Strategies Resilient to Delay: Games under Delayed Control vs. Delay Games

TL;DR

This paper compares two types of infinite games modeling asynchronicity in reactive synthesis, establishing a key interreducibility result that transfers complexity bounds from delay games to delayed control games, with some limitations for randomized strategies.

Contribution

It proves the interreducibility of sure winning strategies between delay games and delayed control games, enabling transfer of complexity results and bounds.

Findings

Existence of sure winning strategies is interreducible between the two game types.

Complexity bounds for delay games apply to delayed control games via this interreducibility.

The correspondence breaks down for almost-sure winning strategies with randomized strategies.

Abstract

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, 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 analyze existence of randomized strategies that win almost surely, where this correspondence between the two types of games breaks down.