Bounds for width two branching programs
SIAM Journal on Computing
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Superlinear lower bounds for bounded-width branching programs
Journal of Computer and System Sciences
Automata, Languages, and Machines
Automata, Languages, and Machines
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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In computations realized by finite automata, a rich understanding has come from comparing the algebraic structure of the machines to the combinatorics of the languages being recognized. In this expository paper, we will first survey some basic ideas that have been useful in this model. In the second part, we sketch how this dual approach can be generalized to study some important class of boolean circuits, what results have been obtained, what questions are still open. The intuition gained in the simple model sometimes carry through, sometimes not, so that one has to be careful on what conjectures to make.