Found 2 Possible Name Variants:

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

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

Our main technical contribution is a polynomial-time determinisation procedure for history-deterministic Büchi automata, which settles an open question of Kuperberg and Skrzypczak, 2015. A key conceptual contribution is the lookahead game, which is a variant of Bagnol and Kuperberg’s token game, in which Adam is given a fixed lookahead. We prove that the lookahead game is equivalent to the 1-token game. This allows us to show that the 1-token game characterises history-determinism for semantically-deterministic Büchi automata, which paves the way to our polynomial-time determinisation procedure.

Rohan Acharya, Marcin Jurdziński, and Aditya Prakash. Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 124:1-124:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{acharya_et_al:LIPIcs.ICALP.2024.124, author = {Acharya, Rohan and Jurdzi\'{n}ski, Marcin and Prakash, Aditya}, title = {{Lookahead Games and Efficient Determinisation of History-Deterministic B\"{u}chi Automata}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {124:1--124:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.124}, URN = {urn:nbn:de:0030-drops-202672}, doi = {10.4230/LIPIcs.ICALP.2024.124}, annote = {Keywords: History determinism, Good-for-games, Automata over infinite words, Games} }

Document

**Published in:** LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

The classic McNaughton-Zielonka algorithm for solving parity games has excellent performance in practice, but its worst-case asymptotic complexity is worse than that of the state-of-the-art algorithms. This work pinpoints the mechanism that is responsible for this relative underperformance and proposes a new technique that eliminates it. The culprit is the wasteful manner in which the results obtained from recursive calls are indiscriminately discarded by the algorithm whenever subgames on which the algorithm is run change. Our new technique is based on firstly enhancing the algorithm to compute attractor decompositions of subgames instead of just winning strategies on them, and then on making it carefully use attractor decompositions computed in prior recursive calls to reduce the size of subgames on which further recursive calls are made. We illustrate the new technique on the classic example of the recursive McNaughton-Zielonka algorithm, but it can be applied to other symmetric attractor-based algorithms that were inspired by it, such as the quasi-polynomial versions of the McNaughton-Zielonka algorithm based on universal trees.

K. S. Thejaswini, Pierre Ohlmann, and Marcin Jurdziński. A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 44:1-44:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{thejaswini_et_al:LIPIcs.FSTTCS.2022.44, author = {Thejaswini, K. S. and Ohlmann, Pierre and Jurdzi\'{n}ski, Marcin}, title = {{A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games}}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)}, pages = {44:1--44:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-261-7}, ISSN = {1868-8969}, year = {2022}, volume = {250}, editor = {Dawar, Anuj and Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.44}, URN = {urn:nbn:de:0030-drops-174365}, doi = {10.4230/LIPIcs.FSTTCS.2022.44}, annote = {Keywords: Parity games, Attractor decomposition, Quasipolynomial Algorithms, Universal trees} }

Document

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

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

The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices n and linear in (d/(2k))^k, where d is the number of priorities and k is the Strahler number. This complexity is quasi-polynomial because the Strahler number is at most logarithmic in the number of vertices. The proof is based on a new construction of small Strahler-universal trees.
It is shown that the Strahler number of a parity game is a robust, and hence arguably natural, parameter: it coincides with its alternative version based on trees of progress measures and - remarkably - with the register number defined by Lehtinen (2018). It follows that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices and linear in (d/(2k))^k, where k is the register number. This significantly improves the running times and space achieved for parity games of bounded register number by Lehtinen (2018) and by Parys (2020).
The running time of the algorithm based on small Strahler-universal trees yields a novel trade-off k ⋅ lg(d/k) = O(log n) between the two natural parameters that measure the structural complexity of a parity game, which allows solving parity games in polynomial time. This includes as special cases the asymptotic settings of those parameters covered by the results of Calude, Jain Khoussainov, Li, and Stephan (2017), of Jurdziński and Lazić (2017), and of Lehtinen (2018), and it significantly extends the range of such settings, for example to d = 2^O(√{lg n}) and k = O(√{lg n}).

Laure Daviaud, Marcin Jurdziński, and K. S. Thejaswini. The Strahler Number of a Parity Game. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 123:1-123:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2020.123, author = {Daviaud, Laure and Jurdzi\'{n}ski, Marcin and Thejaswini, K. S.}, title = {{The Strahler Number of a Parity Game}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {123:1--123:19}, 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.2020.123}, URN = {urn:nbn:de:0030-drops-125304}, doi = {10.4230/LIPIcs.ICALP.2020.123}, annote = {Keywords: parity game, attractor decomposition, progress measure, universal tree, Strahler number} }

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

An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is quasi-polynomial, and it is polynomial if the asymptotic number of priorities is at most logarithmic in the number of states. This is an exponential improvement on the translation of Kupferman and Vardi (2001) and a quasi-polynomial improvement on the translation of Boker and Lehtinen (2018). Any slightly better such translation would (if - like all presently known such translations - it is efficiently constructive) lead to algorithms for solving parity games that are asymptotically faster in the worst case than the current state of the art (Calude, Jain, Khoussainov, Li, and Stephan, 2017; Jurdziński and Lazić, 2017; and Fearnley, Jain, Schewe, Stephan, and Wojtczak, 2017), and hence it would yield a significant breakthrough.

Laure Daviaud, Marcin Jurdziński, and Karoliina Lehtinen. Alternating Weak Automata from Universal Trees. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{daviaud_et_al:LIPIcs.CONCUR.2019.18, author = {Daviaud, Laure and Jurdzi\'{n}ski, Marcin and Lehtinen, Karoliina}, title = {{Alternating Weak Automata from Universal Trees}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {18:1--18:14}, 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.2019.18}, URN = {urn:nbn:de:0030-drops-109208}, doi = {10.4230/LIPIcs.CONCUR.2019.18}, annote = {Keywords: alternating automata, weak automata, B\"{u}chi automata, parity automata, parity games, universal trees} }

Document

**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous.

Laure Daviaud, Marcin Jurdzinski, Ranko Lazic, Filip Mazowiecki, Guillermo A. Pérez, and James Worrell. When is Containment Decidable for Probabilistic Automata?. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 121:1-121:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2018.121, author = {Daviaud, Laure and Jurdzinski, Marcin and Lazic, Ranko and Mazowiecki, Filip and P\'{e}rez, Guillermo A. and Worrell, James}, title = {{When is Containment Decidable for Probabilistic Automata?}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {121:1--121:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.121}, URN = {urn:nbn:de:0030-drops-91251}, doi = {10.4230/LIPIcs.ICALP.2018.121}, annote = {Keywords: Probabilistic automata, Containment, Emptiness, Ambiguity} }

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

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players - Player Min and Player Max - by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space.

Shibashis Guha, Marcin Jurdzinski, Shankara Narayanan Krishna, and Ashutosh Trivedi. Mean-Payoff Games on Timed Automata. 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. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2016.44, author = {Guha, Shibashis and Jurdzinski, Marcin and Krishna, Shankara Narayanan and Trivedi, Ashutosh}, title = {{Mean-Payoff Games on Timed Automata}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {44:1--44:14}, 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.2016.44}, URN = {urn:nbn:de:0030-drops-68797}, doi = {10.4230/LIPIcs.FSTTCS.2016.44}, annote = {Keywords: Timed Automata, Mean-Payoff Games, Controller-Synthesis} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

The covering and boundedness problems for
branching vector addition systems
are shown complete for doubly-exponential time.

Stéphane Demri, Marcin Jurdzinski, Oded Lachish, and Ranko Lazic. The Covering and Boundedness Problems for Branching Vector Addition Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 181-192, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{demri_et_al:LIPIcs.FSTTCS.2009.2317, author = {Demri, St\'{e}phane and Jurdzinski, Marcin and Lachish, Oded and Lazic, Ranko}, title = {{The Covering and Boundedness Problems for Branching Vector Addition Systems}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {181--192}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2317}, URN = {urn:nbn:de:0030-drops-23173}, doi = {10.4230/LIPIcs.FSTTCS.2009.2317}, annote = {Keywords: Vector addition systems, Petri nets, covering, boundedness, computational complexity} }

Document

**Published in:** LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

An average-time game is played on the infinite graph of
configurations of a finite timed automaton.
The two players, Min and Max, construct an infinite run of the
automaton by taking turns to perform a timed transition.
Player Min wants to minimize the average time per transition and
player Max wants to maximize it.
A solution of average-time games is presented using a reduction to
average-price game on a finite graph.
A direct consequence is an elementary proof of determinacy for
average-time games.
This complements our results for reachability-time games and
partially solves a problem posed by Bouyer et al., to design an
algorithm for solving average-price games on priced timed
automata.
The paper also establishes the exact computational complexity of
solving average-time games: the problem is EXPTIME-complete for
timed automata with at least two clocks.

Marcin Jurdzinski and Ashutosh Trivedi. Average-Time Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 340-351, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{jurdzinski_et_al:LIPIcs.FSTTCS.2008.1765, author = {Jurdzinski, Marcin and Trivedi, Ashutosh}, title = {{Average-Time Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {340--351}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-08-8}, ISSN = {1868-8969}, year = {2008}, volume = {2}, editor = {Hariharan, Ramesh and Mukund, Madhavan and Vinay, V}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1765}, URN = {urn:nbn:de:0030-drops-17650}, doi = {10.4230/LIPIcs.FSTTCS.2008.1765}, annote = {Keywords: Games on Timed Automata, Mean-payoff Games, Average-Time Games, Game Theory} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 7471, Equilibrium Computation (2008)

From 18 to 23 November 2007, the Dagstuhl Seminar 07471 ``Equilibrium Computation'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

P. Jean-Jacques Herings, Marcin Jurdzinski, Peter Bro Miltersen, Eva Tardos, and Bernhard von Stengel. 07471 Abstracts Collection – Equilibrium Computation. In Equilibrium Computation. Dagstuhl Seminar Proceedings, Volume 7471, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{herings_et_al:DagSemProc.07471.1, author = {Herings, P. Jean-Jacques and Jurdzinski, Marcin and Bro Miltersen, Peter and Tardos, Eva and von Stengel, Bernhard}, title = {{07471 Abstracts Collection – Equilibrium Computation}}, booktitle = {Equilibrium Computation}, pages = {1--15}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7471}, editor = {P. Jean-Jacques Herings and Marcin Jurdzinski and Peter Bro Miltersen and Eva Tardos and Bernhard von Stengel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07471.1}, URN = {urn:nbn:de:0030-drops-15286}, doi = {10.4230/DagSemProc.07471.1}, annote = {Keywords: Equilibrium, algorithm, polynomial time, game theory, economics} }

Document

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

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

Our main technical contribution is a polynomial-time determinisation procedure for history-deterministic Büchi automata, which settles an open question of Kuperberg and Skrzypczak, 2015. A key conceptual contribution is the lookahead game, which is a variant of Bagnol and Kuperberg’s token game, in which Adam is given a fixed lookahead. We prove that the lookahead game is equivalent to the 1-token game. This allows us to show that the 1-token game characterises history-determinism for semantically-deterministic Büchi automata, which paves the way to our polynomial-time determinisation procedure.

Rohan Acharya, Marcin Jurdziński, and Aditya Prakash. Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 124:1-124:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{acharya_et_al:LIPIcs.ICALP.2024.124, author = {Acharya, Rohan and Jurdzi\'{n}ski, Marcin and Prakash, Aditya}, title = {{Lookahead Games and Efficient Determinisation of History-Deterministic B\"{u}chi Automata}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {124:1--124:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.124}, URN = {urn:nbn:de:0030-drops-202672}, doi = {10.4230/LIPIcs.ICALP.2024.124}, annote = {Keywords: History determinism, Good-for-games, Automata over infinite words, Games} }

Document

**Published in:** LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

The classic McNaughton-Zielonka algorithm for solving parity games has excellent performance in practice, but its worst-case asymptotic complexity is worse than that of the state-of-the-art algorithms. This work pinpoints the mechanism that is responsible for this relative underperformance and proposes a new technique that eliminates it. The culprit is the wasteful manner in which the results obtained from recursive calls are indiscriminately discarded by the algorithm whenever subgames on which the algorithm is run change. Our new technique is based on firstly enhancing the algorithm to compute attractor decompositions of subgames instead of just winning strategies on them, and then on making it carefully use attractor decompositions computed in prior recursive calls to reduce the size of subgames on which further recursive calls are made. We illustrate the new technique on the classic example of the recursive McNaughton-Zielonka algorithm, but it can be applied to other symmetric attractor-based algorithms that were inspired by it, such as the quasi-polynomial versions of the McNaughton-Zielonka algorithm based on universal trees.

K. S. Thejaswini, Pierre Ohlmann, and Marcin Jurdziński. A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 44:1-44:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{thejaswini_et_al:LIPIcs.FSTTCS.2022.44, author = {Thejaswini, K. S. and Ohlmann, Pierre and Jurdzi\'{n}ski, Marcin}, title = {{A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games}}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)}, pages = {44:1--44:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-261-7}, ISSN = {1868-8969}, year = {2022}, volume = {250}, editor = {Dawar, Anuj and Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.44}, URN = {urn:nbn:de:0030-drops-174365}, doi = {10.4230/LIPIcs.FSTTCS.2022.44}, annote = {Keywords: Parity games, Attractor decomposition, Quasipolynomial Algorithms, Universal trees} }

Document

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

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

The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices n and linear in (d/(2k))^k, where d is the number of priorities and k is the Strahler number. This complexity is quasi-polynomial because the Strahler number is at most logarithmic in the number of vertices. The proof is based on a new construction of small Strahler-universal trees.
It is shown that the Strahler number of a parity game is a robust, and hence arguably natural, parameter: it coincides with its alternative version based on trees of progress measures and - remarkably - with the register number defined by Lehtinen (2018). It follows that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices and linear in (d/(2k))^k, where k is the register number. This significantly improves the running times and space achieved for parity games of bounded register number by Lehtinen (2018) and by Parys (2020).
The running time of the algorithm based on small Strahler-universal trees yields a novel trade-off k ⋅ lg(d/k) = O(log n) between the two natural parameters that measure the structural complexity of a parity game, which allows solving parity games in polynomial time. This includes as special cases the asymptotic settings of those parameters covered by the results of Calude, Jain Khoussainov, Li, and Stephan (2017), of Jurdziński and Lazić (2017), and of Lehtinen (2018), and it significantly extends the range of such settings, for example to d = 2^O(√{lg n}) and k = O(√{lg n}).

Laure Daviaud, Marcin Jurdziński, and K. S. Thejaswini. The Strahler Number of a Parity Game. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 123:1-123:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2020.123, author = {Daviaud, Laure and Jurdzi\'{n}ski, Marcin and Thejaswini, K. S.}, title = {{The Strahler Number of a Parity Game}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {123:1--123:19}, 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.2020.123}, URN = {urn:nbn:de:0030-drops-125304}, doi = {10.4230/LIPIcs.ICALP.2020.123}, annote = {Keywords: parity game, attractor decomposition, progress measure, universal tree, Strahler number} }

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

An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is quasi-polynomial, and it is polynomial if the asymptotic number of priorities is at most logarithmic in the number of states. This is an exponential improvement on the translation of Kupferman and Vardi (2001) and a quasi-polynomial improvement on the translation of Boker and Lehtinen (2018). Any slightly better such translation would (if - like all presently known such translations - it is efficiently constructive) lead to algorithms for solving parity games that are asymptotically faster in the worst case than the current state of the art (Calude, Jain, Khoussainov, Li, and Stephan, 2017; Jurdziński and Lazić, 2017; and Fearnley, Jain, Schewe, Stephan, and Wojtczak, 2017), and hence it would yield a significant breakthrough.

Laure Daviaud, Marcin Jurdziński, and Karoliina Lehtinen. Alternating Weak Automata from Universal Trees. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{daviaud_et_al:LIPIcs.CONCUR.2019.18, author = {Daviaud, Laure and Jurdzi\'{n}ski, Marcin and Lehtinen, Karoliina}, title = {{Alternating Weak Automata from Universal Trees}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {18:1--18:14}, 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.2019.18}, URN = {urn:nbn:de:0030-drops-109208}, doi = {10.4230/LIPIcs.CONCUR.2019.18}, annote = {Keywords: alternating automata, weak automata, B\"{u}chi automata, parity automata, parity games, universal trees} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous.

Laure Daviaud, Marcin Jurdzinski, Ranko Lazic, Filip Mazowiecki, Guillermo A. Pérez, and James Worrell. When is Containment Decidable for Probabilistic Automata?. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 121:1-121:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2018.121, author = {Daviaud, Laure and Jurdzinski, Marcin and Lazic, Ranko and Mazowiecki, Filip and P\'{e}rez, Guillermo A. and Worrell, James}, title = {{When is Containment Decidable for Probabilistic Automata?}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {121:1--121:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.121}, URN = {urn:nbn:de:0030-drops-91251}, doi = {10.4230/LIPIcs.ICALP.2018.121}, annote = {Keywords: Probabilistic automata, Containment, Emptiness, Ambiguity} }

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

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players - Player Min and Player Max - by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space.

Shibashis Guha, Marcin Jurdzinski, Shankara Narayanan Krishna, and Ashutosh Trivedi. Mean-Payoff Games on Timed Automata. 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. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2016.44, author = {Guha, Shibashis and Jurdzinski, Marcin and Krishna, Shankara Narayanan and Trivedi, Ashutosh}, title = {{Mean-Payoff Games on Timed Automata}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {44:1--44:14}, 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.2016.44}, URN = {urn:nbn:de:0030-drops-68797}, doi = {10.4230/LIPIcs.FSTTCS.2016.44}, annote = {Keywords: Timed Automata, Mean-Payoff Games, Controller-Synthesis} }

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**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

The covering and boundedness problems for
branching vector addition systems
are shown complete for doubly-exponential time.

Stéphane Demri, Marcin Jurdzinski, Oded Lachish, and Ranko Lazic. The Covering and Boundedness Problems for Branching Vector Addition Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 181-192, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{demri_et_al:LIPIcs.FSTTCS.2009.2317, author = {Demri, St\'{e}phane and Jurdzinski, Marcin and Lachish, Oded and Lazic, Ranko}, title = {{The Covering and Boundedness Problems for Branching Vector Addition Systems}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {181--192}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2317}, URN = {urn:nbn:de:0030-drops-23173}, doi = {10.4230/LIPIcs.FSTTCS.2009.2317}, annote = {Keywords: Vector addition systems, Petri nets, covering, boundedness, computational complexity} }

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**Published in:** LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

An average-time game is played on the infinite graph of
configurations of a finite timed automaton.
The two players, Min and Max, construct an infinite run of the
automaton by taking turns to perform a timed transition.
Player Min wants to minimize the average time per transition and
player Max wants to maximize it.
A solution of average-time games is presented using a reduction to
average-price game on a finite graph.
A direct consequence is an elementary proof of determinacy for
average-time games.
This complements our results for reachability-time games and
partially solves a problem posed by Bouyer et al., to design an
algorithm for solving average-price games on priced timed
automata.
The paper also establishes the exact computational complexity of
solving average-time games: the problem is EXPTIME-complete for
timed automata with at least two clocks.

Marcin Jurdzinski and Ashutosh Trivedi. Average-Time Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 340-351, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{jurdzinski_et_al:LIPIcs.FSTTCS.2008.1765, author = {Jurdzinski, Marcin and Trivedi, Ashutosh}, title = {{Average-Time Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {340--351}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-08-8}, ISSN = {1868-8969}, year = {2008}, volume = {2}, editor = {Hariharan, Ramesh and Mukund, Madhavan and Vinay, V}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1765}, URN = {urn:nbn:de:0030-drops-17650}, doi = {10.4230/LIPIcs.FSTTCS.2008.1765}, annote = {Keywords: Games on Timed Automata, Mean-payoff Games, Average-Time Games, Game Theory} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 7471, Equilibrium Computation (2008)

From 18 to 23 November 2007, the Dagstuhl Seminar 07471 ``Equilibrium Computation'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

P. Jean-Jacques Herings, Marcin Jurdzinski, Peter Bro Miltersen, Eva Tardos, and Bernhard von Stengel. 07471 Abstracts Collection – Equilibrium Computation. In Equilibrium Computation. Dagstuhl Seminar Proceedings, Volume 7471, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{herings_et_al:DagSemProc.07471.1, author = {Herings, P. Jean-Jacques and Jurdzinski, Marcin and Bro Miltersen, Peter and Tardos, Eva and von Stengel, Bernhard}, title = {{07471 Abstracts Collection – Equilibrium Computation}}, booktitle = {Equilibrium Computation}, pages = {1--15}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7471}, editor = {P. Jean-Jacques Herings and Marcin Jurdzinski and Peter Bro Miltersen and Eva Tardos and Bernhard von Stengel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07471.1}, URN = {urn:nbn:de:0030-drops-15286}, doi = {10.4230/DagSemProc.07471.1}, annote = {Keywords: Equilibrium, algorithm, polynomial time, game theory, economics} }