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

Shaull Almagor, Orna Kupferman, Yaron Velner

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


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 languageAmerican English
Title of host publication27th International Conference on Concurrency Theory, CONCUR 2016
EditorsJosee Desharnais, Radha Jagadeesan
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770170
StatePublished - 1 Aug 2016
Event27th International Conference on Concurrency Theory, CONCUR 2016 - Quebec City, Canada
Duration: 23 Aug 201626 Aug 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference27th International Conference on Concurrency Theory, CONCUR 2016
CityQuebec City

Bibliographical note

Publisher Copyright:
© Shaull Almagor, Orna Kupferman, and Yaron Velner; licensed under Creative Commons License CC-BY.


  • Mean payoff games
  • Sensing
  • Stochastic and quantitative synthesis


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