Typically we think of randomness for searching, for example finding disagreements with Fermat's little theorem to show a number is composite or taking random walks on graphs to show they are connected. Derandomization results have given us reasons to believe we can replace the randomness in these computations with pseudorandom number generators.

Randomness can also play the role of hiding, since no one can predict future coin tosses. In interactive proofs we make the jump from NP to PSPACE because of randomness. For PCPs with O(log n) queries the jump goes from P to NP and with poly queries from NP to NEXP, in the later case classes which are provable different. In all these cases the prover cannot cheat because it cannot predict coin tosses not yet made by the verifier. A verifier using a pseudorandom generator will fail here, since the prover could then predict the verifier's actions.

AM protocols have the verifier flip coins first so no hiding going on, rather searching for a statement Merlin can prove and we expect some derandomization for AM. The result that MA is in AM says that sometimes we can replace hiding randomness with searching randomness.

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