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Temporal Logic for Properties with Relative Frequency

Publication Date
Universität Stuttgart, Fakultät 5, Germany, Computer Science Archive
  • Mathematical Logic (Cr F.4.1)
  • Software Engineering Software/Program Verification (Cr D.2.4)
  • Specifying And Verifying And Reasoning About Programs (Cr F.3.1)
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Abstract. Inherently unreliable or fault-tolerant systems demand for a specification formalism that allows the user to express a required ratio of certain observations. Such a requirement can be, e.g. that deadlines in a real-time system must be met in at least 80% of all cases. Logics and in particular temporal logics provide powerful, flexible and well established specification formalisms. We therefore propose fLTL, an extension to linear-time temporal logic that allows for expressing relative frequencies by an intuitive generalization of the temporal operators. We develop a game theoretical methodology and a semantics for temporal logic with counters. For our novel logic, we establish an undecidability result regarding the satisfiability problem but identify a decidable fragment which strictly increases the expressiveness of linear-time temporal logic by allowing, e.g., to express non-context-free properties. Keywords. Specification and Verification, Temporal Logic, Relative Frequency, Availability, Counter Logic

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