Abstract
We describe a method for translating a satisfaction problem of the modal μ-calculus into a problem of finding a certain marking of a boolean graph. By giving algorithms to solve the graph problem, we present a global model checking algorithm for a subset of the modal μ-calculus, which has time-complexity O(| A|| T|), where | A| is the size of the assertion and | T| is the size of the model (a labelled transition system). This algorithm is extended to an algorithm for the full modal μ-calculus running in time O(| A| ad | S| ad−1 | T|), where ad is the alternation depth and | S| is the number of states in the transition system, improving on earlier presented algorithms. Moreover, a local algorithm is presented for alternation depth one. This algorithm runs in time O(| A|| T|log(| A|| T|)) and is also an improvement over earlier algorithms.
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