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
Two lower bounds for branching programs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On the complexity of branching programs and decision trees for clique functions
Journal of the ACM (JACM)
Computing algebraic formulas with a constant number of registers
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Towards optimal simulations of formulas by bounded-width programs
STOC '90 Proceedings of the twenty-second 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
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Branching programs for the computation of Boolean functions were first studied in the Master's thesis of Masek.7 In a rather straightforward manner they generalize the concept of a decision tree to a decision graph. Let P be a branching program with edges labelled by the Boolean variables, x1,...,xn and their complements. Given an input a&equil;(a1,...,an) &egr; {0,1}n, program P computes a function value fp(a) in the following way. The nodes of P play the role of states or configurations. In particular, sinks play the role of final states or stopping configurations. The length of program P is the length of the longest path in P. Following Cobham,2capacity of the program is defined to be the logarithm to the base 2 of the number of nodes in P. Length and capacity are lower bounds on time and space requirements for any reasonable model of sequential computation. Clearly, any n-variable Boolean function can be computed by a branching program of length n if the capacity is not constrained. Since space lower bounds in excess of log n remain a fundamental challenge, we consider restricted branching programs in the hope of gaining insight into this problem and the closely related problem of time-space trade-offs.