Andreev et al.~\cite{ABCR97} give constructions of Boolean functions (computable by polynomial-size circuits) that require large read-once branching program (1-b.p.'s): a function in P that requires 1-b.p. of size at least $2^{n-\polylog(n)}$, a function in quasipolynomial time that requires 1-b.p. of size at least $2^{n-O(\log n)}$, and a function in LINSPACE ...
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