Abstract
Representations of Boolean functions by exclusive-OR sums (modulo 2) of pseudoproducts is studied. An ExOR-sum of pseudoproducts (ESPP) is the sum modulo 2 of products of affine (linear) Boolean functions. The length of an ESPP is defined as the number of summands in this form, and the length of a Boolean function in the class of ESPPs is defined as the minimum length of an ESPP representing this function. The Shannon function LESPP(n) of the length of Boolean functions in the class of ESPPs is considered, which equals the maximum length of a Boolean function of n variables in this class. Lower and upper bounds for the Shannon function LESPP(n) are found. The upper bound is proved by using an algorithm which can be applied to construct representations by ExOR-sums of pseudoproducts for particular Boolean functions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
