Christian Dax, Martin Hofmann, and Martin Lange (2006)

# A Proof System for the Linear Time µ-Calculus

In: FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science, 26th International Conference, Kolkata, India, December 13-15, 2006, Proceedings, ed. by S. Arun-Kumar and Naveen Garg, vol. 4337, pp. 273-284, Springer. Lecture Notes in Computer Science (ISBN: 3-540-49994-6).

The linear time μ-calculus extends LTL with arbitrary least and greatest fixpoint operators. This gives it the power to express all ω-regular languages, i.e. strictly more than LTL. The validity problem is PSPACE-complete for both LTL and the linear time μ-calculus. In practice it is more difficult for the latter because of nestings of fixpoint operators and variables with several occurrences. We present a simple sound and complete infinitary proof system for the linear time μ-calculus and then present two decision procedures for provability in the system, hence validity of formulas. One uses nondeterministic Büchi automata, the other one a generalisation of size-change termination analysis (SCT) known from functional programming. The main novelties of this paper are the connection with SCT and the fact that both decision procedures have a better asymptotic complexity than earlier ones and have been implemented. $~$

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