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)


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∣).


Model Check Temporal Logic Space Complexity Conjunctive Normal Form Propositional Variable 
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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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