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black-box model

RAIRO - Theoretical Informatics and Applications (1)

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Some results on complexity of μ-calculusevaluation in the black-box model ∗
Paweł Parys
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 47 / Issue 1 / January 2013

Published online by Cambridge University Press:

10 January 2013, pp. 97-109

Print publication:

January 2013
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We consider μ-calculus formulas in a normal form: after a prefix offixed-point quantifiers follows a quantifier-free expression. We are interested in theproblem of evaluating (model checking) such formulas in a powerset lattice. We assume thatthe quantifier-free part of the expression can be any monotone function given by ablack-box – we may only ask for its value for given arguments. As a first result we provethat when the lattice is fixed, the problem becomes polynomial (the assumption about thequantifier-free part strengthens this result). As a second result we show that anyalgorithm solving the problem has to ask at least about n2(namely Ω(n2/log n)) queries to the function, even when the expressionconsists of one μ and one ν (the assumption about thequantifier-free part weakens this result).

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Some results on complexity of μ-calculusevaluation in the black-box model ∗

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Some results on complexity of μ-calculusevaluation in the black-box model∗

Some results on complexity of μ-calculusevaluation in the black-box model ∗