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On Distributive Fixed-Point Expressions

Published online by Cambridge University Press:  15 August 2002

Helmut Seidl  and
Damian Niwiński
Helmut Seidl
Affiliation:
FB IV – Informatik, Universität Trier, 54286 Trier, Germany
Damian Niwiński
Affiliation:
Institute of Informatics, University of Warsaw, Ul. Banacha 2, 02-097 Warsaw, Poland
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Abstract

For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e' of alternation-depth 2 and size ${\cal O}(r\cdot|e|)$. Expression e' is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of the resulting expression.

Keywords

Fixed-point expressionsdistributivityalternation-depthlower bounds.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 4-5 , July 1999 , pp. 427 - 446
Copyright
© EDP Sciences, 1999

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