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A Proof System for the Linear Time μ-Calculus

  • Christian Dax
  • Martin Hofmann
  • Martin Lange
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4337)

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christian Dax
    • 1
  • Martin Hofmann
    • 2
  • Martin Lange
    • 2
  1. 1.Department of Computer ScienceETH Zürich 
  2. 2.Institut für InformatikLMU München 

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