategy.

Benjamin Monmege, Julie Parreaux, and Pierre-Alain Reynier. Reaching Your Goal Optimally by Playing at Random with No Memory. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{monmege_et_al:LIPIcs.CONCUR.2020.26, author = {Monmege, Benjamin and Parreaux, Julie and Reynier, Pierre-Alain}, title = {{Reaching Your Goal Optimally by Playing at Random with No Memory}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {26:1--26:21}, 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.2020.26}, URN = {urn:nbn:de:0030-drops-128381}, doi = {10.4230/LIPIcs.CONCUR.2020.26}, annote = {Keywords: Weighted games, Algorithmic game theory, Randomisation} }

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

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

Transducers extend finite state automata with outputs, and describe transformations from strings to strings. Sequential transducers, which have a deterministic behaviour regarding their input, are of particular interest. However, unlike finite-state automata, not every transducer can be made sequential. The seminal work of Choffrut allows to characterise, amongst the functional one-way transducers, the ones that admit an equivalent sequential transducer.
In this work, we extend the results of Choffrut to the class of transducers that produce their output string by adding simultaneously, at each transition, a string on the left and a string on the right of the string produced so far. We call them the string-to-context transducers. We obtain a multiple characterisation of the functional string-to-context transducers admitting an equivalent sequential one, based on a Lipschitz property of the function realised by the transducer, and on a pattern (a new twinning property). Last, we prove that given a string-to-context transducer, determining whether there exists an equivalent sequential one is in coNP.

Pierre-Alain Reynier and Didier Villevalois. Sequentiality of String-to-Context Transducers (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 128:1-128:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{reynier_et_al:LIPIcs.ICALP.2019.128, author = {Reynier, Pierre-Alain and Villevalois, Didier}, title = {{Sequentiality of String-to-Context Transducers}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {128:1--128:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.128}, URN = {urn:nbn:de:0030-drops-107042}, doi = {10.4230/LIPIcs.ICALP.2019.128}, annote = {Keywords: Transducers, Sequentiality, Twinning Property, Two-Way 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)

Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the accumulated weight while reaching a target. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. For non-negative weights, the largest class that can be analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the value problem is undecidable, the authors show how to approximate the value by considering regions with a refined granularity. In this work, we extend this class to incorporate negative weights, allowing one to model energy for instance, and prove that the value can still be approximated, with the same complexity. In addition, we show that a symbolic algorithm, relying on the paradigm of value iteration, can be used as an approximation schema on this class.

Damien Busatto-Gaston, Benjamin Monmege, and Pierre-Alain Reynier. Symbolic Approximation of Weighted Timed Games. 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. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{busattogaston_et_al:LIPIcs.FSTTCS.2018.28, author = {Busatto-Gaston, Damien and Monmege, Benjamin and Reynier, Pierre-Alain}, title = {{Symbolic Approximation of Weighted Timed Games}}, booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, pages = {28:1--28:16}, 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.2018.28}, URN = {urn:nbn:de:0030-drops-99277}, doi = {10.4230/LIPIcs.FSTTCS.2018.28}, annote = {Keywords: Weighted timed games, Real-time systems, Game theory, Approximation} }

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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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