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Martin Fränzle ; Paul Kröger ; Sarah Winter ; Martin Zimmermann - On the Existence of Reactive Strategies Resilient to Delay

lmcs:13220 - Logical Methods in Computer Science, March 12, 2025, Volume 21, Issue 1 - https://doi.org/10.46298/lmcs-21(1:24)2025
On the Existence of Reactive Strategies Resilient to DelayArticle

Authors: Martin Fränzle ; Paul Kröger ; Sarah Winter ; Martin Zimmermann

    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 communication, while in delay games, the protagonist has to grant lookahead to the alter player. Our first main result, the interreducibility of the existence of sure winning strategies for the protagonist, allows to transfer known complexity results and bounds on the delay from delay games to games under delayed control, for which no such results had been known. We furthermore analyse existence of randomized strategies that win almost surely, where this correspondence between the two types of games breaks down. In this setting, some games surely won by the alter player in delay games can now be won almost surely by the protagonist in the corresponding game under delayed control, showing that it indeed makes a difference whether the protagonist has to grant lookahead or both players suffer from partial informedness. These results get even more pronounced when we finally address the quantitative goal of winning with a probability in [0,1]. We show that for any rational threshold θ[0,1] there is a game that can be won by the protagonist with exactly probability θ under delayed control, while being surely won by alter in the delay game setting. All these findings refine our original result that games under delayed control are not determined.


    Volume: Volume 21, Issue 1
    Published on: March 12, 2025
    Accepted on: February 10, 2025
    Submitted on: March 13, 2024
    Keywords: Computer Science - Computer Science and Game Theory,Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science

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