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arXiv · 1408.1995

Characterizing Arithmetic Read-Once Formulae

Ilya Volkovich
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Abstract

An \emph{arithmetic read-once formula} (ROF for short) is a formula (i.e. a tree of computation) in which the operations are $\{+,\times\}$ and such that every input variable labels at most one leaf. We give a simple characterization of such formulae. Other than being interesting in its own right, our characterization gives rise to a property testing algorithm for functions computable by such formulae. To the best of our knowledge, prior to our work no characterization and/or property testing algorithm was known for this kind of formulae.

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Ilya Volkovich. 2014-08-08. Characterizing Arithmetic Read-Once Formulae. https://arxiv.org/abs/1408.1995

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