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

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(?) ? 2 and has time complexity O(|?|2 ? (|S|+|T|)) and space complexity O(|?|2 ? |S|), where |S| and |T| are the number of states and transitions of the acyclic LTS and |?| is the number of operators in ?. The second algorithm handles formulas ? with alternation depth ad(?) = 1 and has time complexity O(|?| ? (|S| + |T|)) and space complexity O(|?| ? |S|).

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