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Deterministic Approximate Counting of Depth-2 Circuits

By Michael Luby, Boban Velickovic and Avi Wigderson


We describe deterministic algorithms which for a given depth-2 circuit F approximate the probability that on a random input F outputs a specific value α. Our approach gives an algorithm which for a given GF[2] multivariate polynomial p and given ε > 0 approximates the number of zeros of p within a multiplicative factor 1+ε. The algorithm runs in time exp(exp(O( p log(n=ffl)))), where n is the size of the circuit. We also obtain an algorithm which given a DNF formula F and ε > 0 approximates the number of satisfying assignments of F within a factor of 1 + ε and runs in time exp(O((log(n/ε))^4))

Year: 1993
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