On the Existential Theories of Büchi Arithmetic and Linear p-adic Fields

Florent Guepin, Christoph Haase, James Worrell
2019 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
We consider the complexity of the satisfiability problems for the existential fragment of Büchi 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
more » ... n the description of the formula. A key technical contribution is to show that the existence of a path between two states of a finitestate automaton whose language encodes the set of solutions of a given system of linear Diophantine equations can be witnessed in NP.
doi:10.1109/lics.2019.8785681 dblp:conf/lics/GuepinH019 fatcat:j6zijkzgenhtjot7bkyrtbtc4e