Bounded-depth, polynomial-size circuits for symmetric functions
Theoretical Computer Science
Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
A taxonomy of problems with fast parallel algorithms
Information and Control
The NP-completeness column: An ongoing guide
Journal of Algorithms
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Semigroups and languages of dot-depth 2
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Parallel computation with threshold functions
Proc. of the conference on Structure in complexity theory
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Non-uniform automata over groups
14th International Colloquium on Automata, languages and programming
Automata, Languages, and Machines
Automata, Languages, and Machines
Unbounded fan-in circuits and associative functions
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
BOUNDED WIDTH BRANCHING PROGRAMS
BOUNDED WIDTH BRANCHING PROGRAMS
Threshold circuits of bounded depth
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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Recently a new connection was discovered between the parallel complexity class NC1 and the theory of finite automata, in the work of Barrington [Ba86] on bounded width branching programs. There (non-uniform) NC1 was characterized as those languages recognized by a certain non-uniform version of a DFA. Here we extend this characterization to show that the internal structures of NC1 and the class of automata are closely related.In particular, using Thérien's classification of finite monoids [Th81], we give new characterizations of the classes AC0, depth-k AC0, and ACC, the last being the AC0 closure of the mod q functions for all constant q. We settle some of the open questions in [Ba86], give a new proof that the dot-depth hierarchy of algebraic automata theory is infinite [BK78], and offer a new framework for understanding the internal structure of NC1.