License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2016.9
URN: urn:nbn:de:0030-drops-61689
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6168/
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Almagor, Shaull ; Kupferman, Orna ; Velner, Yaron

Minimizing Expected Cost Under Hard Boolean Constraints, with Applications to Quantitative Synthesis

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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.}
}

Keywords: Stochastic and Quantitative Synthesis, Mean Payoff Games, Sensing.
Collection: 27th International Conference on Concurrency Theory (CONCUR 2016)
Issue Date: 2016
Date of publication: 24.08.2016

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