Summary
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.
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Anish Arora is currently completing his Ph.D. degree at the University of Texas at Austin, and has been working in the Software Technology Program at MCC since December 1988. Anish received a B.Tech. degree in Computer Science and Engineering from the Indian Institute of Technology, New Dehli in 1986, and an M.S. degree in Computer Sciences from the University of Texas at Austin in 1988. His research interests inclde fault-tolerance, distributed computing, program correctness, and semantics of concurrency.
Paul Attie is currently completing his Ph.D. degree of the University of Texas at Austin, and has been a member of technical staff in the Software Technology Program of the MCC since January 1990. Paul received a B.A. degree in Engineering Science from Oxford University in 1981, and an M.Sc. degree from the University of London in 1982. His research interests include distributed computing, temporal logic, and algebraic process theory.
Michael Evangelist received his Ph.D. in 1978 from Northwestern, where he did research in formal language theory, graph theory, logic, and computational complexity theory. He taught computer science at Colgate University and, in 1982, became a member of technical staff at Bell Labs and did research in software engineering. Three years later, he joined the Software Technology Program at MCC, where he spent five years working on theoretical and practical issues in the design of distributed systems. Evangelist now heads the Software Engineering Laboratory in the Chicago research center of Andersen Consulting.
Mohamed G. Gouda currently works on and teaches the stabilization of computing systems at the University of Texas at Austin. He designs “cute” communication protocols as a hobby, and proves them correct for fun.
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Arora, A., Attie, P., Evangelist, M. et al. Convergence of iteration systems. Distrib Comput 7, 43–53 (1993). https://doi.org/10.1007/BF02278855
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DOI: https://doi.org/10.1007/BF02278855