A purely algebraic proof of the omega-reducibility of pseudovarieties representing low half levels of concatenation hierarchies
Year: 2026
Type: article
Abstract: We are concerned with the $$\omega $$ ω -reducibility of pseudovarieties of ordered monoids representing half levels of concatenation hierarchies. In the author’s paper (Int. J. Algebra Comput. 64 (01), 87–135, 2024), the $$\omega $$ ω -reducibility of pseudovarieties representing levels 1/2 and 3/2 of concatenation hierarchies with a locally finite basic pseudovariety has been proven, using results of the paper by Place (Log. Methods Comput. Sci. 14 (4:16), 1–58, 2018) on so called covering of corresponding sets of regular languages. In this paper, we prove the same results on the $$\omega $$ ω -reducibility, not using the results of the mentioned paper by Place, although still inspired by their proofs. This new method of the proofs of the $$\omega $$ ω -reducibility prepares us to their potential extension to higher half levels of concatenation hierarchies. The process of a gradual generalization is initiated in this paper.
Source: Semigroup Forum
Author: Jana Volaříková
Institutions: Tomas Bata University in Zlín, Masaryk University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7126034873