A Note on Amortized Branching Program Complexity

Aaron Potechin

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arXiv · 1611.06632

A Note on Amortized Branching Program Complexity

Aaron Potechin

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Abstract

In this paper, we show that while almost all functions require exponential size branching programs to compute, for all functions $f$ there is a branching program computing a doubly exponential number of copies of $f$ which has linear size per copy of $f$. This result disproves a conjecture about non-uniform catalytic computation, rules out a certain type of bottleneck argument for proving non-monotone space lower bounds, and can be thought of as a constructive analogue of Razborov's result that submodular complexity measures have maximum value $O(n)$.

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Aaron Potechin. 2017-02-22. A Note on Amortized Branching Program Complexity. https://arxiv.org/abs/1611.06632

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