Comparison of different features of quaternary Reed-Muller canonical forms and some new statistical results

On the optimisation of Reed-Muller expressions

“…An integrated suite of C programs used to optimise functions expressed in an arbitrary basis and algebra is described in [Adams et al 2002] and [Adams et al 2003]. We implemented the above technique and incorporated it into our system.…”

“…[Stankovic et al 1998] compared two algebras for 2 and 3-variable functions for a sample size of 20,000 and [Adams et al 2002] compared five algebras using sample sizes of 20,000 2-variable functions. In [Adams et al 2003], we compared six algebras with functions of up to 5 variables with a sample size of 1,000, and found evidence that the optimisation procedures deliver less and less reduction in the number of non-zero terms, and that the bases perform similarly and converge in performance, as the number of variables increases.…”

“…These are the Reed-MullerFourier of [Stankovic et al 1998], the algebra of [Dubrova et al 1996], Level Detector algebra described in [Adams et al 2002], and an extension of the algebra proposed by [Calingairt 1961], described in [Adams et al 1999]. These all use MOD 4 arithmetic.…”

“…These all use MOD 4 arithmetic. The fifth is the finite field arithmetic of [Green et al 1974] and lastly we include the McGregor/Adams basis introduced in [Adams et al 2002] . These latter two use GF(4) arithmetic.…”