Computation of Probability Coefficients using Binary Decision Diagram and their Application in Test Vector Generation

This paper deals with efficient computation of probability coefficients which offers computational simplicity as compared to spectral coefficients. It eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function. The method for computation of probability coefficients using transform matrix, fast transform method and using BDD is given. 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>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

Conditions of the Affine Extension of an Incompletely Defined Boolean Function

The paper presents conditions of extension of the weakly defined Boolean functions to their full affine form. The main goal of the analysis is a fast estimation whether a given incompletely defined function can be extended to a full affine form. If it is possible a simple algorithm of the states completion has been proposed. In such a case undefined points are clearly replaced by 0, 1 values. Spectral coefficients of a Boolean function allow to determine whether a partially defined function can be realised as affine