On theories of bounded arithmetic for NC1

被引：5
|
作者：
Jerabek, Emil [1 ]
机构：
[1] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic
来源：
ANNALS OF PURE AND APPLIED LOGIC | 2011年 / 162卷 / 04期
关键词：
Bounded arithmetic; Circuit complexity; Propositional translation;
D O I：
10.1016/j.apal.2010.10.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop an arithmetical theory VNC*1 and its variant (VNC) over bar (1)(*), corresponding to "slightly nonuniform" NC1. Our theories sit between VNC1 and VL, and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propositional translations of Sigma(B)(0)(L-(VNC*1) over bar)-formulas provable in L (VNC) over bar (1)(*) admit L-uniform polynomial-size Frege proofs. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：322 / 340
页数：19
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