Size-Change Termination and Satisfiability for Linear-Time Temporal Logics

  • Martin Lange
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6989)

Abstract

In the automata-theoretic framework, finite-state automata are used as a machine model to capture the operational content of temporal logics. Decision problems like satisfiability, subsumption, equivalence, etc. then translate into questions on automata like emptiness, inclusion, language equivalence, etc. Linear-time temporal logics like LTL, PSL and the linear-time μ-calculus have relatively simple translations into alternating parity automata, and this automaton model is closed under all Boolean operations with very simple constructions. Thus, the typical decision problems for such linear-time temporal logics reduce relatively simply to the emptiness problem for alternating parity automata. In this paper we present a method for decision this emptiness problem without going through intermediate automaton models like nondeterministic ones. The method is a direct adaptation of the size-change termination principle which was orgininally used to decide termination of abstract functional programs.

Keywords

Temporal Logic Linear Temporal Logic Atomic Proposition Boolean Expression Nest Depth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Lange
    • 1
  1. 1.School of Electr. Eng. and Computer ScienceUniversity of KasselGermany

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