Ensuring Average Recovery with Adversarial Scheduler

In this paper, we focus on revising a given program so that the average recovery time in the presence of an adversarial scheduler is bounded by a given threshold lambda. Specifically, we consider the scenario where the fault (or other unexpected action) perturbs the program to a state that is outside its set of legitimate states. Starting from this state, the program executes its actions/transitions to recover to legitimate states. However, the adversarial scheduler can force the program to reach one illegitimate state that requires a longer recovery time. To ensure that the average recovery time is less than lambda, we need to remove certain transitions/behaviors. We show that achieving this average response time while removing minimum transitions is NP-hard. In other words, there is a tradeoff between the time taken to synthesize the program and the transitions preserved to reduce the average convergence time. We present six different heuristics and evaluate this tradeoff with case studies. Finally, we note that the average convergence time considered here requires formalization of hyperproperties. Hence, this work also demonstrates feasibility of adding (certain) hyperproperties to an existing program.