Axiomatizing the subsumption and subword preorders on finite and infinite partial words

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Abstract

We consider two-sorted algebras of finite and infinite partial words equipped with the subsumption preorder and the operations of series and parallel product and omega power. It is shown that the valid equations and inequations of these algebras can be described by an infinite collection of simple axioms, and that no finite axiomatization exists. We also prove similar results for two related preorders, namely for the induced partial subword preorder and the partial subword preorder. Along the way of proving these results, we provide a concrete description of the free algebras in the corresponding varieties in terms of generalized series-parallel partial words.

Original languageEnglish
Pages (from-to)225-248
Number of pages24
JournalTheoretical Computer Science
Volume273
Issue number1-2
DOIs
Publication statusPublished - Feb 28 2002

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Partial Words
Subword
Preorder
Algebra
Partial
Free Algebras
Series
Axiomatization
Axioms
Valid

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Axiomatizing the subsumption and subword preorders on finite and infinite partial words. / Ésik, Z.

In: Theoretical Computer Science, Vol. 273, No. 1-2, 28.02.2002, p. 225-248.

Research output: Contribution to journalArticle

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