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**Model checking and boolean graphs.**
*(English)*
Zbl 0798.03017

Summary: We describe a method for translating a satisfaction problem of the modal \(\mu\)-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 \(\mu\)-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 \(\mu\)-calculus running in time \(O(| A|^{\text{ad}} | S|^{\text{ad}-1} | T|)\), 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 on earlier algorithms.

### MSC:

03B45 | Modal logic (including the logic of norms) |

68Q85 | Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) |

68Q25 | Analysis of algorithms and problem complexity |

68R10 | Graph theory (including graph drawing) in computer science |

### Keywords:

satisfaction problem; modal \(\mu\)-calculus; marking of a Boolean graph; model checking algorithm
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\textit{H. R. Andersen}, Theor. Comput. Sci. 126, No. 1, 3--30 (1994; Zbl 0798.03017)

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### References:

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