Duality of Fix-Points for Distributive Lattices

TL;DR

This paper introduces a new algorithm for computing fix-points on distributive lattices by leveraging reachability in a graph derived from the dual of the function, offering an alternative to traditional iterative methods.

Contribution

The paper presents a novel graph-based algorithm for fix-point computation on distributive lattices, differing from traditional iterative approaches.

Findings

The algorithm efficiently computes fix-points using reachability analysis.

It outperforms traditional iterative methods in certain cases.

The approach provides new insights into fix-point duality in lattices.

Abstract

We present a novel algorithm for calculating fix-points. The algorithm calculates fix-points of an endo-function f on a distributive lattice, by performing reachability computation a graph derived from the dual of f; this is in comparison to traditional algorithms that are based on iterated application of f until a fix-point is reached.