Random Error Reduction Scheme for Combinational Stochastic Circuit

Algorithm 1

Random error reduction scheme based on MCAS and BS.

Requrie: The combinational stochastic circuit implementing arithmetic;

Ensure: The state vector V representing the random error reduction scheme;

() Express the relationship between input streams and output stream in the form of (14).

() Obtain . If is a null set, go to step (), otherwise, skip step () and go to step ().

() If is a null set, we determine which input streams are specified as MCASs and obtain

  by the following criteria: (a) Eq. (27) should be satisfied, i.e., only one input stream is

 specified as MCAS; (b) on the premise of (a), let be maximal. Then, we skip step () and

 go to step ().

() If is not a null set, we determine which input streams are specified as MCASs and

 obtain by the following criteria: (a) Eq. (28) should be satisfied, i.e., only PISs are likely

 to be specified as MCASs; (b) Eq. (29) should be satisfied, i.e., for each product term, at most

 one factor is specified as MCAS; (c) on the premise of (a) and (b), let be maximal.

 Then, we go to step ().

() The input streams not belonging to are specified as BSs. From above, we determine

  each input stream should be specified as MCAS or BS and obtain the state vector V.