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Some results on complexity of μ-calculus evaluation 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.. parys@mimuw.edu.pl
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Abstract

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