Research note
On the complexity of deadlock-free programs on a ring of processors

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Abstract

A combinatorial view of deadlock (as in Dijkstra's self-stabilizing systems) is presented which leads to precise lower bounds on the complexity of programs. Specifically, we consider a directed ring of k individual processors, each having n states, identical programs, and asynchronous activity. Our main theorem establishes the minimum size (i.e., complexity) of a program for which no global state is in deadlock.

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