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Characterizing Arithmetic Read-Once Formulae

Discrete Mathematics 2014-08-12 v1

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.

Cite

@article{arxiv.1408.1995,
  title  = {Characterizing Arithmetic Read-Once Formulae},
  author = {Ilya Volkovich},
  journal= {arXiv preprint arXiv:1408.1995},
  year   = {2014}
}
R2 v1 2026-06-22T05:23:43.440Z