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.
|Original language||American English|
|Title of host publication||27th International Conference on Concurrency Theory, CONCUR 2016|
|Editors||Josee Desharnais, Radha Jagadeesan|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - 1 Aug 2016|
|Event||27th International Conference on Concurrency Theory, CONCUR 2016 - Quebec City, Canada|
Duration: 23 Aug 2016 → 26 Aug 2016
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||27th International Conference on Concurrency Theory, CONCUR 2016|
|Period||23/08/16 → 26/08/16|
Bibliographical noteFunding Information:
The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 278410, from the Israel Science Foundation (grant no 1229/10), and from the US-Israel Binational Science Foundation (grant no 2010431).
© Shaull Almagor, Orna Kupferman, and Yaron Velner; licensed under Creative Commons License CC-BY.
- Mean payoff games
- Stochastic and quantitative synthesis