Two theorems on random polynomial time

The use of randomness in computation was first studied in abstraction by Gill [4]. In recent years its use in both practical and theoretical areas has become apparent. Strassen and Solovay [10]; Miller [7]; and Rabin [8] have used it to transform primality testing into a (for many purposes) tractible problem. We can see in retrospect that it was implicit in algorithms by Ber1ekamp [2], Lehmer [6], and Cippola [3] (1903!). Where the traditional method of polynomial reduction has been inapplicable, randomness has been used in demonstrating intractibility by Adleman and Manders [1], and in showing problems equivalent by Rabin [9]. In light of these developments and the insights they provide, a new examination of randomness is in order.