Weak length induction and slow growing depth boolean circuits
Logic in Computer Science
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.cs/9907022,
title = {Weak length induction and slow growing depth boolean circuits},
author = {Satoru Kuroda},
journal= {arXiv preprint arXiv:cs/9907022},
year = {2007}
}