2024/08/09 by Raad Al Kohli, Kohli, Raad Al, Derek F. Holt +3
Computer Science · #Advanced Database Systems and Queries #FOS: Mathematics #Group Theory (math.GR) #Semantic Web and Ontologies #Service-Oriented Architecture and Web Services
paper · pdf · doi:10.48550/arxiv.2408.05323
openalex publication_date 2024/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study groups whose co-word problems are ET0L languages, which we call coET0L groups, using an automaton based model due to van Leeuwen, and recently studied by Bishop and Elder. In particular we prove a number of closure results for the class of groups with co-word problems in a subclass of `special' ET0L languages; that class of groups contains all groups that we know at the time of writing to be co-ET0L, including all groups that were proved by Holt and Röver to be stack groups, and hence co-indexed. It includes virtually free groups, bounded automata groups, and the Higman-Thompson groups, together with groups constructed from those using finitely generated subgroups, finite extension, free and direct products, and by taking the restricted standard wreath product of a co-\E group by a finitely generated virtually free top group.