x
¸
p = f (y)dy. (1.1)
−∞
In this case, our random source is considered as Uniform distribution [1] in the interval [0, 1], hence, the received probability will be x as expected.
The random source plays the most important role in SNG, because without a good randomness at the beginning, there is no SN. Moreover, a problem must be noticed is that a random source is difficultly achieved in experiment, therefore, the pseudo–random source or pseudo–random number generator (PRNG) becomes a practical solution. Linear Feedback Shift Register (LFSR) has been recommended in widely SC system for random number generation [9], [19], [4], [24], [13]. Besides, Cellula Automata was equally considered in [4], [11], [22], [7] as a good solution for PRNG.
The SNGs without using comparator was early proposed in [9], [4], [12]. In these designs, the basic logic elements, such as AND, OR, NOT gates and Multiplexer (MUX), were used instead of the comparator to generate the stochastic constants in SC with a high accuracy. Recently, a general synthesis method to design Finite State Machines (FSMs) for generating SN was developped in [21] with the improvement comparing to previous works.
Furthermore, each SNG provides a specific probability, hence it is problematic when the application requires many probabilities. Since on the one hand, it is expensive to generate directly all required probabilities from the random sources, on the other hand, it takes time for this process. Consequently, a synthesis method was proposed in [20] as a solution for this problem. The aim of this approach is to synthesize combinational logic that generates the expected probability from a specified source. However, this method is successful in considering the input probabilities being exact and independent. For that reason, there will be a lot of study forcusing on this problem of SNG in future work.