1 Department of Computer Science, Faculty of Science, Aarhus University, Aarhus University2 Department of Computer Science, ETH Zürich3 Institut für Informatik, LMU München
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.
Fsttcs '06: Foundations of Software Technology and Theoretical Computer Science, 26th International Conference, 2006, p. 273-284
Main Research Area:
Lecture Notes in Computer Science
A Proof System for the Linear Time <em>μ</em>-Calculus, 2006