Tight Polynomial Bounds for Loop Programs in Polynomial Space

We consider the following problem: given a program, find tight asymptotic bounds on values of some variables at end computation (or any program point) in terms its input values. focus case polynomially-bounded variables, and weak programming language for which we have recently shown that are computable. These sets multivariate polynomials. While their computability has been settled, complexity this program-analysis problem remained open. In paper, show to be PSPACE-complete. The main contribution is new, space-efficient analysis algorithm. This algorithm obtained few steps. First, develop an univariate bounds, sub-problem already PSPACE-hard. Then, decision procedure achieved by reducing case; reduction orthogonal solution uses observations geometry set vectors represent bounds. Finally, transform univariate-bound produce