# Some results on complexity of μ-calculus evaluation in the black-box model

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2013)

- Volume: 47, Issue: 1, page 97-109
- ISSN: 0988-3754

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topParys, Paweł. "Some results on complexity of μ-calculus evaluation in the black-box model." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 47.1 (2013): 97-109. <http://eudml.org/doc/273068>.

@article{Parys2013,

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).},

author = {Parys, Paweł},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {μ-calculus; black-box model; lower bound; expression complexity; -calculus},

language = {eng},

number = {1},

pages = {97-109},

publisher = {EDP-Sciences},

title = {Some results on complexity of μ-calculus evaluation in the black-box model},

url = {http://eudml.org/doc/273068},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Parys, Paweł

TI - Some results on complexity of μ-calculus evaluation in the black-box model

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 1

SP - 97

EP - 109

AB - 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).

LA - eng

KW - μ-calculus; black-box model; lower bound; expression complexity; -calculus

UR - http://eudml.org/doc/273068

ER -

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