On the orthographic dimension of definable sets

Authors:
Stavros Cosmadakis;Gabriel Kuper;Leonid Libkin
Affiliations:
University of Patras, Greece;Bell Laboratories, Murray Hill, NJ;Bell Laboratories, Murray Hill, NJ, and University of Toronto, Ontario, Ont., Canada
Venue:
Information Processing Letters
Year:
2001

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Abstract

A formula &psgr; (x1,...,xn) conforms to a partition P of {x 1, ...,xn} if is equivalent to a Boolean combination of formulae that do not have free variables from more than one block of P. We show that if &psgr; conforms to two partitions P1 and P1 and P2, it also conforms to their greatest lower bound in the partition lattice. As a corollary, we obtain that the concept of orthographic dimension of a constraint-definable set, introduced in the field of constraint databases, is well-defined. 2001 Elsevier Science B.V. All rights reserved.