Two lower bounds for branching programs
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A simple function that requires exponential size read-once branching programs
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STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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A very simple function that requires exponential size read-once branching programs
Information Processing Letters
A Lower Bound for Integer Multiplication with Read-Once Branching Programs
SIAM Journal on Computing
An Exponential Lower Bound for One-Time-Only Branching Programs
Proceedings of the Mathematical Foundations of Computer Science 1984
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ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Lower bounds on the complexity of 1-time only branching programs
FCT '85 Fundamentals of Computation Theory
Lower Bounds for Deterministic and Nondeterministic Branching Programs
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
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We construct Boolean functions (computable by polynomial-size circuits) with large lower bounds for read-once branching program (1-b.p.'s): a function in P with the lower bound 2n-polylog(n), a function in quasipolynomial time with the lower bound 2n-O(log n), and a function in LINSPACE with the lower bound 2n-log n-O(1). Our constructions are simpler than those of Andreev et al. (Electronic Colloq. on Computational Complexity, TR97-053, 1997), as we apply the idea of almost k-wise independence more directly, without the use of discrepancy set generators for large affine subspaces. The simplicity of our constructions also allows us to observe that there exists a Boolean function in AC0[2] (computable by a depth 3, polynomial-size circuit over the basis {Λ, ⊕, 1}) with the optimal lower bound 2n-log n-O(1) for 1-b.p.'s.