Convergence of iteration systems

Anish Arora, Paul Attie, Michael Evangelist, Mohamed Gouda

Research output: Contribution to journalArticle

10 Scopus citations

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 statement 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.

Original languageEnglish (US)
Pages (from-to)43-53
Number of pages11
JournalDistributed Computing
Volume7
Issue number1
DOIs
StatePublished - Nov 1 1993
Externally publishedYes

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Keywords

  • Convergence
  • Dependency graph
  • Iteration systems
  • Stabilization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computational Theory and Mathematics

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