MoL-2016-09: Temporal Logics, Automata and the Modal $\mu$-Calculus

MoL-2016-09: in 't Veld, Sander (2016) Temporal Logics, Automata and the Modal $\mu$-Calculus. [Report]

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Abstract

Computation tree logic (CTL) and its extension CTL offer a rigorous approach to program verification. The highly expressive modal μ-calculus subsumes both CTL and CTL∗ while remaining computationally well-behaved. Translations from CTL and CTL* into the modal μ-calculus are known, but the resulting fragments have not been identified syntactically. Having an exact characterization of a logic as a fragment of the modal μ-calculus gives a better understanding of the expressivity of both logics involved. An automata theoretic approach serves to form a bridge between logics and game semantics are instrumental when comparing formulas with automata. In this thesis CTL∗ is translated into a class of modal parity automata. An exact characterization of this class of automata as a fragment of the modal μ-calculus is given. Furthermore CTL is fully characterized both as a class of modal automata with singleton clusters and as a one-variable fragment of the modal μ-calculus.

Item Type: Report
Report Nr: MoL-2016-09
Series Name: Master of Logic Thesis (MoL) Series
Year: 2016
Uncontrolled Keywords: computation tree logic, game semantics, automata theory, modal μ-calculus
Subjects: Computation
Date Deposited: 12 Oct 2016 14:39
Last Modified: 12 Oct 2016 14:39
URI: https://eprints.illc.uva.nl/id/eprint/981

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