On-Line Reevaluation of Functions

Abstract

Given a finite set S and a function f : S^n -> S^m, we consider the problem of making a data structure which maintains a value of x in S^n and allows us to efficiently change an arbitrary coordinate of x and efficiently evaluate f_i(x) for arbitrary i. We both examine the problem for specific choices of f and relate the possibility of an efficient solution to general properties of f: expressibility as a formula, space complexity and time complexity.