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Coin Flipping in Dynamic Programming Is Almost Useless

Published:01 June 2020Publication History
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Abstract

We consider probabilistic circuits working over the real numbers and using arbitrary semialgebraic functions of bounded description complexity as gates. In particular, such circuits can use all arithmetic operations (+, −, ×, ÷), optimization operations (min and max), conditional branching (if-then-else), and many more. We show that probabilistic circuits using any of these operations as gates can be simulated by deterministic circuits with only about a quadratical blowup in size. A slightly larger blowup in circuit size is also shown when derandomizing approximating circuits. The algorithmic consequence, motivating the title, is that randomness cannot substantially speed up dynamic programming algorithms.

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