Quantitative assume guarantee synthesis

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

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


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 languageEnglish
Title of host publicationComputer Aided Verification - 29th International Conference, CAV 2017, Proceedings
EditorsViktor Kuncak, Rupak Majumdar
Number of pages22
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


Conference29th International Conference on Computer Aided Verification, CAV 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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