Weak length induction and slow growing depth boolean circuits

Details Weak length induction and slow growing depth boolean circuits Weak length induction and slow growing depth boolean circuits

1999-07-16

arxiv.org/abs/cs/9907022v1

Computer Science

Logic in Computer Science

Scientific paper

We define a hierarchy of circuit complexity classes LD^i, whose depth are the inverse of a function in Ackermann hierarchy. Then we introduce extremely weak versions of length induction and construct a bounded arithmetic theory L^i_2 whose provably total functions exactly correspond to functions computable by LD^i circuits. Finally, we prove a non-conservation result between L^i_2 and a weaker theory AC^0CA which corresponds to the class AC^0. Our proof utilizes KPT witnessing theorem.

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