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Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with…

Computer Science and Game Theory · Computer Science 2015-09-25 Martin Zimmermann

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with…

Computer Science and Game Theory · Computer Science 2016-01-28 Martin Zimmermann

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. Recently, such games with quantitative winning conditions in weak MSO with the unbounding…

Computer Science and Game Theory · Computer Science 2016-10-11 Felix Klein , Martin Zimmermann

We present an exponential-time algorithm approximating the minimal lookahead necessary to win an $\omega$-regular delay game.

Formal Languages and Automata Theory · Computer Science 2022-03-02 Martin Zimmermann

We demonstrate the usefulness of adding delay to infinite games with quantitative winning conditions. In a delay game, one of the players may delay her moves to obtain a lookahead on her opponent's moves. We show that determining the winner…

Computer Science and Game Theory · Computer Science 2017-04-21 Martin Zimmermann

We investigate determinacy of delay games with Borel winning conditions, infinite-duration two-player games in which one player may delay her moves to obtain a lookahead on her opponent's moves. First, we prove determinacy of such games…

Logic in Computer Science · Computer Science 2015-04-13 Felix Klein , Martin Zimmermann

We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his…

Formal Languages and Automata Theory · Computer Science 2015-07-01 Michael Holtmann , Lukasz Kaiser , Wolfgang Thomas

We compare games under delayed control and delay games, two types of infinite games modelling asynchronicity in reactive synthesis. In games under delayed control both players suffer from partial informedness due to symmetrically delayed…

Computer Science and Game Theory · Computer Science 2025-03-19 Martin Fränzle , Paul Kröger , Sarah Winter , Martin Zimmermann

We show that solving delay games with winning conditions given by deterministic and nondeterministic weak Muller automata is 2EXPTIME-complete respectively 3EXPTIME-complete. Furthermore, doubly and triply exponential lookahead is necessary…

Formal Languages and Automata Theory · Computer Science 2022-10-20 Sarah Winter , Martin Zimmermann

We compare games under delayed control and delay games, two types of infinite games modelling asynchronicity in reactive synthesis. Our main result, the interreducibility of the existence of sure winning strategies for the protagonist,…

Computer Science and Game Theory · Computer Science 2023-10-03 Martin Fränzle , Sarah Winter , Martin Zimmermann

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question and present a very general framework for computing such strategies: they exist for all winning conditions that are recognized by automata with…

Computer Science and Game Theory · Computer Science 2017-09-13 Martin Zimmermann

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

Computer Science and Game Theory · Computer Science 2015-07-29 Dietmar Berwanger , Anup Basil Mathew

We study in depth the class of games with opacity condition, which are two-player games with imperfect information in which one of the players only has imperfect information, and where the winning condition relies on the information he has…

Computer Science and Game Theory · Computer Science 2011-06-08 Bastien Maubert , Sophie Pinchinat , Laura Bozzelli

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the…

Computer Science and Game Theory · Computer Science 2019-12-16 Sarah Winter , Martin Zimmermann

Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…

Computer Science and Game Theory · Computer Science 2020-02-04 Stéphane Le Roux

Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one…

Computer Science and Game Theory · Computer Science 2020-03-20 Christian Kroer , Tuomas Sandholm

We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…

Optimization and Control · Mathematics 2026-02-17 Dean Kraizberg

We study games with reachability objectives under energy constraints. We first prove that under strict energy constraints (either only lower-bound constraint or interval constraint), those games are LOGSPACE-equivalent to energy games with…

Computer Science and Game Theory · Computer Science 2019-09-18 Loïc Hélouët , Nicolas Markey , Ritam Raha

Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…

Logic in Computer Science · Computer Science 2024-01-30 Pete Austin , Sougata Bose , Patrick Totzke

We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound…

Logic in Computer Science · Computer Science 2017-01-16 Patricia Bouyer , Piotr Hofman , Nicolas Markey , Mickael Randour , Martin Zimmermann
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