Abstract
An arithmetic Read-Once Formula (ROF for short) is a formula (i.e., a tree of computation) in which the operations are { +, ×} 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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Index Terms
Characterizing Arithmetic Read-Once Formulae
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