On Interpolating Arithmetic Read-Once Formulas with Exponentiation

摘要

A formula is a read-once formula if each variable appears at most once in it. An arithmetic read-once formula (AROF) with exponentiation is one in which the operations are addition, substraction, multiplication, division and exponentiation to an arbitrary integer. We present a polynomial time algorithm for interpolating AROF withexponentiationusing randomized substitutions. Interpolating AROF without exponentiation is studied in (Bshouty, Hancock, and Hellerstein,SIAM J. Comput.24, No. 4, 1995). To add the exponentiation operation to the basis we develop a new technique.