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Quantitative Assume Guarantee Synthesis
conference contribution
posted on 2018-05-30, 11:24 authored by Shaull Almagor, Orna Kupferman, Jan Oliver Ringert, Yaron VelnerIn assume-guarantee synthesis, we are given a specification hA, Gi,
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.
Funding
The research leading to these results has received funding from the European Research Council under the European Union’s 7th Framework Programme (FP7/2007-2013, ERC grant no 278410). Shaull Almagor is supported by ERC grant AVS-ISS (648701).
History
Citation
Computer Aided Verification. CAV 2017. Lecture Notes in Computer Science, 2017, 10427.Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of InformaticsSource
Computer Aided Verification - 29th International Conference, CAV 2017, Heidelberg, GermanyVersion
- AM (Accepted Manuscript)