Problem
Research questions and friction points this paper is trying to address.
Compare delayed control and delay games
Analyze winning strategies under partial informedness
Determine probability thresholds for game outcomes
On the Existence of Reactive Strategies Resilient to Delay
🤖 AI Summary
This work investigates the impact of delay on strategy existence in reactive synthesis, focusing on delay control games and delay games. To address information incompleteness induced by symmetric communication delays, we establish the first mutual reduction between these two models concerning deterministic strategy existence. We reveal their inherent non-determinacy under randomized strategies and prove that any rational probability threshold can be *exactly* realized in delay control games. By transferring complexity results and delay-bound characterizations from delay games to delay control games, we rigorously refute their strategic equivalence, proving the former to be strictly weaker. Finally, we construct explicit counterexamples that achieve *exact* winning probabilities equal to any given rational number, thereby systematically characterizing the fundamental limitations imposed by delay structure and information asymmetry on strategic capability.
📝 Abstract
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 $ heta in [0,1]$ there is a game that can be won by the protagonist with exactly probability $ heta$ 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Interreducibility of sure winning strategies
Randomized strategies for almost certain wins
Quantitative winning probability in delayed control
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