Proceedings ArticleDOI
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
D A Barrington
- Vol. 38, Iss: 1, pp 1-5
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TLDR
The method of proof is extended to investigate the complexity of the word problem for a fixed permutation group and show that polynomial size circuits of width 4 also recognize exactly nonuniform NC 1.Abstract:
We show that any language recognized by an NC 1 circuit (fan-in 2, depth O (log n )) can be recognized by a width-5 polynomial-size branching program. As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly nonuniform NC 1 . Further, following Ruzzo ( J. Comput. System Sci. 22 (1981), 365–383) and Cook ( Inform. and Control 64 (1985) 2–22) , if the branching programs are restricted to be ATIME(logn)-uniform, they recognize the same languages as do ATIME(log n )-uniform NC 1 circuits, that is, those languages in ATIME(log n ). We also extend the method of proof to investigate the complexity of the word problem for a fixed permutation group and show that polynomial size circuits of width 4 also recognize exactly nonuniform NC 1 .read more
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