Minimizing expected cost under hard boolean constraints, with applications to quantitative synthesis

Conference item

In Boolean synthesis, we are given an LTL specification, and the goal is to construct a transducer that realizes it against an adversarial environment. Often, a specification contains both Boolean requirements that should be satisfied against an adversarial environment, and multi-valued components that refer to the quality of the satisfaction and whose expected cost we would like to minimize with respect to a probabilistic environment. In this work we study, for the first time, mean-payoff games in which the system aims at minimizing the expected cost against a probabilistic environment, while surely satisfying an ω-regular condition against an adversarial environment. We consider the case the ω-regular condition is given as a parity objective or by an LTL formula. We show that in general, optimal strategies need not exist, and moreover, the limit value cannot be approximated by finite-memory strategies. We thus focus on computing the limit-value, and give tight complexity bounds for synthesizing ϵ-optimal strategies for both finite-memory and infinite-memory strategies. We show that our game naturally arises in various contexts of synthesis with Boolean and multi-valued objectives. Beyond direct applications, in synthesis with costs and rewards to certain behaviors, it allows us to compute the minimal sensing cost of ω-regular specifications - a measure of quality in which we look for a transducer that minimizes the expected number of signals that are read from the input.

Authors: Almagor, S; Kupferman, O; Velner, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Leibniz Center for Informatics
• Host title: 27th International Conference on Concurrency Theory (CONCUR 2016)
• Journal: 27th International Conference on Concurrency Theory (CONCUR 2016)
• Publication date: 2016-08-01
• Acceptance date: 2016-06-08
• DOI: 10.4230/LIPIcs.CONCUR.2016.9
• ISSN: 1868-8969
• Keywords: Sensing; Mean Payoff Games; Stochastic and Quantitative Synthesis