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 omega-regular condition against an adversarial environment.
We consider the case the omega-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 epsilon-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 omega-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.
BibTeX - Entry
@InProceedings{almagor_et_al:LIPIcs:2016:6168,
author = {Shaull Almagor and Orna Kupferman and Yaron Velner},
title = {{Minimizing Expected Cost Under Hard Boolean Constraints, with Applications to Quantitative Synthesis}},
booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)},
pages = {9:1--9:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-017-0},
ISSN = {1868-8969},
year = {2016},
volume = {59},
editor = {Jos{\'e}e Desharnais and Radha Jagadeesan},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6168},
URN = {urn:nbn:de:0030-drops-61689},
doi = {10.4230/LIPIcs.CONCUR.2016.9},
annote = {Keywords: Stochastic and Quantitative Synthesis, Mean Payoff Games, Sensing.}
}
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Keywords: |
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Stochastic and Quantitative Synthesis, Mean Payoff Games, Sensing. |
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Collection: |
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27th International Conference on Concurrency Theory (CONCUR 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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24.08.2016 |
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)