Interpolating Arithmetic Read-Once Formulas in Parallel

  title={Interpolating Arithmetic Read-Once Formulas in Parallel},
  author={Nader H. Bshouty and Richard Cleve},
  journal={SIAM J. Comput.},
A formula is read-once if each variable appears in it at most once. An arithmetic formula is one in which the operations are addition, subtraction, multiplication, and division (and constants are allowed). We present a randomized (Las Vegas) parallel algorithm for the exact interpolation of arithmetic read-once formulas over sufficiently large fields. More specifically, for $n$-variable read-once formulas and fields of size at least 3(n2+3n-2), our algorithm runs in $O(\log^2 n)$ parallel steps… 

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