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Local Model-Checking of Modal Mu-Calculus on Acyclic Labeled Transition Systems

  • Radu Mateescu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2280)

Abstract

Model-checking is a popular technique for verifying finitestate concurrent systems, whose behaviour can be modeled using Labeled Transition Systems (Ltss). In this paper, we study the model-checking problem for the modal µ-calculus on acyclic Ltss. This has various applications of practical interest such as trace analysis, log information auditing, run-time monitoring, etc. We show that on acyclic Ltss, the full µ-calculus has the same expressive power as its alternation-free fragment. We also present two new local model-checking algorithms based upon a translation to boolean equation systems. The first algorithm handles μ-calculus formulas. with alternation depth ad(ϕ)≥ 2 and has time complexity O(∣ϕ∣)2⋅(∣S∣+∣T∣)) and space complexity O(∣ϕ∣2⋅∣S∣), where ∣S∣ and ∣T∣ are the number of states and transitions of the acyclic Lts and ∣ϕ∣ is the number of operators in ϕ The second algorithm handles formulas ϕ with alternation depth ad(ϕ)= 1 and has time complexity O(∣ϕ∣⋅(∣S∣+∣T∣)) and space complexity O(∣ϕ∣⋅∣S∣).

Keywords

Model Check Temporal Logic Space Complexity Conjunctive Normal Form Propositional Variable 
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 2002

Authors and Affiliations

  • Radu Mateescu
    • 1
  1. 1.INRIA Rhône-Alpes / VASYMontbonnot Saint MartinFrance

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