# On model-checking for fragments of μ-calculus

## Abstract

In this paper we considered two different fragments of μ-calculus, logics *L*_{1} and *L*_{2}. We gave model checking algorithms for logics *L*_{1} and *L*_{2} which are of complexity *O*(*m*^{2}*n*) where *m* is the length of the formula and *n* is the size of the structure. We have shown that the logic *L*_{2} is as expressive as ECTL* given in [13]. In additions to these results, we have shown that the model checking problem for the *μ*-calculus is equivalent to the non-emptiness problem of parity tree automata.

It will be interesting to investigate if there is a model checking algorithm for the logics *L*_{1} and *L*_{2} which is only of complexity *O(mn)* instead of *O(m*^{2}*n*. Of course, determining if the model checking problem for the full *μ*-calculus is in P or not, is also an open problem.

## Keywords

Model Check Atomic Proposition Kripke Structure Tree Automaton Model Check Problem## References

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