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

Published online by Cambridge University Press:  10 January 2013

Paweł Parys
Paweł Parys*
Affiliation:
Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland.. [email protected]
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Abstract

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).

Keywords

μ-calculusblack-box modellower boundexpression complexity
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 1 , January 2013 , pp. 97 - 109
Copyright
© EDP Sciences 2013

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