Cargando…

Approaching Arithmetic Theories with Finite-State Automata

The automata-theoretic approach provides an elegant method for deciding linear arithmetic theories. This approach has recently been instrumental for settling long-standing open problems about the complexity of deciding the existential fragments of Büchi arithmetic and linear arithmetic over p-adic f...

Descripción completa

Detalles Bibliográficos
Autor principal: Haase, Christoph
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206625/
http://dx.doi.org/10.1007/978-3-030-40608-0_3
Descripción
Sumario:The automata-theoretic approach provides an elegant method for deciding linear arithmetic theories. This approach has recently been instrumental for settling long-standing open problems about the complexity of deciding the existential fragments of Büchi arithmetic and linear arithmetic over p-adic fields. In this article, which accompanies an invited talk, we give a high-level exposition of the NP upper bound for existential Büchi arithmetic, obtain some derived results, and further discuss some open problems.