Synthesizing robust systems

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.