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• W2966181201 abstract "We consider the complexity of the satisfiability problems for the existential fragment of Buchi arithmetic and for the existential fragment of linear arithmetic over p-adic fields. Our main results are that both problems are NP-complete. The NP upper bound for existential linear arithmetic over p-adic fields resolves an open question posed by Weispfenning [J. Symb. Comput., 5(1/2) (1988)] and holds despite the fact that satisfying assignments in both theories may have bit-size super-polynomial in the description of the formula. A key technical contribution is to show that the existence of a path between two states of a finite-state automaton whose language encodes the set of solutions of a given system of linear Diophantine equations can be witnessed in NP." @default.
• W2966181201 created "2019-08-13" @default.
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• W2966181201 date "2019-06-01" @default.
• W2966181201 modified "2023-09-23" @default.
• W2966181201 title "On the Existential Theories of Büchi Arithmetic and Linear p-adic Fields" @default.
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• W2966181201 doi "https://doi.org/10.1109/lics.2019.8785681" @default.
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