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Algebraic and graph-theoretic properties ofinfinite n-posets

Published online by Cambridge University Press:  15 March 2005

Zoltán Ésik  and
Zoltán L. Németh
Zoltán Ésik
Affiliation:
Department of Computer Science, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary; [email protected]
Zoltán L. Németh
Affiliation:
Department of Computer Science, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary; [email protected]
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Abstract

A Σ-labeled n-poset is an (at most) countable set, labeled in the set Σ, equipped with n partial orders. The collection of all Σ-labeled n-posets is naturally equipped with n binary product operations and nω-ary product operations. Moreover, the ω-ary product operations give rise to nω-power operations. We show that those Σ-labeled n-posets that can be generated from the singletons by the binary and ω-ary product operations form the free algebra on Σ in a variety axiomatizable by an infinite collection of simple equations. When n = 1, this variety coincides with the class of ω-semigroups of Perrin and Pin. Moreover, we show that those Σ-labeled n-posets that can be generated from the singletons by the binary product operations and the ω-power operations form the free algebra on Σ in a related variety that generalizes Wilke's algebras. We also give graph-theoretic characterizations of those n-posets contained in the above free algebras. Our results serve as a preliminary study to a development of a theory of higher dimensional automata and languages on infinitary associative structures.

Keywords

Posetn-posetcompositionfree algebraequational logic
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 305 - 322
Copyright
© EDP Sciences, 2005

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