Finding fixpoints in finite function spaces using neededness analysis and chaotic iteration

Abstract

A new and efficient algorithm for computing the least fixpoint of a functional on a finite function space is defined. The algorithm applies to the computation of the least fixpoint (global or local) induced by an arbitrary system of functional equations in a certain formalism. The algorithm employs a variant of Cousot and Cousot's chaotic iteration [2], and uses neededness (or dependency) information to guide the fixpoint iteration, as for instance in Kildall's early algorithm [12]. The neededness analysis is dynamic as in the algorithms proposed by Muthukumar and Hermenegildo [7] and Le Charlier et al. [10], with the main difference being that our neededness analysis is of a more “shallow” nature, and that our approach is more iterative and less recursive. The complexity result implies that the worst-case number of iterations per equation is independent of the total number of equations in the equation system, where an iteration corresponds to evaluating an equation once with respect to given values of the functional and primitive parameters.