# A superpolynomial lower bound for (1,+*k(n)*)-branching programs

## Abstract

By (1,+*k*(*n*))-branching programs (b. p.s) we mean those b. p.s which during each of their computations are allowed to test at most *k*(*n*) input bits repeatedly. For a Boolean function *J* computable within polynomial time a trade-off has been proven between the number of repeatedly tested bits and the size of each b. p. *P* which computes *J*. If at most ≫√n/48(*log*(c(*n*)))^{2}⌋ — 1 repeated tests are allowed then the size of *P* is at least c(*n*). This yields superpolynomial lower bounds for e. g. (1, +√n/48(*log*(*n*)*loglog*(*n*))^{2}) *-b.* p.'s and for (1, +√n/48(*log*(*n*))^{4})-b. p.'s.

The presented result is a step towards a superpolynomial lower bound for 2-b. p.'s which is an open problem since 1984 when the first superpolynomial lower bounds for 1-b. p.s were proven [6], [7].

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