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

Model-checking is a popular technique for verifying finite-state concurrent systems, the behaviour of which can be modeled using Labeled Transition Systems (Ltss). In this report, we study the model-checking problem for the modal mu-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 mu-calculus has the same expressive power as its alternation-free fragment. We also present two new algorithms for local model-checking of mu-calculus formulas on acyclic Ltss. Our algorithms are based upon a translation to boolean equation systems and exhibit a better performance than existing model-checking algorithms applied to acyclic Ltss. The first algorithm handles mu-calculus formulas phi with alternation depth ad (phi) greater or equal than 2 and has time complexity O (|phi|^2 * (|S|+|T|)) and space complexity O (|phi|^2 * |S|), where |S| and |T| are the number of states and transitions of the acyclic Lts and |phi| is the number of operators in phi. The second algorithm handles formulas with alternation depth ad (phi) = 1 and has time complexity O (|phi| * (|S|+|T|)) and space complexity O (|phi| * |S|)