1. Introduction to Read-Muller Logic 2002. 10. 8. Ahn, Ki-yong

2. Positive Polarity Reed-Muller Form o f(x1,x2,…xn) = a0 ^ a1x1 ^ a2x2 ^…^ anxn ^ … ^ amx1x2x3…xn o All variables are positive polarities o There is only 1 PPRM o EX) l F = 1 ^ x1 ^ x2 ^ x1x2

3. Fixed Polarity Reed-Muller Form o Each variable has positive or negative polarity o Polarity of variable is fixed o There is only 2 n FPRMs o EX) l F = 1 ^ x1 ^ x2’ ^ x1x2’

4. Generalized Reed-Muller Forms o Each variable can have any polarity o Polarity of variable is not fixed o There is only 2 n2 n-1 GRMs o EX) l F = 1 ^ x1 ^ x2’ ^ x1’x2’

5. Fundamental Expansions o Shannon Expansion – S l f(x1,x2,…,xn) = x1’f0(x2,…xn) ^ x1f1(x2,…xn) o Positive Davio Expansion – pD l f(x1,x2,…,xn) = 1 f0(x2,…xn) ^ x1f2(x2,…xn) l f2 = f0 ^ f1 S X1’ X1 pD 1 X1

6. Fundamental Expansions(2) o Negative Davio Expansion – nD l f(x1,x2,…,xn) = 1 f0(x2,…xn) ^ x1’f2(x2,…xn) o Generalized Davio Expansion – D l f(x1,x2,…,xn) = 1 f0(x2,…xn) ^ x1f2(x2,…xn) l x1 means both negative and positive nD 1 X1’ D 1 X1

7. Kronecker Forms - KRO o Using S, pD, nD for each variable o The same expansion must be used for the same variable S a’ a pD 1 b pD 1 b nD 1 nD nD nD c’ 1 c’ 1 c’ 1 c’

8. Pseudo-KRO Form - PDSKRO o Using S, pD, nD for each variable S a’ a pD 1 b S b’ b nD 1 pD pD S c’ c’ c 1 c 1 c

9. S/D Tree o Using Shannon(S) and Generalized Davio(D) S a’ a D 1 b S b’ b D 1 D DS c c’ c 1 c 1 c a’ a’c a’bc’ a’bc ab’ ab’c ab abc

10. Inclusive Forms for Two Variables o N IF = (1+2+2+4)+(4+8+8+16) = 45 S SS a’a b’ b b’ b a’b’a’b ab’ ab S DS a’a b’ b 1 b a’b’a’b a abababab S SD a’a 1 b b’ b a’ a’b ab’ ab S DD a’a 1 b 1 b a’ a abababab D SS 1a b’ b b’ b b’b ab’ abababab D DS 1a b’ b 1 b b’b a ab D SD 1a 1 b b’ b 1b abababab D DD 1a 1 b 1 b 1b a ab N=1N=2N=2N=4 N=4N=8N=8N=16