A theorem on the formalized arithmetic with function symbols ' and $+$

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Analyzing Automata with Presburger Arithmetic and Uninterpreted Function Symbols

A Randomized Satisfiability Procedure for Arithmetic and Uninterpreted Function Symbols

We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., i...

A formalized proof of Dirichlet's theorem on primes in arithmetic progression

Dirichlet’s theorem asserts that for all pairs of positive integers k and d that are coprime (have no common integer factor besides 1), there are infinitely many primes p such that p ≡ k (mod d), i.e. that the infinite arithmetic progression k, k+ d, k+ 2d, k+ 3d, . . . contains infinitely many primes. (The coprimality condition is easily seen to be necessary, for any common divisor of k and d ...

A Randomized Satisfability Procedure for Arithmetic and Uninterpreted Function Symbols

We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., i...