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Branching Temporal Logics, Automata and Games


Suitable for

MSc in Computer Science
Computer Science and Philosophy, Part C
Computer Science, Part B
Mathematics and Computer Science, Part C
Computer Science, Part C


Model checking has emerged as a powerful method for the formal verification of programs. Temporal logics such as CTL (computational tree logic) and CTL* are widely used to specify programs because they are expressive and easy to understand. Given an abstract model of a program, a model checker (which typically implements the acceptance problem for a class of automata) verifies whether the model meets a given specification. A conceptually attractive method for solving the model checking problem is by reducing it to the solution of (a suitable subclass of) parity games. These are a type of two player infinite game played on a finite graph. The project concerns the connexions between the temporal logics CTL and / or CTL*, automata, and games. Some of the following directions may be explored. 1. Representing CTL / CTL* as classes of alternating tree automata. 2. Inter-translation between CTL / CTL* and classes of alternating tree automata 3. Using B¨uchi games and other subclasses of parity games to analyse the CTL / CTL* model checking problem 4. Efficient implementation of model checking algorithms 5. Application of the model checker to higher-order model checking.


Orna Kupferman, Moshe Y. Vardi, Pierre Wolper: An automata-theoretic approach to branchingtime model checking. J. ACM 47(2): 312-360 (2000).

Rachel Bailey: A Comparative Study of Alorithmics for Solving B¨uchi Games. University of Oxford MSc Dissertation, 2010.