A Theoretical Framework for Probability Coefficients: A New Methodology for Fault Detection

A new spectral method that eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function is described. The signature is obtained using probability coefficients of the function instead of conventional spectral signature. Theoretical relations for achievable computational advantage in terms of required additions in computing all 2n probability coefficients of "n" variable function have been developed. It is shown that for n ges 5, only 50% additions are needed to compute all probability coefficients as compared to spectral coefficients. The fault detection techniques based on spectral signature can be used with probability signature also to offer computational advantage.