2025/12/15 by Ganna Kudryavtseva, Ajda Lemut Furlani, Kudryavtseva, Ganna +1
Computer Science · Mathematics · #Geometric and Algebraic Topology #Polynomial and algebraic computation #math.RA #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2512.13332
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
We provide a geometric model for the free X-generated F-restriction semigroup in the extended signature (⋅ , +,\mx,λ), where the unary operation \mx maps an element a to the maximum element \mxa of its σ-class, and the constant λ is the unique left identity. This model is based on a certain quotient of the Cayley graph expansion of the free monoid X^* with respect to the extended set of generators X∪ X^*, where the generators from X^* are in a bijection with the free monoid X^* and serve to capture the maximum elements of σ-classes of the quotient. We also provide models for the free X-generated strong and perfect F-restriction semigroups in the same extended signature. The constructed models enable us to solve the word problems for all the free objects under consideration.