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THE ACHILLES PARADOX URI ABRAHAM
 

Summary: THE ACHILLES PARADOX
URI ABRAHAM
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
BEN-GURION UNIVERSITY, BE'ER SHEVA, ISRAEL
1. Introduction
Those of you that were in our 1993 CS&P meeting in Nieborow (Poland) and
heard my talk 1 can guess that I intend to speak about models for concurrency,
and not to discuss a problem in philosophy. I should admit outright that since
my reconstruction of the Achilles involves the notion of de nability in the theory
of models it cannot be a faithful rendering of Zeno's argument. However so little
and indirect is our information about Zeno that the experts do not seem to be in
agreement, and this may leave some place for a naive admirer.
I intend to formalize the paradox with system executions. These are mathe-
matical structures (as de ned by Tarski) that satisfy a certain niteness property.
(Lamport introduced system executions in [7] which has considerably in uenced
my work; his system executions, however, di er from those de ned here in several
aspects.) In my experience system executions are very useful to analyze concurrent
systems, and I wish to exemplify this with the Achilles paradox. First I explain
what system executions are, then I show how they are used to de ne concurrency,
and nally I use them to analyze the paradox. Before let me discuss some of the

  

Source: Abraham, Uri - Departments of Computer Science & Mathematics, Ben-Gurion University

 

Collections: Mathematics; Computer Technologies and Information Sciences