On the Expressiveness of Büchi Arithmetic

We show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its [Formula: see text] -fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable...

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Detalles Bibliográficos
Autores principales: Haase, Christoph, Różycki, Jakub
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984115/
http://dx.doi.org/10.1007/978-3-030-71995-1_16
Descripción
Sumario:We show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its [Formula: see text] -fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable in the existential fragment of Büchi arithmetic.

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