## Abstract

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 language | American English |
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Title of host publication | Computer Aided Verification - 29th International Conference, CAV 2017, Proceedings |

Editors | Viktor Kuncak, Rupak Majumdar |

Publisher | Springer Verlag |

Pages | 353-374 |

Number of pages | 22 |

ISBN (Print) | 9783319633893 |

DOIs | |

State | Published - 2017 |

Event | 29th International Conference on Computer Aided Verification, CAV 2017 - Heidelberg, Germany Duration: 24 Jul 2017 → 28 Jul 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10427 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 29th International Conference on Computer Aided Verification, CAV 2017 |
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Country/Territory | Germany |

City | Heidelberg |

Period | 24/07/17 → 28/07/17 |

### Bibliographical note

Funding Information: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).

Publisher Copyright:

© Springer International Publishing AG 2017