  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 +, -, x, /,
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 not much larger blow up 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.
