Adleman's theorem
This article gives the statement, and proof, of one complexity class being contained in another one. The smaller complexity class is BPP and the larger complexity class is P/poly.
Statement
In terms of complexity classes
The complexity class BPP (bounded error probabilistic polynomial time -- polynomial time where the probability of error is bounded below ) is contained in the complexity class P/poly (languages where, for every length of input string, there is an advice string using which the algorithm runs in polynomial time).
Loose philosophical formulation
The statement is that:
Probabilistic algorithm that is independent of length Failed to parse (unknown function "\leadsto"): {\displaystyle \leadsto} Deterministic algorithm that depends on length
In other words, we can shed the probabilistic nature of the algorithm but must instead accept length-specific advice that shapes the algorithm.