Affiliation:
1. Univ. of Massachusetts, Amherst
2. McGill Univ., Montre´al, Quebec, Canada
Abstract
Recently a new connection was discovered between the parallel complexity class
NC
1
and the theory of finite automata in the work of Barrington on bounded width branching programs. There (nonuniform)
NC
1
was characterized as those languages recognized by a certain nonuniform version of a DFA. Here we extend this characterization to show that the internal structures of
NC
1
and the class of automata are closely related.
In particular, using Thérien's classification of finite monoids, we give new characterizations of the classes
AC
0
, depth-
k
AC
0
, and
ACC
, the last being the
AC
0
closure of the mod
q
functions for all constant
q
. We settle some of the open questions in [3], give a new proof that the dot-depth hierarchy of algebraic automata theory is infinite [8], and offer a new framework for understanding the internal structure of
NC
1
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference30 articles.
1. formulae on finite structures;AJTAI M.;Ann. Pure Appl. Logic,1983
2. BARRINGTON D.A. Bounded-width polynomial-size branching programs recognize exactly those languages in NCj. J. Comput. Syst. Sci. in press. 10.1016/0022-0000(89)90037-8 BARRINGTON D.A. Bounded-width polynomial-size branching programs recognize exactly those languages in NCj. J. Comput. Syst. Sci. in press. 10.1016/0022-0000(89)90037-8
3. Lecture Notes in Computer Science;BARRINGTON D. A.,1987
4. Log Depth Circuits for Division and Related Problems
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