Weak length induction and slow growing depth boolean circuits
| dc.creator | Kuroda, Satoru | |
| dc.date | 1999-07-16 | |
| dc.date.accessioned | 2026-07-07T03:24:14Z | |
| dc.date.available | 2026-07-07T03:24:14Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/cs/9907022 | |
| dc.identifier | http://arxiv.org/abs/cs/9907022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33246 | |
| dc.subject | Logic in Computer Science | |
| dc.subject | F.4.1 | |
| dc.title | Weak length induction and slow growing depth boolean circuits | |
| dc.type | text |