Well Quasi-Orders Arising from Finite Ordered Semigroups

Klíma, Ondřej; Jonatan, Kolegar,

doi:10.1007/978-3-031-05578-2_16

Cited by 1 publication

(3 citation statements)

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“…Now we give some basic consequences of Theorem 4.3. A straighforward combinatorial proof of the following corollary was given in [9]. As a special case of Corollary 4.6, we obtain that every unordered congenial semigroup satisfies s = s ω+1 , which means that the semigroup S is completely regular.…”

Section: Consequences Of the Characterizationmentioning

confidence: 76%

“…In the conference version of the paper [9], such an algorithm is presented in detail. However, that algorithm can be seen as a special case of a well-known algorithm testing the unavoidability of a given regular language which we recall next.…”

Section: Testing Unavoidabilitymentioning

confidence: 99%

“…Notice that the conference version [9] contains an alternative elementary argument for the previous result, which does not use Theorem 4.3, i.e., without the application of Proposition 3.1.…”

Section: Theorem 410 ([11]) Let S Be a Finite Semigroup Ordered By Eq...mentioning

confidence: 99%

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Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words

Klíma,

Kolegar

2024

Theory Comput Syst

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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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Section: Consequences Of the Characterizationmentioning

confidence: 76%

Section: Testing Unavoidabilitymentioning

confidence: 99%