Quantitative assume guarantee synthesis

Shaull Almagor, Orna Kupferman, Jan Oliver Ringert, Yaron Velner*

*Corresponding author for this work

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

14 Scopus citations


In assume-guarantee synthesis, we are given a specification <A, G>, describing an assumption on the environment and a guarantee for the system, and we construct a system that interacts with an environment and is guaranteed to satisfy G whenever the environment satisfies A. While assume-guarantee synthesis is 2EXPTIME-complete for specifications in LTL, researchers have identified the GR(1) fragment of LTL, which supports assume-guarantee reasoning and for which synthesis has an efficient symbolic solution. In recent years we see a transition to quantitative synthesis, in which the specification formalism is multi-valued and the goal is to generate high-quality systems, namely ones that maximize the satisfaction value of the specification. We study quantitative assume-guarantee synthesis. We start with specifications in LTL[F], an extension of LTL by 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. We define the quantitative extension GR(1)[F] of GR(1). We show that the implication relation, which is at the heart of assume-guarantee reasoning, has two natural semantics in the quantitative setting. Indeed, in addition to max{1 − A, G}, which is the multi-valued counterpart of Boolean implication, there are settings in which maximizing the ratio G/A is more appropriate. We show that GR(1)[F] formulas in both semantics are hard to synthesize. Still, in the implication semantics, we can reduce GR(1)[F] synthesis to GR(1) synthesis and apply its efficient symbolic algorithm. For the ratio semantics, we present a sound approximation, which can also be solved efficiently. Our experimental results show that our approach can successfully synthesize GR(1)[F] specifications with over a million of concrete states.

Original languageAmerican English
Title of host publicationComputer Aided Verification - 29th International Conference, CAV 2017, Proceedings
EditorsViktor Kuncak, Rupak Majumdar
PublisherSpringer Verlag
Number of pages22
ISBN (Print)9783319633893
StatePublished - 2017
Event29th International Conference on Computer Aided Verification, CAV 2017 - Heidelberg, Germany
Duration: 24 Jul 201728 Jul 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10427 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th International Conference on Computer Aided Verification, CAV 2017

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017


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