—Many specifications include assumptions on the environment. If the environment satisfies the assumptions then a correct system reacts as intended. However, when the environment deviates from its expected behavior, a correct system can behave arbitrarily. We want to synthesize robust systems that degrade gracefully, i.e., a small number of environment failures should induce a small number of system failures. We define ratio games and show that an optimal robust system corresponds to the winning strategy of a ratio game, where the system minimizes the ratio of system errors to environment errors. We show that ratio games can be solved in pseudopolynomial time.
Roderick Bloem, Karin Greimel, Thomas A. Henzinger