Modular Confluency of Cooperative Constraint Solvers ?

Hoon Hong
Research Institute for Symbolic Computation
Johannes Kepler University
A-4040 Linz, Austria
e-mail: hhong@risc.uni-linz.ac.at

February 9, 1994

Abstract

This paper is a sequel to a previous paper titled Confluency of Cooperative Constraint Solvers" where we gave a sufficient condition for confluency of cooperative constraint solvers. (the output is unique). In this paper, we generalize the theory such that equality relation is replaced with a more general notion of an equivalence relation. As a result, we obtain a condition for modular confluency (the output is unique modulo the equivalence relation).

1 Introduction

This paper is a sequel to a previous paper [1] where we gave a sufficient condition for confluency of cooperative constraint solvers. While trying to apply the theory to practical situations (such as differential equations), we found:

ffl The confluency (uniqueness of output) is too strong to be achieved in several cases.

ffl Often the confluency is not needed. In practice, one is satisfied with the weaker property that the outputs for a given input are similar" (for instance, with respect to how much they are diagonalized).

In this paper, we reflect these findings on the theory developed in the previous paper. This essentially amounts to replacing the equality relation used in the paper with a more general notion of an equivalence relation. As a result, we obtain a condition for the modular confluency (the output is unique modulo a certain equivalence relation).
Since this paper is a sequel, we omit all the motivating expositions on the confluency and jump into the core matter. For the motivational matters, see the previous paper [1].

?This research was done in the framework of ACCLAIM, a research project of the basic research action in ESPRIT sponsored by the European Community.