Lower Bound for Integer Addition

Abstract

"The theory of integer addition, Th(Z, +, ≤), also known as Presburger arithmetic, is complete for the complexity class STA(∗, 22nO(1) , n)—one exponential up from Th(R, +, ≤). In this lecture we describe how to obtain the lower bound. The decidability of Presburger arithmetic is due to Presburger [98]. The precise upper and lower bounds are due to Berman [14], based on work of Fischer and Rabin [42], Cooper [33], Oppen [91], and Ferrante and Rackoff [41]."