You May Delay, but Time Will Not: Timed Games Under Delayed Control

Abstract

Inspired by Martin Fr\"anzle's persistent and influential work on capturing and handling delay inherent to cyber-physical systems in the formal verification of such systems, we study timed games where controllable actions do not take effect immediately, but only after some delay, i.e., they are scheduled for later execution. We show that solving such games is undecidable if an unbounded number of actions can be pending. On the other hand, we present a doubly-exponential time algorithm for games with a bound on the number of pending actions, based on a reduction to classical timed games. This makes timed games under delayed control with bounded schedules solvable with existing tools like UPPAAL.