Condition-Sensitive Computation of Approximate Fixed Points

Digital Fixed Points, Approximate Fixed Points, and Universal Functions

A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approxima...

Approximate Fixed Points in Abstract Interpretation

Much of the earlier development of abstract interpretation, and its application to imperative programming languages, has concerned techniques for finding fixed points in large (often infinite) lattices. The standard approach in the abstract interpretation of functional languages has been to work with small, finite lattices and this supposedly circumvents the need for such techniques. However, p...

A Survey of Categorical Computation: Fixed Points, . . .

E. Moggi, Categories of Partial Morphism and the p -calculus, In Category Theory and Computer Programming, Lecture Notes in Computer Science 240, SpringerVerlag, 1986. [Mog88a] E. Moggi, Computational Lambda-Calculus and Monads, Technical Report ECSLFCS-88-66, University of Edinburgh, October, 1988. [Mog88b] E. Moggi, Partial Morphisms in Categories of E ective Objects, Information and Computat...

On the Computation of Nonhyperbolic Fixed Points

Local Computation of Simultaneous Fixed-Points*

We present a very simple, yet general algorithm for computing simultaneous, minimum fixed-points of monotonic functions, or turning the viewpoint slightly, an algorithm for computing minimum solutions to a system of monotonic equations. The algorithm is local (demand-driven, lazy, ), i.e. it will try to determine the value of a single component in the simultaneous fixed-point by investigating o...