2 research outputs found
On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes
Given an existential formula Φ of linear arithmetic over p-adic integers together with valuation constraints, we study the p-universality problem which consists of deciding whether Φ is satisfiable for all primes p, and the analogous problem for the closely related existential theory of Büchi arithmetic. Our main result is a coNEXP upper bound for both problems, together with a matching
lower bound for existential BĂĽchi arithmetic. On a technical level, our results are obtained from analysing properties of a certain class of p-automata, finite-state automata whose languages encode
sets of tuples of natural numbers
An Extension of The Cobham-Semënov Theorem
International audienceno abstrac