Quantifying Bounds in Strategy Logic

Authors Nathanaël Fijalkow , Bastien Maubert , Aniello Murano, Sasha Rubin

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Nathanaël Fijalkow
  • CNRS, LaBRI, Bordeaux, France, Alan Turing Institute of data science, London, United Kingdom
Bastien Maubert
  • University of Naples "Federico II", Naples, Italy
Aniello Murano
  • University of Naples "Federico II", Naples, Italy
Sasha Rubin
  • University of Naples "Federico II", Naples, Italy

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Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, and Sasha Rubin. Quantifying Bounds in Strategy Logic. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Program synthesis constructs programs from specifications in an automated way. Strategy Logic (SL) is a powerful and versatile specification language whose goal is to give theoretical foundations for program synthesis in a multi-agent setting. One limitation of Strategy Logic is that it is purely qualitative. For instance it cannot specify quantitative properties of executions such as "every request is quickly granted", or quantitative properties of trees such as "most executions of the system terminate". In this work, we extend Strategy Logic to include quantitative aspects in a way that can express bounds on "how quickly" and "how many". We define Prompt Strategy Logic, which encompasses Prompt LTL (itself an extension of LTL with a prompt eventuality temporal operator), and we define Bounded-Outcome Strategy Logic which has a bounded quantifier on paths. We supply a general technique, based on the study of automata with counters, that solves the model-checking problems for both these logics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Prompt LTL
  • Strategy Logic
  • Model checking
  • Automata with counters


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