High-quality synthesis against stochastic environments

Shaull Almagor, Orna Kupferman

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

5 Scopus citations


In the classical synthesis problem, we are given a linear temporal logic (LTL) formula over sets of input and output signals, and we synthesize a transducer that realizes : with every sequence of input signals, the transducer associates a sequence of output signals so that the generated computation satisfies. One weakness of automated synthesis in practice is that it pays no attention to the quality of the synthesized system. Indeed, the classical setting is Boolean: a computation satisfies a specification or does not satisfy it. Accordingly, while the synthesized system is correct, there is no guarantee about its quality. In recent years, researchers have considered extensions of the classical Boolean setting to a quantitative one. The logic LTL[F] is a multi-valued logic that augments LTL with quality operators. The satisfaction value of an LTL[F] formula is a real value in [0, 1], where the higher the value is, the higher is the quality in which the computation satisfies the specification. Decision problems for LTL become search or optimization problems for LTL[F]. In particular, in the synthesis problem, the goal is to generate a transducer that satisfies the specification in the highest possible quality. Previous work considered the worst-case setting, where the goal is to maximize the quality of the computation with the minimal quality. We introduce and solve the stochastic setting, where the goal is to generate a transducer that maximizes the expected quality of a computation, subject to a given distribution of the input signals. Thus, rather than being hostile, the environment is assumed to be probabilistic, which corresponds to many realistic settings. We show that the problem is 2EXPTIME-complete, like classical LTL synthesis. The complexity stays 2EXPTIME also in two extensions we consider: one that maximizes the expected quality while guaranteeing that the minimal quality is, with probability 1, above a given threshold, and one that allows assumptions on the environment.

Original languageAmerican English
Title of host publicationComputer Science Logic 2016, CSL 2016
EditorsJean-Marc Talbot, Laurent Regnier
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770224
StatePublished - 1 Aug 2016
Event25th EACSL Annual Conference on Computer Science Logic, CSL 2016 and the 30th Workshop on Computer Science Logic - Marseille, France
Duration: 29 Aug 20161 Sep 2016

Publication series

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


Conference25th EACSL Annual Conference on Computer Science Logic, CSL 2016 and the 30th Workshop on Computer Science Logic

Bibliographical note

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


  • Markov decision process
  • Stochastic and quantitative synthesis


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