Publication details

Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words

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Authors

KLÍMA Ondřej KOLEGAR Jonatan

Year of publication 2024
Type Article in Periodical
Magazine / Source Theory of Computing Systems
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007/s00224-024-10172-0
Doi http://dx.doi.org/10.1007/s00224-024-10172-0
Keywords Finite semigroups; Well quasi-orders; Unavoidable words; Derivation relations; Ordered semigroups
Description The notion of a quasi-order generated by a homomorphism from the semigroup of all words onto a finite ordered semigroup was introduced by Bucher et al. (Theor. Comput. Sci. 40, 131-148 1985). It naturally occurred in their studies of derivation relations associated with a given set of context-free rules, and they asked a crucial question, whether the resulting relation is a well quasi-order. We answer this question in the case of the quasi-order generated by a semigroup homomorphism. We show that the answer does not depend on the homomorphism, but it is a property of its image. Moreover, we give an algebraic characterization of those finite semigroups for which we get well quasi-orders. This characterization completes the structural characterization given by Kunc (Theor. Comput. Sci. 348, 277-293 2005) in the case of semigroups ordered by equality. Compared with Kunc's characterization, the new one has no structural meaning, and we explain why that is so. In addition, we prove that the new condition is testable in polynomial time.
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