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

Optimally Resilient Strategies in Pushdown Safety Games