 
Summary: Convergence of Iteration Systems
Anish ARORA 1;2 Paul ATTIE 1;2 Michael EVANGELIST 1
Mohamed GOUDA 1;2
1. Microelectronics and Computer Technology Corporation, Austin
2. Department of Computer Sciences, The University of Texas at Austin
Abstract
An iteration system is a set of assignment statements whose computation proceeds in
steps: at each step, an arbitrary subset of the statements is executed in parallel. The set
of statements thus executed may differ at each step; however, it is required that each state
ment is executed infinitely often along the computation. The convergence of such systems
(to a fixed point) is typically verified by showing that the value of a given variant function
is decreased by each step that causes a state change. Such a proof requires an exponential
number of cases (in the number of assignment statements) to be considered. In this paper,
we present alternative methods for verifying the convergence of iteration systems. In most
of these methods, upto a linear number of cases need to be considered.
1 Introduction
Iteration systems are a useful abstraction for computational, physical and biological systems
that involve ``truly concurrent'' events. In computing science, they can be used to represent
selfstabilizing programs, neural networks, transition systems and array processors. This wide
