On a class of poly-context-free groups generated by automata

Cavaleri, Matteo; D'Angeli, Daniele; Donno, Alfredo; Rodaro, Emanuele

doi:10.1016/j.jalgebra.2023.03.023

Journal of Algebra

2023

DOI: 10.1016/j.jalgebra.2023.03.023

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On a class of poly-context-free groups generated by automata

Matteo Cavaleri

Daniele D'Angeli

Alfredo Donno

et al.

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2024

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Generalizations of the Muller–Schupp theorem and tree‐like inverse graphs

Rodaro

2024

Journal of London Math Soc

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We extend the characterization of context‐free groups of Muller and Schupp in two ways. We first show that for a quasi‐transitive inverse graph , being quasi‐isometric to a tree, or context‐free in the sense of Muller–Schupp (finitely many end‐cone up to end‐isomorphism), or having the automorphism group that is virtually free, are all equivalent conditions. Furthermore, we add to the previous equivalences a group theoretic analog to the representation theorem of Chomsky–Schützenberger that is fundamental in solving a weaker version of a conjecture of Brough which also extends Muller and Schupp's result to the class of groups that are virtually finitely generated subgroups of the direct product of free groups. We show that such groups are precisely those whose word problem is the intersection of a finite number of languages accepted by quasi‐transitive, tree‐like inverse graphs.

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Generalizations of the Muller–Schupp theorem and tree‐like inverse graphs

Rodaro

2024

Journal of London Math Soc

Self Cite

View full text Add to dashboard Cite

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On a class of poly-context-free groups generated by automata

Cited by 1 publication

References 30 publications

Generalizations of the Muller–Schupp theorem and tree‐like inverse graphs

Generalizations of the Muller–Schupp theorem and tree‐like inverse graphs

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