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.
CITATION STYLE
Haase, C. (2020). Approaching arithmetic theories with finite-state automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12038 LNCS, pp. 33–43). Springer. https://doi.org/10.1007/978-3-030-40608-0_3
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