Abstract
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 | English |
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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 |
ISBN (Electronic) | 9783959770170 |
DOIs | |
State | Published - 1 Aug 2016 |
Event | 27th International Conference on Concurrency Theory, CONCUR 2016 - Quebec City, Canada Duration: 23 Aug 2016 → 26 Aug 2016 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 59 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 27th International Conference on Concurrency Theory, CONCUR 2016 |
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Country/Territory | Canada |
City | Quebec City |
Period | 23/08/16 → 26/08/16 |
Bibliographical note
Publisher Copyright:© Shaull Almagor, Orna Kupferman, and Yaron Velner; licensed under Creative Commons License CC-BY.
Keywords
- Mean payoff games
- Sensing
- Stochastic and quantitative synthesis