Majority Logic Synthesis Based on Nauty Algorithm - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 116

Table 1. A list of primitives for four-variable functions

No. Boolean logic Majority logic No. Boolean logic Majority logic

d 0 + c M(d 0 ,1,c) 1 0 0 46

2 1 1 47 a + b M(a,1,b)

3 a a 48 a + c M(a,1,c)

a 0 a 0

4 49 a + d M(a,1,d)

5 b b 50 b + c M(b,1,c)

b 0 b 0 6 51 b + d M(b,1,d)

7 c c 52 c + d M(c,1,d)

c 0 c 0 a 0 b 0 M(a,1,b) 0 8 53

a 0 c 0 M(a,1,c) 0

9 d d 54

10 d 0 d 0 55 a 0 d 0 M(a,1,d) 0

11 ab M(a,0,b) 56 b 0 c 0 M(b,1,c) 0

12 ac M(a,0,c) 57 b 0 d 0 M(b, 1,d) 0

13 ad M(a,0,d) 58 c 0 d 0 M(c,1,d) 0

14 bc M(b,0,c) 59 ab + ac + bc M(a,b,c)

a 0 b 0 + a 0 c 0 + b 0 c 0 M(a,b,c) 0

15 bd M(b,0,d) 60

a 0 b + a 0 c + bc M(a 0 ,b,c) 16 cd M(c,0,d) 61

a 0 + b 0 M(a,0,b) 0 ab 0 + ac 0 + b 0 c 0 M(a,b 0 ,c 0 ) 17 62

a 0 + c 0 M(a,0,c) 0 ab 0 + ac + b 0 c 0 M(a,b 0 ,c)

18 63

a 0 + d 0 M(a,0,d) 0 a 0 b + a 0 c 0 + bc 0 M(a 0 ,b,c 0 ) 19 64

b 0 + c 0 M(b,0,c) 0 ab + ac 0 + bc 0 M(a,b,c 0 )

20 65

b 0 + d 0 M(b,0,d) 0 a 0 b 0 + a 0 c + b 0 c M(a 0 ,b 0 ,c) 21 66

c 0 + d 0 M(c,0,d) 0 22 67 ab + ad + bd M(a,b,d)

ab 0 M(a,0,b 0 ) a 0 b 0 + a 0 d 0 + b 0 d 0 M(a,b,d) 0

23 68

ac 0 M(a,0,c 0 ) a 0 b + a 0 d + bd M(a 0 ,b,d) 24 69

ad 0 M(a,0,d 0 ) ab 0 + ad 0 + b 0 d 0 M(a,b 0 ,d 0 )

25 70

bc 0 M(b,0,c 0 ) ab 0 + ad + b 0 d M(a,b 0 ,d) 26 71

bd 0 M(b,0,d 0 ) a 0 b + a 0 d 0 + bd 0 M(a 0 ,b,d 0 ) 27 72

a 0 b M(b,0,a 0 ) ab + ad 0 + bd 0 M(a,b,d 0 )

28 73

a 0 c M(c,0,a 0 ) a 0 b 0 + a 0 d + b 0 d M(a 0 ,b 0 ,d) 29 74

b 0 c M(c,0,b 0 )

30 75 ac + cd + ad M(a,c,d)

cd 0 M(c,0,d 0 ) a 0 c 0 + c 0 d 0 + a 0 d 0 M(a,c,d) 0 31 76

da 0 M(d,0,a 0 ) a 0 c + cd + a 0 d M(a 0 ,c,d) 32 77

db 0 M(d,0,b 0 ) ac 0 + c 0 d 0 + ad 0 M(a,c 0 ,d 0 )

33 78

34 dc 0 M(d,0,c 0 ) 79 ac 0 + c 0 d + ad M(a,c 0 ,d)

35 a 0 + b M(a 0 ,1,b) 80 a 0 c + cd 0 + a 0 d 0 M(a 0 ,c,d 0 )

36 a 0 + c M(a 0 ,1,c) 81 ac + cd 0 + ad 0 M(a,c,d 0 )

37 a 0 + d M(a 0 ,1,d) 82 a 0 c 0 + c 0 d + a 0 d M(a 0 ,c 0 ,d)

b 0 + a M(b 0 ,1,a) 38 83 bc + cd + bd M(b,c,d)

b 0 + c M(b 0 ,1,c) b 0 c 0 + c 0 d 0 + b 0 d 0 M(b,c,d) 0

39 84

b 0 + d M(b 0 ,1,d) b 0 c + cd + b 0 d M(b 0 ,c,d) 40 85

c 0 + a M(c 0 ,1,a) bc 0 + c 0 d 0 + bd 0 M(b,c 0 ,d 0 )

41 86

c 0 + b M(c 0 ,1,b) bc 0 + c 0 d + bd M(b,c 0 ,d) 42 87

c 0 + d M(c 0 ,1,d) b 0 c + cd 0 + b 0 d 0 M(b 0 ,c,d 0 ) 43 88

d 0 + a M(d 0 ,1,a) bc + cd 0 + bd 0 M(b,c,d 0 )

44 89

d 0 + b M(d 0 ,1,b) b 0 c 0 + c 0 d + b 0 d M(b 0 ,c 0 ,d) 45 90