On the Density of the Probabilistic Polynomial Classes
There are many results on which intractable problems can be solved quickly using randomized algorithms, starting with the classical paper by Rabin . Comparisons of probabilistic and deterministic performances have stimulated several possibilities for randomization by considering the structure of the probabilistic classes . The study of expected complexity has been developed from two basic points of view . In the first one, the so called distributional approach, the input probability must be known and the theory is developed under these input assumptions. The second one, called the randomized approach, allows stochastic moves in the computations. In this paper, we study a distributional randomized approach. By defining density for probabilistic machines, we consider probability on the inputs and we adopt the probabilistic Turing machine as our formal model of computation.
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