Stably computable relations and predicates

James Aspnes

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arXiv · 2412.02008

Stably computable relations and predicates

James Aspnes

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Abstract

A population protocol stably computes a relation R(x,y) if its output always stabilizes and R(x,y) holds if and only if y is a possible output for input x. Alternatively, a population protocol computes a predicate R( ) on pairs if its output stabilizes on the truth value of the predicate when given as input. We consider how stably computing R(x,y) and R( ) relate to each other. We show that for population protocols running on a complete interaction graph with n>=2, if R( ) is a stably computable predicate such that R(x,y) holds for at least one y for each x, then R(x,y) is a stably computable relation. In contrast, the converse is not necessarily true unless R(x,y) holds for exactly one y for each x.

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BibTeX RIS

James Aspnes. 2024-12-02. Stably computable relations and predicates. https://arxiv.org/abs/2412.02008

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