Optimally Resilient Strategies in Pushdown Safety Games

TL;DR

This paper extends the concept of resilience in infinite-duration games to pushdown systems, providing algorithms for computing optimally resilient strategies with high computational complexity.

Contribution

It introduces methods to compute optimally resilient strategies in pushdown safety games, including complexity bounds and specialized results for one-counter configurations.

Findings

Computing optimally resilient strategies in pushdown games is triply-exponential.

Resilience degree in one-counter games is PSPACE-complete.

Strategies can be computed in doubly-exponential time for one-counter cases.

Abstract

Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic external influence. This concerns events where the observed system behavior differs from the intended one prescribed by the controller. For games played on finite arenas it is known that computing optimally resilient strategies only incurs a polynomial overhead over solving classical games. This paper studies safety games with disturbances played on infinite arenas induced by pushdown systems. We show how to compute optimally resilient strategies in triply-exponential time. For the subclass of safety games played on one-counter configuration graphs, we show that determining the degree of resilience of the initial configuration is PSPACE-complete and that optimally resilient strategies can be computed in doubly-exponential time.