Fast transforms for multiple-valued input binary output PLI logic

Abstract

Fast forward and inverse transforms for multiplevalued input binary output PLI logic are derived. New matrix functions are introduced which allow feasible tranformation of arbitrary q-valued input binary output functions. This allows representation of the function in the algebra of GF(2), where q m 2 . The representation of MVB functions in various functional bases having always fast algorithms is the foundation for the efficient synthesis of PLI expansions of MVB functions. The computational complexity of such algorithms is essentially reduced when compared to standard matrix multiplication and inversion based methods of the earlier work in PLI logic.

Family of fast transforms over GF(3) logic

“…Generalization of LI transforms for multiple-valued input binary functions was proposed in [6]. Properties of LI transformation matrices and their complexity analysis for multiple-valued input binary output functions with appropriate coding and new matrix functions were discussed in [4].…”

Polynomial expansions over GF(3)based on fastest transformation

“…Further research showed that there are some LI transforms having the smallest computational cost that is lower than that of the binary Reed-Muller transform [11]. Generalization of LI transforms for multiple-valued input binary functions was proposed in [8] and some efficient class of such transformations was identified in [4]. Binary fixed polarity Reed-Muller expansions have been extended to ternary field GF (3) and in general to a prime field GF(p) [2,5,7].…”