Low depth circuit design
View Patent ↗A method of designing a logic circuit based on one of the functions of the form f n =x 1 (x 2 & (x 3 (x 4 & . . . x n . . . ))) and f′ n =x 1 & (x 2 (x 3 & (x 4 . . . x n . . . ))), by (a) selecting n as the number of variables of the logic circuit, (b) testing n against a threshold, (c) for values of n less than the threshold, using a first algorithm to design the logic circuit, (d) for values of n greater than the threshold, using a second algorithm to design the logic circuit.
1. A computer-based process of implementing a logic circuit for logical operations, comprising the steps of:
a) selecting N as a number of variables for the logic circuit,
b) designing the logic circuit with N max inputs, where N max is selected from the group consisting only of 33, 60, 109, 202, and 375,
c) using the computer, selectively basing the logic circuit on only one of,
i) a function x 0 & (x 1 (x 2 & (x 3 . . . x N−1 . . . ))), where N lo <N<N max , and setting inputs x i (i=N, N+1, . . . , N max −1) to a first binary value (0) for even values of i and to a second binary value (1) for odd values of i, and
ii) a function x 0 (x 1 & (x 2 (x 3 & . . . x N−1 . . . ))), where N lo <N<N max , and setting inputs x i (i=N, N+1, . . . , N max −1) to a first binary value (0) for odd values of i and to a second binary value (1) for even values of i,
d) removing gates that do not contribute to the function, and
e) implementing the logic circuit with two-input gates to a depth of Z.
2. The process of claim 1 , wherein N lo= 19, N max =33, and Z=6.
3. The process of claim 1 , wherein N lo= 33, N max =60, and Z=7.
4. The process of claim 1 , wherein N lo= 60, N max =109, and Z=8.
5. The process of claim 1 , wherein N lo= 109, N max =202, and Z=9.
6. The process of claim 1 , wherein N lo= 202, N max =375, and Z=10.
7. The process of claim 2 , further comprising: storing a netlist, the netlist defined by:
f0 =
[(x0 & x1)
|
(x0 & x2)]
&
[(x1 | x3)
|
(x4 & x5)]
f0a =
[(x0 & x2)
&
(x4 & x6)]
&
[(x5 | x7)
|
(x8 & x9)]
f0b =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x11 | x12)]
f1 =
[(x1 | x3)
|
(x5 | x7)]
|
[(x9 | x11)
|
(x13 | x15)]
f11 =
[(x11 | x13)
|
(x14 & x15)]
|
[(x14 & x16)
&
(x17 | x18)]
f14 =
[(x14 & x16)
&
(x18 & x20)]
&
[(x22 & x24)
&
(x25 | x26)]
f17 =
[(x17 | x19)
|
(x20 & x21)]
|
[(x18 & x20)
&
(x22 & x23)]
f25 =
[(x25 | x27)
|
(x28 & x29)]
|
[(x28 & x30)
&
(x31 | x32)]
out =
[(f0 | f0a)
|
(f0b & f11)]
&
[(f1 | f17)
|
(f14 & f25)].
8. The process of claim 2 , further comprising: storing a netlist, the netlist defined by:
f0 =
[(x0 | x1)
&
(x0 | x2)]
|
[(x1 & x3)
&
(x4 | x5)]
f0a =
[(x0 | x2)
|
(x4 | x6)]
|
[(x5 & x7)
&
(x8 | x9)]
f0b =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x11 & x12)]
f1 =
[(x1 & x3)
&
(x5 & x7)]
&
[(x9 & x11)
&
(x13 & x15)]
f11 =
[(x11 & x13)
&
(x14 | x15)]
&
[(x14 | x16)
|
(x17 & x18)]
f14 =
[(x14 | x16)
|
(x18 | x20)]
|
[(x22 | x24)
|
(x25 & x26)]
f17 =
[(x17 & x19)
&
(x20 | x21)]
&
[(x18 | x20)
|
(x22 | x23)]
f25 =
[(x25 & x27)
&
(x28 | x29)]
&
[(x28 | x30)
|
(x31 & x32)]
out =
[(f0 & f0a)
&
(f0b | f11)]
|
[(f1 & f17)
&
(f14 | f25)].
9. The process of claim 3 , further comprising: storing a netlist, the netlist defined by:
f0 =
[x0
&
(x1 | x2)]
&
[(x1 | x3)
|
(x4 & x5)]
f0a =
[(x0 & x2)
&
(x4 & x6)]
&
[(x5 | x7)
|
(x8 & x9)]
f0b =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x11 | x12)]
f1 =
[(x1 | x3)
|
(x5 | x7)]
|
[(x9 | x11)
|
(x13 | x15)]
f11 =
[(x11 | x13)
|
(x14 & x15)]
|
[(x14 & x16)
&
(x17 | x18)]
f14 =
[(x14 & x16)
&
(x18 & x20)]
&
[(x22 & x24)
&
(x25 | x26)]
f17 =
[(x17 | x19)
|
(x20 & x21)]
|
[(x18 & x20)
&
(x22 & x23)]
f17a =
[(x17 | x19)
|
(x21 | x23)]
|
[(x25 | x27)
|
(x29 | x31)]
f25 =
[(x25 | x27)
|
(x28 & x29)]
|
[(x28 & x30)
&
(x31 | x32)]
f30 =
[(x30 & x32)
&
(x33 | x34)]
&
[(x33 | x35)
|
(x36 & x37)]
f32 =
[(x32 & x34)
&
(x36 & x38)]
&
[(x37 | x39)
|
(x40 & x41)]
f32a =
[(x32 & x34)
&
(x36 & x38)]
&
[(x40 & x42)
&
(x43 | x44)]
f41 =
[(x41 | x43)
|
(x45 | x47)]
|
[(x49 | x51)
|
(x52 & x53)]
f43 =
[(x43 | x45)
|
(x46 & x47)]
|
[(x46 & x48)
&
(x49 | x50)]
f52 =
[(x52 & x54)
&
(x55 | x56)]
&
[(x55 | x57)
|
(x58 & x59)]
g0 =
[(f0 | f0a)
|
(f0b & f11)]
&
[(f1 | f17)
|
(f14 & f25)]
g1 =
[(f1 | f17a)
|
(f30 | f32)]
|
[(f32a & f43)
&
(f41 | f52)]
out =
g0 & g1.
10. The process of claim 3 , further comprising: storing a netlist, the netlist defined by:
f0 =
[x0
|
(x1 & x2)]
|
[(x1 & x3)
&
(x4 | x5)]
f0a =
[(x0 | x2)
|
(x4 | x6)]
|
[(x5 & x7)
&
(x8 | x9)]
f0b =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x11 & x12)]
f1 =
[(x1 & x3)
&
(x5 & x7)]
&
[(x9 & x11)
&
(x13 & x15)]
f11 =
[(x11 & x13)
&
(x14 | x15)]
&
[(x14 | x16)
|
(x17 & x18)]
f14 =
[(x14 | x16)
|
(x18 | x20)]
|
[(x22 | x24)
|
(x25 & x26)]
f17 =
[(x17 & x19)
&
(x20 | x21)]
&
[(x18 | x20)
|
(x22 | x23)]
f17a =
[(x17 & x19)
&
(x21 & x23)]
&
[(x25 & x27)
&
(x29 & x31)]
f25 =
[(x25 & x27)
&
(x28 | x29)]
&
[(x28 | x30)
|
(x31 & x32)]
f30 =
[(x30 | x32)
|
(x33 & x34)]
|
[(x33 & x35)
&
(x36 | x37)]
f32 =
[(x32 | x34)
|
(x36 | x38)]
|
[(x37 & x39)
&
(x40 | x41)]
f32a =
[(x32 | x34)
|
(x36 | x38)]
|
[(x40 | x42)
|
(x43 & x44)]
f41 =
[(x41 & x43)
&
(x45 & x47)]
&
[(x49 & x51)
&
(x52 | x53)]
f43 =
[(x43 & x45)
&
(x46 | x47)]
&
[(x46 | x48)
|
(x49 & x50)]
f52 =
[(x52 | x54)
|
(x55 & x56)]
|
[(x55 & x57)
&
(x58 | x59)]
g0 =
[(f0 & f0a)
&
(f0b | f11)]
|
[(f1 & f17)
&
(f14 | f25)]
g1 =
[(f1 & f17a)
&
(f30 & f32)]
&
[(f32a | f43)
|
(f41 & f52)]
out =
g0 | g1.
11. The process of claim 4 , further comprising: storing a netlist, the netlist defined by:
f0 =
[(x0 & x1)
|
(x0 & x2)]
&
[(x1 | x3)
|
(x4 & x5)]
f0a =
[(x0 & x2)
&
(x4 & x6)]
&
[(x5 | x7)
|
(x8 & x9)]
f0b =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x11 | x12)]
f0c =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x12 & x14)]
f1 =
[(x1 | x3)
|
(x5 | x7)]
|
[(x9 | x11)
|
(x13 | x15)]
f11 =
[(x11 | x13)
|
(x14 & x15)]
|
[(x12 & x14)
&
(x16 & x17)]
f13 =
[(x13 | x15)
|
(x17 | x19)]
|
[(x21 | x23)
|
(x24 & x25)]
f16 =
[(x16 & x18)
&
(x19 | x20)]
&
[(x17 | x19)
|
(x21 | x22)]
f16a =
[(x16 & x18)
&
(x20 & x22)]
&
[(x24 & x26)
&
(x28 & x30)]
f17 =
[(x17 | x19)
|
(x21 | x23)]
|
[(x25 | x27)
|
(x29 | x31)]
f24 =
[(x24 & x26)
&
(x27 | x28)]
&
[(x27 | x29)
|
(x30 & x31)]
f29 =
[(x29 | x31)
|
(x32 & x33)]
|
[(x32 & x34)
&
(x35 | x36)]
f31 =
[(x31 | x33)
|
(x35 | x37)]
|
[(x36 & x38)
&
(x39 | x40)]
f31a =
[(x31 | x33)
|
(x35 | x37)]
|
[(x39 | x41)
|
(x42 & x43)]
f33 =
[(x33 | x35)
|
(x37 | x39)]
|
[(x41 | x43)
|
(x45 | x47)]
f40 =
[(x40 & x42)
&
(x44 & x46)]
&
[(x48 & x50)
&
(x51 | x52)]
f42 =
[(x42 & x44)
&
(x45 | x46)]
&
[(x45 | x47)
|
(x48 & x49)]
f49 =
[(x49 | x51)
|
(x53 | x55)]
|
[(x57 | x59)
|
(x60 & x61)]
f50 =
[(x50 & x52)
&
(x54 & x56)]
&
[(x58 & x60)
&
(x62 & x64)]
f51 =
[(x51 | x53)
|
(x54 & x55)]
|
[(x54 & x56)
&
(x57 | x58)]
f52 =
[(x52 & x54)
&
(x56 & x58)]
&
[(x60 & x62)
&
(x63 | x64)]
f61 =
[(x61 | x63)
|
(x65 | x67)]
|
[(x69 | x71)
|
(x72 & x73)]
f63 =
[(x63 | x65)
|
(x66 & x67)]
|
[(x66 & x68)
&
(x69 | x70)]
f66 =
[(x66 & x68)
&
(x70 & x72)]
&
[(x74 & x76)
&
(x78 & x80)]
f72 =
[(x72 & x74)
&
(x75 | x76)]
&
[(x75 | x77)
|
(x78 & x79)]
f79 =
[(x79 | x81)
|
(x82 & x83)]
|
[(x82 & x84)
&
(x85 | x86)]
f81 =
[(x81 | x83)
|
(x85 | x87)]
|
[(x86 & x88)
&
(x89 | x90)]
f81a =
[(x81 | x83)
|
(x85 | x87)]
|
[(x89 | x91)
|
(x92 & x93)]
f90 =
[(x90 & x92)
&
(x94 & x96)]
&
[(x98 & x100)
&
(x101 | x102)]
f92 =
[(x92 & x94)
&
(x95 | x96)]
&
[(x95 | x97)
|
(x98 & x99)]
f101 =
[(x101 | x103)
|
(x104 & x105)]
|
[(x104 & x106)
&
(x107 | x108)]
g0 =
[(f0 | f0a)
|
(f0b & f11)]
|
[(f0c & f16)
&
(f13 | f24)]
g0a =
[(f0c & f16a)
&
(f29 & f31)]
&
[(f31a | f42)
|
(f40 & f51)]
g1 =
[(f1 | f17)
|
(f33 | f49)]
|
[(f52 & f63)
&
(f61 | f72)]
g51 =
[(f50 & f66)
&
(f79 & f81)]
&
[(f81a | f92)
|
(f90 & f101)]
out =
(g0 | g0a)
&
(g1 | g51).
12. The process of claim 4 , further comprising: storing a netlist, the netlist defined by:
f0 =
[(x0 | x1)
&
(x0 | x2)]
|
[(x1 & x3)
&
(x4 | x5)]
f0a =
[(x0 | x2)
|
(x4 | x6)]
|
[(x5 & x7)
&
(x8 | x9)]
f0b =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x11 & x12)]
f0c =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x12 | x14)]
f1 =
[(x1 & x3)
&
(x5 & x7)]
&
[(x9 & x11)
&
(x13 & x15)]
f11 =
[(x11 & x13)
&
(x14 | x15)]
&
[(x12 | x14)
|
(x16 | x17)]
f13 =
[(x13 & x15)
&
(x17 & x19)]
&
[(x21 & x23)
&
(x24 | x25)]
f16 =
[(x16 | x18)
|
(x19 & x20)]
|
[(x17 & x19)
&
(x21 & x22)]
f16a =
[(x16 | x18)
|
(x20 | x22)]
|
[(x24 | x26)
|
(x28 | x30)]
f17 =
[(x17 & x19)
&
(x21 & x23)]
&
[(x25 & x27)
&
(x29 & x31)]
f24 =
[(x24 | x26)
|
(x27 & x28)]
|
[(x27 & x29)
&
(x30 | x31)]
f29 =
[(x29 & x31)
&
(x32 | x33)]
&
[(x32 | x34)
|
(x35 & x36)]
f31 =
[(x31 & x33)
&
(x35 & x37)]
&
[(x36 | x38)
|
(x39 & x40)]
f31a =
[(x31 & x33)
&
(x35 & x37)]
&
[(x39 & x41)
&
(x42 | x43)]
f33 =
[(x33 & x35)
&
(x37 & x39)]
&
[(x41 & x43)
&
(x45 & x47)]
f40 =
[(x40 | x42)
|
(x44 | x46)]
|
[(x48 | x50)
|
(x51 & x52)]
f42 =
[(x42 | x44)
|
(x45 & x46)]
|
[(x45 & x47)
&
(x48 | x49)]
f49 =
[(x49 & x51)
&
(x53 & x55)]
&
[(x57 & x59)
&
(x60 | x61)]
f50 =
[(x50 | x52)
|
(x54 | x56)]
|
[(x58 | x60)
|
(x62 | x64)]
f51 =
[(x51 & x53)
&
(x54 | x55)]
&
[(x54 | x56)
|
(x57 & x58)]
f52 =
[(x52 | x54)
|
(x56 | x58)]
|
[(x60 | x62)
|
(x63 & x64)]
f61 =
[(x61 & x63)
&
(x65 & x67)]
&
[(x69 & x71)
&
(x72 | x73)]
f63 =
[(x63 & x65)
&
(x66 | x67)]
&
[(x66 | x68)
|
(x69 & x70)]
f66 =
[(x66 | x68)
|
(x70 | x72)]
|
[(x74 | x76)
|
(x78 | x80)]
f72 =
[(x72 | x74)
|
(x75 & x76)]
|
[(x75 & x77)
&
(x78 | x79)]
f79 =
[(x79 & x81)
&
(x82 | x83)]
&
[(x82 | x84)
|
(x85 & x86)]
f81 =
[(x81 & x83)
&
(x85 & x87)]
&
[(x86 | x88)
|
(x89 & x90)]
f81a =
[(x81 & x83)
&
(x85 & x87)]
&
[(x89 & x91)
&
(x92 | x93)]
f90 =
[(x90 | x92)
|
(x94 | x96)]
|
[(x98 | x100)
|
(x101 & x102)]
f92 =
[(x92 | x94)
|
(x95 & x96)]
|
[(x95 & x97)
&
(x98 | x99)]
f101 =
[(x101 & x103)
&
(x104 | x105)]
&
[(x104 | x106)
|
(x107 & x108)]
g0 =
[(f0 & f0a)
&
(f0b | f11)]
&
[(f0c | f16)
|
(f13 & f24)]
g0a =
[(f0c | f16a)
|
(f29 | f31)]
|
[(f31a & f42)
&
(f40 | f51)]
g1 =
[(f1 & f17)
&
(f33 & f49)]
&
[(f52 | f63)
|
(f61 & f72)]
g51 =
[(f50 | f66)
|
(f79 | f81)]
|
[(f81a & f92)
&
(f90 | f101)]
out =
(g0 & g0a)
|
(g1 & g51).
13. The process of claim 5 , further comprising: storing a netlist, the netlist defined by:
f0 =
[x0
&
(x1 | x2)]
&
[(x1 | x3)
|
(x4 & x5)]
f0a =
[(x0 & x2)
&
(x4 & x6)]
&
[(x5 | x7)
|
(x8 & x9)]
f0b =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x11 | x12)]
f1 =
[(x1 | x3)
|
(x5 | x7)]
|
[(x9 | x11)
|
(x13 | x15)]
f11 =
[(x11 | x13)
|
(x14 & x15)]
|
[(x14 & x16)
&
(x17 | x18)]
f14 =
[(x14 & x16)
&
(x18 & x20)]
&
[(x22 & x24)
&
(x25 | x26)]
f17 =
[(x17 | x19)
|
(x20 & x21)]
|
[(x18 & x20)
&
(x22 & x23)]
f17a =
[(x17 | x19)
|
(x21 | x23)]
|
[(x25 | x27)
|
(x29 | x31)]
f25 =
[(x25 | x27)
|
(x28 & x29)]
|
[(x28 & x30)
&
(x31 | x32)]
f30 =
[(x30 & x32)
&
(x33 | x34)]
&
[(x33 | x35)
|
(x36 & x37)]
f32 =
[(x32 & x34)
&
(x36 & x38)]
&
[(x37 | x39)
|
(x40 & x41)]
f32a =
[(x32 & x34)
&
(x36 & x38)]
&
[(x40 & x42)
&
(x43 | x44)]
f33 =
[(x33 | x35)
|
(x37 | x39)]
|
[(x41 | x43)
|
(x45 | x47)]
f41 =
[(x41 | x43)
|
(x45 | x47)]
|
[(x49 | x51)
|
(x52 & x53)]
f43 =
[(x43 | x45)
|
(x46 & x47)]
|
[(x46 & x48)
&
(x49 | x50)]
f49 =
[(x49 | x51)
|
(x53 | x55)]
|
[(x57 | x59)
|
(x60 & x61)]
f49a =
[(x49 | x51)
|
(x53 | x55)]
|
[(x57 | x59)
|
(x61 | x63)]
f50 =
[(x50 & x52)
&
(x54 & x56)]
&
[(x58 & x60)
&
(x62 & x64)]
f52 =
[(x52 & x54)
&
(x55 | x56)]
&
[(x53 | x55)
|
(x57 | x58)]
f52a =
[(x52 & x54)
&
(x56 & x58)]
&
[(x60 & x62)
&
(x63 | x64)]
f61 =
[(x61 | x63)
|
(x65 | x67)]
|
[(x69 | x71)
|
(x72 & x73)]
f63 =
[(x63 | x65)
|
(x66 & x67)]
|
[(x66 & x68)
&
(x69 | x70)]
f65 =
[(x65 | x67)
|
(x69 | x71)]
|
[(x73 | x75)
|
(x77 | x79)]
f66 =
[(x66 & x68)
&
(x70 & x72)]
&
[(x74 & x76)
&
(x78 & x80)]
f72 =
[(x72 & x74)
&
(x75 | x76)]
&
[(x75 | x77)
|
(x78 & x79)]
f79 =
[(x79 | x81)
|
(x82 & x83)]
|
[(x82 & x84)
&
(x85 | x86)]
f81 =
[(x81 | x83)
|
(x85 | x87)]
|
[(x86 & x88)
&
(x89 | x90)]
f81a =
[(x81 | x83)
|
(x85 | x87)]
|
[(x89 | x91)
|
(x92 & x93)]
f81b =
[(x81 | x83)
|
(x85 | x87)]
|
[(x89 | x91)
|
(x93 | x95)]
f90 =
[(x90 & x92)
&
(x94 & x96)]
&
[(x98 & x100)
&
(x101 | x102)]
f92 =
[(x92 & x94)
&
(x95 | x96)]
&
[(x95 | x97)
|
(x98 & x99)]
f97 =
[(x97 | x99)
|
(x101 | x103)]
|
[(x105 | x107)
|
(x108 & x109)]
f101 =
[(x101 | x103)
|
(x104 & x105)]
|
[(x104 & x106)
&
(x107 | x108)]
f102 =
[(x102 & x104)
&
(x106 & x108)]
&
[(x110 & x112)
&
(x114 & x116)]
f104 =
[(x104 & x106)
&
(x108 & x110)]
&
[(x112 & x114)
&
(x116 & x118)]
f108 =
[(x108 & x110)
&
(x111 | x112)]
&
[(x111 | x113)
|
(x114 & x115)]
f113 =
[(x113 | x115)
|
(x117 | x119)]
|
[(x121 | x123)
|
(x124 & x125)]
f115 =
[(x115 | x117)
|
(x118 & x119)]
|
[(x118 & x120)
&
(x121 | x122)]
f117 =
[(x117 | x119)
|
(x121 | x123)]
|
[(x125 | x127)
|
(x129 | x131)]
f120 =
[(x120 & x122)
&
(x124 & x126)]
&
[(x128 & x130)
&
(x132 & x134)]
f124 =
[(x124 & x126)
&
(x127 | x128)]
&
[(x125 | x127)
|
(x129 | x130)]
f128 =
[(x128 & x130)
&
(x132 & x134)]
&
[(x136 & x138)
&
(x139 | x140)]
f130 =
[(x130 & x132)
&
(x133 | x134)]
&
[(x133 | x135)
|
(x136 & x137)]
f136 =
[(x136 & x138)
&
(x140 & x142)]
&
[(x144 & x146)
&
(x147 | x148)]
f139 =
[(x139 | x141)
|
(x142 & x143)]
|
[(x140 & x142)
&
(x144 & x145)]
f143 =
[(x143 | x145)
|
(x147 | x149)]
|
[(x151 | x153)
|
(x155 | x157)]
f145 =
[(x145 | x147)
|
(x149 | x151)]
|
[(x153 | x155)
|
(x156 & x157)]
f147 =
[(x147 | x149)
|
(x150 & x151)]
|
[(x150 & x152)
&
(x153 | x154)]
f154 =
[(x154 & x156)
&
(x158 & x160)]
&
[(x162 & x164)
&
(x165 | x166)]
f156 =
[(x156 & x158)
&
(x159 | x160)]
&
[(x159 | x161)
|
(x162 & x163)]
f159 =
[(x159 | x161)
|
(x163 | x165)]
|
[(x167 | x169)
|
(x171 | x173)]
f165 =
[(x165 | x167)
|
(x168 & x169)]
|
[(x168 & x170)
&
(x171 | x172)]
f172 =
[(x172 & x174)
&
(x175 | x176)]
&
[(x175 | x177)
|
(x178 & x179)]
f174 =
[(x174 & x176)
&
(x178 & x180)]
&
[(x179 | x181)
|
(x182 & x183)]
f174a =
[(x174 & x176)
&
(x178 & x180)]
&
[(x182 & x184)
&
(x185 | x186)]
f183 =
[(x183 | x185)
|
(x187 | x189)]
|
[(x191 | x193)
|
(x194 & x195)]
f185 =
[(x185 | x187)
|
(x188 & x189)]
|
[(x188 & x190)
&
(x191 | x192)]
f194 =
[(x194 & x196)
&
(x197 | x198)]
&
[(x197 | x199)
|
(x200 & x201)]
g0 =
[(f0 | f0a)
|
(f0b & f11)]
&
[(f1 | f17)
|
(f14 & f25)]
g1 =
[(f1 | f17a)
|
(f30 | f32)]
|
[(t32a & f43)
&
(f41 | f52)]
g1a =
[(f1 | f17a)
|
(f33 | f49)]
|
[(t52a & f63)
&
(f61 | f72)]
g1b =
[(f1 | f17a)
|
(f33 | f49a)]
|
[(f65 | f81b)
|
(f97 | f108)]
g50 =
[(f50 & f66)
&
(f79 & f81)]
&
[(f81a | f92)
|
(f90 & f101)]
g102 =
[(f102 & f115)
&
(f113 | f124)]
&
[(f117 | f130)
|
(f128 & f139)]
g104 =
[(f104 & f120)
&
(f136 & f147)]
&
[(f145 | f156)
|
(f154 & f165)]
g143 =
[(f143 | f159)
|
(f172 | f174)]
|
[(f174a & f185)
&
(f183 | f194)]
out =
[(g0 & g1)
&
(g1a | g50)]
&
[(g1b | g102)
|
(g104 & g143)].
14. The process of claim 5 , further comprising: storing a netlist, the netlist defined by:
f0 =
[x0
|
(x1 & x2)]
|
[(x1 & x3)
&
(x4 | x5)]
f0a =
[(x0 | x2)
|
(x4 | x6)]
|
[(x5 & x7)
&
(x8 | x9)]
f0b =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x11 & x12)]
f1 =
[(x1 & x3)
&
(x5 & x7)]
&
[(x9 & x11)
&
(x13 & x15)]
f11 =
[(x11 & x13)
&
(x14 | x15)]
&
[(x14 | x16)
|
(x17 & x18)]
f14 =
[(x14 | x16)
|
(x18 | x20)]
|
[(x22 | x24)
|
(x25 & x26)]
f17 =
[(x17 & x19)
&
(x20 | x21)]
&
[(x18 | x20)
|
(x22 | x23)]
f17a =
[(x17 & x19)
&
(x21 & x23)]
&
[(x25 & x27)
&
(x29 & x31)]
f25 =
[(x25 & x27)
&
(x28 | x29)]
&
[(x28 | x30)
|
(x31 & x32)]
f30 =
[(x30 | x32)
|
(x33 & x34)]
|
[(x33 & x35)
&
(x36 | x37)]
f32 =
[(x32 | x34)
|
(x36 | x38)]
|
[(x37 & x39)
&
(x40 | x41)]
f32a =
[(x32 | x34)
|
(x36 | x38)]
|
[(x40 | x42)
|
(x43 & x44)]
f33 =
[(x33 & x35)
&
(x37 & x39)]
&
[(x41 & x43)
&
(x45 & x47)]
f41 =
[(x41 & x43)
&
(x45 & x47)]
&
[(x49 & x51)
&
(x52 | x53)]
f43 =
[(x43 & x45)
&
(x46 | x47)]
&
[(x46 | x48)
|
(x49 & x50)]
f49 =
[(x49 & x51)
&
(x53 & x55)]
&
[(x57 & x59)
&
(x60 | x61)]
f49a =
[(x49 & x51)
&
(x53 & x55)]
&
[(x57 & x59)
&
(x61 & x63)]
f50 =
[(x50 | x52)
|
(x54 | x56)]
|
[(x58 | x60)
|
(x62 | x64)]
f52 =
[(x52 | x54)
|
(x55 & x56)]
|
[(x53 & x55)
&
(x57 & x58)]
f52a =
[(x52 | x54)
|
(x56 | x58)]
|
[(x60 | x62)
|
(x63 & x64)]
f61 =
[(x61 & x63)
&
(x65 & x67)]
&
[(x69 & x71)
&
(x72 | x73)]
f63 =
[(x63 & x65)
&
(x66 | x67)]
&
[(x66 | x68)
|
(x69 & x70)]
f65 =
[(x65 & x67)
&
(x69 & x71)]
&
[(x73 & x75)
&
(x77 & x79)]
f66 =
[(x66 | x68)
|
(x70 | x72)]
|
[(x74 | x76)
|
(x78 | x80)]
f72 =
[(x72 | x74)
|
(x75 & x76)]
|
[(x75 & x77)
&
(x78 | x79)]
f79 =
[(x79 & x81)
&
(x82 | x83)]
&
[(x82 | x84)
|
(x85 & x86)]
f81 =
[(x81 & x83)
&
(x85 & x87)]
&
[(x86 | x88)
|
(x89 & x90)]
f81a =
[(x81 & x83)
&
(x85 & x87)]
&
[(x89 & x91)
&
(x92 | x93)]
f81b =
[(x81 & x83)
&
(x85 & x87)]
&
[(x89 & x91)
&
(x93 & x95)]
f90 =
[(x90 | x92)
|
(x94 | x96)]
|
[(x98 | x100)
|
(x101 & x102)]
f92 =
[(x92 | x94)
|
(x95 & x96)]
|
[(x95 & x97)
&
(x98 | x99)]
f97 =
[(x97 & x99)
&
(x101 & x103)]
&
[(x105 & x107)
&
(x108 | x109)]
f101 =
[(x101 & x103)
&
(x104 | x105)]
&
[(x104 | x106)
|
(x107 & x108)]
f102 =
[(x102 | x104)
|
(x106 | x108)]
|
[(x110 | x112)
|
(x114 | x116)]
f104 =
[(x104 | x106)
|
(x108 | x110)]
|
[(x112 | x114)
|
(x116 | x118)]
f108 =
[(x108 | x110)
|
(x111 & x112)]
|
[(x111 & x113)
&
(x114 | x115)]
f113 =
[(x113 & x115)
&
(x117 & x119)]
&
[(x121 & x123)
&
(x124 | x125)]
f115 =
[(x115 & x117)
&
(x118 | x119)]
&
[(x118 | x120)
|
(x121 & x122)]
f117 =
[(x117 & x119)
&
(x121 & x123)]
&
[(x125 & x127)
&
(x129 & x131)]
f120 =
[(x120 | x122)
|
(x124 | x126)]
|
[(x128 | x130)
|
(x132 | x134)]
f124 =
[(x124 | x126)
|
(x127 & x128)]
|
[(x125 & x127)
&
(x129 & x130)]
f128 =
[(x128 | x130)
|
(x132 | x134)]
|
[(x136 | x138)
|
(x139 & x140)]
f130 =
[(x130 | x132)
|
(x133 & x134)]
|
[(x133 & x135)
&
(x136 | x137)]
f136 =
[(x136 | x138)
|
(x140 | x142)]
|
[(x144 | x146)
|
(x147 & x148)]
f139 =
[(x139 & x141)
&
(x142 | x143)]
&
[(x140 | x142)
|
(x144 | x145)]
f143 =
[(x143 & x145)
&
(x147 & x149)]
&
[(x151 & x153)
&
(x155 & x157)]
f145 =
[(x145 & x147)
&
(x149 & x151)]
&
[(x153 & x155)
&
(x156 | x157)]
f147 =
[(x147 & x149)
&
(x150 | x151)]
&
[(x150 | x152)
|
(x153 & x154)]
f154 =
[(x154 | x156)
|
(x158 | x160)]
|
[(x162 | x164)
|
(x165 & x166)]
f156 =
[(x156 | x158)
|
(x159 & x160)]
|
[(x159 & x161)
&
(x162 | x163)]
f159 =
[(x159 & x161)
&
(x163 & x165)]
&
[(x167 & x169)
&
(x171 & x173)]
f165 =
[(x165 & x167)
&
(x168 | x169)]
&
[(x168 | x170)
|
(x171 & x172)]
f172 =
[(x172 | x174)
|
(x175 & x176)]
|
[(x175 & x177)
&
(x178 | x179)]
f174 =
[(x174 | x176)
|
(x178 | x180)]
|
[(x179 & x181)
&
(x182 | x183)]
f174a =
[(x174 | x176)
|
(x178 | x180)]
|
[(x182 | x184)
|
(x185 & x186)]
f183 =
[(x183 & x185)
&
(x187 & x189)]
&
[(x191 & x193)
&
(x194 | x195)]
f185 =
[(x185 & x187)
&
(x188 | x189)]
&
[(x188 | x190)
|
(x191 & x192)]
f194 =
[(x194 | x196)
|
(x197 & x198)]
|
[(x197 & x199)
&
(x200 | x201)]
g0 =
[(f0 & f0a)
&
(f0b | f11)]
|
[(f1 & f17)
&
(f14 | f25)]
g1 =
[(f1 & f17a)
&
(f30 & f32)]
&
[(f32a | f43)
|
(f41 & f52)]
g1a =
[(f1 & f17a)
&
(f33 & f49)]
&
[(f52a | f63)
|
(f61 & f72)]
g1b =
[(f1 & f17a)
&
(f33 & f49a)]
&
[(f65 & f81b)
&
(f97 & f108)]
g50 =
[(f50 | f66)
|
(f79 | f81)]
|
[(f81a & f92)
&
(f90 | f101)]
g102 =
[(f102 | f115)
|
(f113 & f124)]
|
[(f117 & f130)
&
(f128 | f139)]
g104 =
[(f104 | f120)
|
(f136 | f147)]
|
[(f145 & f156)
&
(f154 | f165)]
g143 =
[(f143 & f159)
&
(f172 & f174)]
&
[(f174a | f185)
|
(f183 & f194)]
out =
[(g0 | g1)
|
(g1a & g50)]
|
[(g1b & g102)
&
(g104 | g143)].
15. The process of claim 6 , further comprising: storing a netlist, the netlist defined by:
f0 =
[(x0 & x1)
|
(x0 & x2)]
&
[(x1 | x3)
|
(x4 & x5)]
f0a =
[(x0 & x2)
&
(x4 & x6)]
&
[(x5 | x7)
|
(x8 & x9)]
f0b =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x11 | x12)]
f0c =
[(x0 & x2)
&
(x4 & x6)]
&
[(x8 & x10)
&
(x12 & x14)]
f1 =
[(x1 | x3)
|
(x5 | x7)]
|
[(x9 | x11)
|
(x13 | x15)]
f11 =
[(x11 | x13)
|
(x14 & x15)]
|
[(x12 & x14)
&
(x16 & x17)]
f13 =
[(x13 | x15)
|
(x17 | x19)]
|
[(x21 | x23)
|
(x24 & x25)]
f16 =
[(x16 & x18)
&
(x19 | x20)]
&
[(x17 | x19)
|
(x21 | x22)]
f16a =
[(x16 & x18)
&
(x20 & x22)]
&
[(x24 & x26)
&
(x28 & x30)]
f17 =
[(x17 | x19)
|
(x21 | x23)]
|
[(x25 | x27)
|
(x29 | x31)]
f24 =
[(x24 & x26)
&
(x27 | x28)]
&
[(x27 | x29)
|
(x30 & x31)]
f29 =
[(x29 | x31)
|
(x32 & x33)]
|
[(x32 & x34)
&
(x35 | x36)]
f31 =
[(x31 | x33)
|
(x35 | x37)]
|
[(x36 & x38)
&
(x39 | x40)]
f31a =
[(x31 | x33)
|
(x35 | x37)]
|
[(x39 | x41)
|
(x42 & x43)]
f32 =
[(x32 & x34)
&
(x36 & x38)]
&
[(x40 & x42)
&
(x44 & x46)]
f33 =
[(x33 | x35)
|
(x37 | x39)]
|
[(x41 | x43)
|
(x45 | x47)]
f40 =
[(x40 & x42)
&
(x44 & x46)]
&
[(x48 & x50)
&
(x51 | x52)]
f42 =
[(x42 & x44)
&
(x45 | x46)]
&
[(x45 | x47)
|
(x48 & x49)]
f48 =
[(x48 & x50)
&
(x52 & x54)]
&
[(x56 & x58)
&
(x60 & x62)]
f49 =
[(x49 | x51)
|
(x53 | x55)]
|
[(x57 | x59)
|
(x60 & x61)]
f49a =
[(x49 | x51)
|
(x53 | x55)]
|
[(x57 | x59)
|
(x61 | x63)]
f50 =
[(x50 & x52)
&
(x54 & x56)]
&
[(x58 & x60)
&
(x62 & x64)]
f51 =
[(x51 | x53)
|
(x54 & x55)]
|
[(x54 & x56)
&
(x57 | x58)]
f52 =
[(x52 & x54)
&
(x56 & x58)]
&
[(x60 & x62)
&
(x63 | x64)]
f61 =
[(x61 | x63)
|
(x65 | x67)]
|
[(x69 | x71)
|
(x72 & x73)]
f63 =
[(x63 | x65)
|
(x66 & x67)]
|
[(x66 & x68)
&
(x69 | x70)]
f64 =
[(x64 & x66)
&
(x68 & x70)]
&
[(x72 & x74)
&
(x76 & x78)]
f65 =
[(x65 | x67)
|
(x69 | x71)]
|
[(x73 | x75)
|
(x77 | x79)]
f66 =
[(x66 & x68)
&
(x70 & x72)]
&
[(x74 & x76)
&
(x78 & x80)]
f72 =
[(x72 & x74)
&
(x75 | x76)]
&
[(x75 | x77)
|
(x78 & x79)]
f79 =
[(x79 | x81)
|
(x82 & x83)]
|
[(x82 & x84)
&
(x85 | x86)]
f80 =
[(x80 & x82)
&
(x84 & x86)]
&
[(x88 & x90)
&
(x92 & x94)]
f81 =
[(x81 | x83)
|
(x85 | x87)]
|
[(x86 & x88)
&
(x89 | x90)]
f81a =
[(x81 | x83)
|
(x85 | x87)]
|
[(x89 | x91)
|
(x92 & x93)]
f81b =
[(x81 | x83)
|
(x85 | x87)]
|
[(x89 | x91)
|
(x93 | x95)]
f90 =
[(x90 & x92)
&
(x94 & x96)]
&
[(x98 & x100)
&
(x101 | x102)]
f92 =
[(x92 & x94)
&
(x95 | x96)]
&
[(x95 | x97)
|
(x98 & x99)]
f96 =
[(x96 & x98)
&
(x100 & x102)]
&
[(x104 & x106)
&
(x108 & x110)]
f97 =
[(x97 | x99)
|
(x101 | x103)]
|
[(x105 | x107)
|
(x108 & x109)]
f101 =
[(x101 | x103)
|
(x104 & x105)]
|
[(x104 & x106)
&
(x107 | x108)]
f102 =
[(x102 & x104)
&
(x106 & x108)]
&
[(x110 & x112)
&
(x114 & x116)]
f104 =
[(x104 & x106)
&
(x108 & x110)]
&
[(x112 & x114)
&
(x116 & x118)]
f108 =
[(x108 & x110)
&
(x111 | x112)]
&
[(x111 | x113)
|
(x114 & x115)]
f112 =
[(x112 & x114)
&
(x116 & x118)]
&
[(x120 & x122)
&
(x124 & x126)]
f113 =
[(x113 | x115)
|
(x117 | x119)]
|
[(x121 | x123)
|
(x124 & x125)]
f115 =
[(x115 | x117)
|
(x118 & x119)]
|
[(x118 & x120)
&
(x121 | x122)]
f117 =
[(x117 | x119)
|
(x121 | x123)]
|
[(x125 | x127)
|
(x129 | x131)]
f120 =
[(x120 & x122)
&
(x124 & x126)]
&
[(x128 & x130)
&
(x132 & x134)]
f124 =
[(x124 & x126)
&
(x127 | x128)]
&
[(x125 | x127)
|
(x129 | x130)]
f128 =
[(x128 & x130)
&
(x132 & x134)]
&
[(x136 & x138)
&
(x139 | x140)]
f128a =
[(x128 & x130)
&
(x132 & x134)]
&
[(x136 & x138)
&
(x140 & x142)]
f130 =
[(x130 & x132)
&
(x133 | x134)]
&
[(x133 | x135)
|
(x136 & x137)]
f136 =
[(x136 & x138)
&
(x140 & x142)]
&
[(x144 & x146)
&
(x147 | x148)]
f139 =
[(x139 | x141)
|
(x142 & x143)]
|
[(x140 & x142)
&
(x144 & x145)]
f143 =
[(x143 | x145)
|
(x147 | x149)]
|
[(x151 | x153)
|
(x155 | x157)]
f144 =
[(x144 & x146)
&
(x148 & x150)]
&
[(x152 & x154)
&
(x156 & x158)]
f145 =
[(x145 | x147)
|
(x149 | x151)]
|
[(x153 | x155)
|
(x156 & x157)]
f147 =
[(x147 | x149)
|
(x150 & x151)]
|
[(x150 & x152)
&
(x153 | x154)]
f154 =
[(x154 & x156)
&
(x158 & x160)]
&
[(x162 & x164)
&
(x165 | x166)]
f156 =
[(x156 & x158)
&
(x159 | x160)]
&
[(x159 | x161)
|
(x162 & x163)]
f159 =
[(x159 | x161)
|
(x163 | x165)]
|
[(x167 | x169)
|
(x171 | x173)]
f160 =
[(x160 & x162)
&
(x164 & x166)]
&
[(x168 & x170)
&
(x172 & x174)]
f165 =
[(x165 | x167)
|
(x168 & x169)]
|
[(x168 & x170)
&
(x171 | x172)]
f172 =
[(x172 & x174)
&
(x175 | x176)]
&
[(x175 | x177)
|
(x178 & x179)]
f174 =
[(x174 & x176)
&
(x178 & x180)]
&
[(x179 | x181)
|
(x182 & x183)]
f174a =
[(x174 & x176)
&
(x178 & x180)]
&
[(x182 & x184)
&
(x185 | x186)]
f176 =
[(x176 & x178)
&
(x180 & x182)]
&
[(x184 & x186)
&
(x188 & x190)]
f183 =
[(x183 | x185)
|
(x187 | x189)]
|
[(x191 | x193)
|
(x194 & x195)]
f185 =
[(x185 | x187)
|
(x188 & x189)]
&
[(x188 & x190)
&
(x191 & x192)]
f192 =
[(x192 & x194)
&
(x196 & x198)]
&
[(x200 & x202)
&
(x203 | x204)]
f194 =
[(x194 & x196)
&
(x197 | x198)]
&
[(x197 | x199)
|
(x200 & x201)]
f195 =
[(x195 | x197)
|
(x199 | x201)]
|
[(x203 | x205)
|
(x207 | x209)]
f201 =
[(x201 | x203)
|
(x205 | x207)]
|
[(x209 | x211)
|
(x212 & x213)]
f203 =
[(x203 | x205)
|
(x206 & x207)]
|
[(x206 & x208)
&
(x209 | x210)]
f203a =
[(x203 | x205)
|
(x207 | x209)]
|
[(x211 | x213)
|
(x215 | x217)]
f211 =
[(x211 | x213)
|
(x215 | x217)]
|
[(x219 | x221)
|
(x223 | x225)]
f212 =
[(x212 & x214)
&
(x215 | x216)]
&
[(x213 | x215)
|
(x217 | x218)]
f214 =
[(x214 & x216)
&
(x218 & x220)]
&
[(x222 & x224)
&
(x225 | x226)]
f216 =
[(x216 & x218)
&
(x219 | x220)]
&
[(x219 | x221)
|
(x222 & x223)]
f218 =
[(x218 & x220)
&
(x222 & x224)]
&
[(x226 & x228)
&
(x230 & x232)]
f225 =
[(x225 | x227)
|
(x228 & x229)]
|
[(x226 & x228)
&
(x230 & x231)]
f227 =
[(x227 | x229)
|
(x231 | x233)]
|
[(x235 | x237)
|
(x239 | x241)]
f229 =
[(x229 | x231)
|
(x233 | x235)]
|
[(x237 | x239)
|
(x240 & x241)]
f231 =
[(x231 | x233)
|
(x234 & x235)]
|
[(x234 & x236)
&
(x237 | x238)]
f234 =
[(x234 & x236)
&
(x238 & x240)]
&
[(x242 & x244)
&
(x246 & x248)]
f240 =
[(x240 & x242)
&
(x243 | x244)]
&
[(x243 | x245)
|
(x246 & x247)]
f243 =
[(x243 | x245)
|
(x247 | x249)]
|
[(x251 | x253)
|
(x255 | x257)]
f247 =
[(x247 | x249)
|
(x250 & x251)]
|
[(x250 & x252)
&
(x253 | x254)]
f249 =
[(x249 | x251)
|
(x253 | x255)]
|
[(x254 & x256)
&
(x257 | x258)]
f249a =
[(x249 | x251)
|
(x253 | x255)]
|
[(x257 | x259)
|
(x260 & x261)]
f258 =
[(x258 & x260)
&
(x262 & x264)]
&
[(x266 & x268)
&
(x269 | x270)]
f259 =
[(x259 | x261)
|
(x263 | x265)]
|
[(x267 | x269)
|
(x271 | x273)]
f260 =
[(x260 & x262)
&
(x263 | x264)]
&
[(x263 | x265)
|
(x266 & x267)]
f269 =
[(x269 | x271)
|
(x272 & x273)]
|
[(x272 & x274)
&
(x275 | x276)]
f272 =
[(x272 & x274)
&
(x276 & x278)]
&
[(x280 & x282)
&
(x283 | x284)]
f275 =
[(x275 | x277)
|
(x278 & x279)]
|
[(x276 & x278)
&
(x280 & x281)]
f276 =
[(x276 & x278)
&
(x280 & x282)]
&
[(x284 & x286)
&
(x288 & x290)]
f278 =
[(x278 & x280)
&
(x282 & x284)]
&
[(x286 & x288)
&
(x290 & x292)]
f283 =
[(x283 | x285)
|
(x286 & x287)]
|
[(x284 & x286)
&
(x288 & x289)]
f287 =
[(x287 | x289)
|
(x291 | x293)]
|
[(x295 | x297)
|
(x298 & x299)]
f289 =
[(x289 | x291)
|
(x292 & x293)]
|
[(x292 & x294)
&
(x295 | x296)]
f291 =
[(x291 | x293)
|
(x295 | x297)]
|
[(x299 | x301)
|
(x303 | x305)]
f294 =
[(x294 & x296)
&
(x298 & x300)]
&
[(x302 & x304)
&
(x306 & x308)]
f298 =
[(x298 & x300)
&
(x301 | x302)]
&
[(x299 | x301)
|
(x303 | x304)]
f302 =
[(x302 & x304)
&
(x306 & x308)]
&
[(x310 & x312)
&
(x313 | x314)]
f304 =
[(x304 & x306)
&
(x307 | x308)]
&
[(x307 | x309)
|
(x310 & x311)]
f310 =
[(x310 & x312)
&
(x314 & x316)]
&
[(x318 & x320)
&
(x321 | x322)]
f313 =
[(x313 | x315)
|
(x316 & x317)]
|
[(x314 & x316)
&
(x318 & x319)]
f317 =
[(x317 | x319)
|
(x321 | x323)]
|
[(x325 | x327)
|
(x329 | x331)]
f319 =
[(x319 | x321)
|
(x323 | x325)]
|
[(x327 | x329)
|
(x330 & x331)]
f321 =
[(x321 | x323)
|
(x324 & x325)]
|
[(x324 & x326)
&
(x327 | x328)]
f328 =
[(x328 & x330)
&
(x332 & x334)]
&
[(x336 & x338)
&
(x339 | x340)]
f330 =
[(x330 & x332)
&
(x333 | x334)]
&
[(x333 | x335)
|
(x336 & x337)]
f333 =
[(x333 | x335)
|
(x337 | x339)]
|
[(x341 | x343)
|
(x345 | x347)]
f339 =
[(x339 | x341)
|
(x342 & x343)]
|
[(x342 & x344)
&
(x345 | x346)]
f346 =
[(x346 & x348)
&
(x349 | x350)]
&
[(x349 | x351)
|
(x352 & x353)]
f348 =
[(x348 & x350)
&
(x352 & x354)]
&
[(x353 | x355)
|
(x356 & x357)]
f348a =
[(x348 & x350)
&
(x352 & x354)]
&
[(x356 & x358)
&
(x359 | x360)]
f357 =
[(x357 | x359)
|
(x361 | x363)]
|
[(x365 | x367)
|
(x368 & x369)]
f359 =
[(x359 | x361)
|
(x362 & x363)]
|
[(x362 & x364)
&
(x365 | x366)]
f368 =
[(x368 & x370)
&
(x371 | x372)]
&
[(x369 | x371)
|
(x373 | x374)]
g0 =
[(f0 | f0a)
|
(f0b & f11)]
|
[(f0c & f16)
&
(f13 | f24)]
g0a =
[(f0c & f16a)
&
(f29 & f31)]
&
[(f31a | f42)
|
(f40 & f51)]
g0b =
[(f0c & f16a)
&
(f32 & f48)]
&
[(f64 & f80)
&
(f96 & f112)]
g1 =
[(f1 | f17)
|
(f33 | f49)]
|
[(f52 & f63)
&
(f61 | f72)]
g1a =
[(f1 | f17)
|
(f33 | f49a)]
|
[(f65 | f81b)
|
(f97 | f108)]
g50 =
[(f50 & f66)
&
(f79 & f81)]
&
[(f81a | f92)
|
(f90 & f101)]
g102 =
[(f102 & f115)
&
(f113 | f124)]
&
[(f117 | f130)
|
(f128 & f139)]
g104 =
[(f104 & f120)
&
(f136 & f147)]
&
[(f145 | f156)
|
(f154 & f165)]
g128 =
[(f128a & f144)
&
(f160 & f176)]
&
[(f192 & f203)
&
(f201 | f212)]
g143 =
[(f143 | f159)
|
(f172 & f174)]
|
[(f174a & f185)
&
(f183 | f194)]
g195 =
[(f195 | f211)
|
(f227 & f243)]
|
[(f259 | f275)
|
(f272 & f283)]
g203 =
[(f203a | f216)
|
(f214 & f225)]
|
[(f218 & f231)
&
(f229 | f240)]
g218 =
[(f218 & f234)
&
(f247 & f249)]
&
[(f249a | f260)
|
(f258 & f269)]
g276 =
[(f276 & f289)
&
(f287 | f298)]
&
[(f291 | f304)
|
(f302 & f313)]
g278 =
[(f278 & f294)
&
(f310 & f321)]
&
[(f319 | f330)
|
(f328 & f339)]
g317 =
[(f317 | f333)
|
(f346 | f348)]
|
[(f348a & f359)
&
(f357 | f368)]
h0 =
[(g0 | g0a)
&
(g1 | g50)]
&
[(g1a | g102)
|
(g104 & g143)]
h0a =
[(g0b & g128)
&
(g203 | g218)]
&
[(g195 | g276)
|
(g278 & g317)]
out =
h0 | h0a.
16. The process of claim 6 , further comprising: storing a netlist, the netlist defined by:
f0 =
[(x0 | x1)
&
(x0 | x2)]
|
[(x1 & x3)
&
(x4 | x5)]
f0a =
[(x0 | x2)
|
(x4 | x6)]
|
[(x5 & x7)
&
(x8 | x9)]
f0b =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x11 & x12)]
f0c =
[(x0 | x2)
|
(x4 | x6)]
|
[(x8 | x10)
|
(x12 | x14)]
f1 =
[(x1 & x3)
&
(x5 & x7)]
&
[(x9 & x11)
&
(x13 & x15)]
f11 =
[(x11 & x13)
&
(x14 | x15)]
&
[(x12 | x14)
|
(x16 | x17)]
f13 =
[(x13 & x15)
&
(x17 & x19)]
&
[(x21 & x23)
&
(x24 | x25)]
f16 =
[(x16 | x18)
|
(x19 & x20)]
|
[(x17 & x19)
&
(x21 & x22)]
f16a =
[(x16 | x18)
|
(x20 | x22)]
|
[(x24 | x26)
|
(x28 | x30)]
f17 =
[(x17 & x19)
&
(x21 & x23)]
&
[(x25 & x27)
&
(x29 & x31)]
f24 =
[(x24 | x26)
|
(x27 & x28)]
|
[(x27 & x29)
&
(x30 | x31)]
f29 =
[(x29 & x31)
&
(x32 | x33)]
&
[(x32 | x34)
|
(x35 & x36)]
f31 =
[(x31 & x33)
&
(x35 & x37)]
&
[(x36 | x38)
|
(x39 & x40)]
f31a =
[(x31 & x33)
&
(x35 & x37)]
&
[(x39 & x41)
&
(x42 | x43)]
f32 =
[(x32 | x34)
|
(x36 | x38)]
|
[(x40 | x42)
|
(x44 | x46)]
f33 =
[(x33 & x35)
&
(x37 & x39)]
&
[(x41 & x43)
&
(x45 & x47)]
f40 =
[(x40 | x42)
|
(x44 | x46)]
|
[(x48 | x50)
|
(x51 & x52)]
f42 =
[(x42 | x44)
|
(x45 & x46)]
|
[(x45 & x47)
&
(x48 | x49)]
f48 =
[(x48 | x50)
|
(x52 | x54)]
|
[(x56 | x58)
|
(x60 | x62)]
f49 =
[(x49 & x51)
&
(x53 & x55)]
&
[(x57 & x59)
&
(x60 | x61)]
f49a =
[(x49 & x51)
&
(x53 & x55)]
&
[(x57 & x59)
&
(x61 & x63)]
f50 =
[(x50 | x52)
|
(x54 | x56)]
|
[(x58 | x60)
|
(x62 | x64)]
f51 =
[(x51 & x53)
&
(x54 | x55)]
&
[(x54 | x56)
|
(x57 & x58)]
f52 =
[(x52 | x54)
|
(x56 | x58)]
|
[(x60 | x62)
|
(x63 & x64)]
f61 =
[(x61 & x63)
&
(x65 & x67)]
&
[(x69 & x71)
&
(x72 | x73)]
f63 =
[(x63 & x65)
&
(x66 | x67)]
&
[(x66 | x68)
|
(x69 & x70)]
f64 =
[(x64 | x66)
|
(x68 | x70)]
|
[(x72 | x74)
|
(x76 | x78)]
f65 =
[(x65 & x67)
&
(x69 & x71)]
&
[(x73 & x75)
&
(x77 & x79)]
f66 =
[(x66 | x68)
|
(x70 | x72)]
|
[(x74 | x76)
|
(x78 | x80)]
f72 =
[(x72 | x74)
|
(x75 & x76)]
|
[(x75 & x77)
&
(x78 | x79)]
f79 =
[(x79 & x81)
&
(x82 | x83)]
&
[(x82 | x84)
|
(x85 & x86)]
f80 =
[(x80 | x82)
|
(x84 | x86)]
|
[(x88 | x90)
|
(x92 | x94)]
f81 =
[(x81 & x83)
&
(x85 & x87)]
&
[(x86 | x88)
|
(x89 & x90)]
f81a =
[(x81 & x83)
&
(x85 & x87)]
&
[(x89 & x91)
&
(x92 | x93)]
f81b =
[(x81 & x83)
&
(x85 & x87)]
&
[(x89 & x91)
&
(x93 & x95)]
f90 =
[(x90 | x92)
|
(x94 | x96)]
|
[(x98 | x100)
|
(x101 & x102)]
f92 =
[(x92 | x94)
|
(x95 & x96)]
|
[(x95 & x97)
&
(x98 | x99)]
f96 =
[(x96 | x98)
|
(x100 | x102)]
|
[(x104 | x106)
|
(x108 | x110)]
f97 =
[(x97 & x99)
&
(x101 & x103)]
&
[(x105 & x107)
&
(x108 | x109)]
f101 =
[(x101 & x103)
&
(x104 | x105)]
&
[(x104 | x106)
|
(x107 & x108)]
f102 =
[(x102 | x104)
|
(x106 | x108)]
|
[(x110 | x112)
|
(x114 | x116)]
f104 =
[(x104 | x106)
|
(x108 | x110)]
|
[(x112 | x114)
|
(x116 | x118)]
f108 =
[(x108 | x110)
|
(x111 & x112)]
|
[(x111 & x113)
&
(x114 | x115)]
f112 =
[(x112 | x114)
|
(x116 | x118)]
|
[(x120 | x122)
|
(x124 | x126)]
f113 =
[(x113 & x115)
&
(x117 & x119)]
&
[(x121 & x123)
&
(x124 | x125)]
f115 =
[(x115 & x117)
&
(x118 | x119)]
&
[(x118 | x120)
|
(x121 & x122)]
f117 =
[(x117 & x119)
&
(x121 & x123)]
&
[(x125 & x127)
&
(x129 & x131)]
f120 =
[(x120 | x122)
|
(x124 | x126)]
|
[(x128 | x130)
|
(x132 | x134)]
f124 =
[(x124 | x126)
|
(x127 & x128)]
|
[(x125 & x127)
&
(x129 & x130)]
f128 =
[(x128 | x130)
|
(x132 | x134)]
|
[(x136 | x138)
|
(x139 & x140)]
f128a =
[(x128 | x130)
|
(x132 | x134)]
|
[(x136 | x138)
|
(x140 | x142)]
f130 =
[(x130 | x132)
|
(x133 & x134)]
|
[(x133 & x135)
&
(x136 | x137)]
f136 =
[(x136 | x138)
|
(x140 | x142)]
|
[(x144 | x146)
|
(x147 & x148)]
f139 =
[(x139 & x141)
&
(x142 | x143)]
&
[(x140 | x142)
|
(x144 | x145)]
f143 =
[(x143 & x145)
&
(x147 & x149)]
&
[(x151 & x153)
&
(x155 & x157)]
f144 =
[(x144 | x146)
|
(x148 | x150)]
|
[(x152 | x154)
|
(x156 | x158)]
f145 =
[(x145 & x147)
&
(x149 & x151)]
&
[(x153 & x155)
&
(x156 | x157)]
f147 =
[(x147 & x149)
&
(x150 | x151)]
&
[(x150 | x152)
|
(x153 & x154)]
f154 =
[(x154 | x156)
|
(x158 | x160)]
|
[(x162 | x164)
|
(x165 & x166)]
f156 =
[(x156 | x158)
|
(x159 & x160)]
|
[(x159 & x161)
&
(x162 | x163)]
f159 =
[(x159 & x161)
&
(x163 & x165)]
&
[(x167 & x169)
&
(x171 & x173)]
f160 =
[(x160 | x162)
|
(x164 | x166)]
|
[(x168 | x170)
|
(x172 | x174)]
f165 =
[(x165 & x167)
&
(x168 | x169)]
&
[(x168 | x170)
|
(x171 & x172)]
f172 =
[(x172 | x174)
|
(x175 & x176)]
|
[(x175 & x177)
&
(x178 | x179)]
f174 =
[(x174 | x176)
|
(x178 | x180)]
|
[(x179 & x181)
&
(x182 | x183)]
f174a =
[(x174 | x176)
|
(x178 | x180)]
|
[(x182 | x184)
|
(x185 & x186)]
f176 =
[(x176 | x178)
|
(x180 | x182)]
|
[(x184 | x186)
|
(x188 | x190)]
f183 =
[(x183 & x185)
&
(x187 & x189)]
&
[(x191 & x193)
&
(x194 | x195)]
f185 =
[(x185 & x187)
&
(x188 | x189)]
&
[(x188 | x190)
|
(x191 & x192)]
f192 =
[(x192 | x194)
|
(x196 | x198)]
|
[(x200 | x202)
|
(x203 & x204)]
f194 =
[(x194 | x196)
|
(x197 & x198)]
|
[(x197 & x199)
&
(x200 | x201)]
f195 =
[(x195 & x197)
&
(x199 & x201)]
&
[(x203 & x205)
&
(x207 & x209)]
f201 =
[(x201 & x203)
&
(x205 & x207)]
&
[(x209 & x211)
&
(x212 | x213)]
f203 =
[(x203 & x205)
&
(x206 | x207)]
&
[(x206 | x208)
|
(x209 & x210)]
f203a =
[(x203 & x205)
&
(x207 & x209)]
&
[(x211 & x213)
&
(x215 & x217)]
f211 =
[(x211 & x213)
&
(x215 & x217)]
&
[(x219 & x221)
&
(x223 & x225)]
f212 =
[(x212 | x214)
|
(x215 & x216)]
|
[(x213 & x215)
&
(x217 & x218)]
f214 =
[(x214 | x216)
|
(x218 | x220)]
|
[(x222 | x224)
|
(x225 & x226)]
f216 =
[(x216 | x218)
|
(x219 & x220)]
|
[(x219 & x221)
&
(x222 | x223)]
f218 =
[(x218 | x220)
|
(x222 | x224)]
|
[(x226 | x228)
|
(x230 | x232)]
f225 =
[(x225 & x227)
&
(x228 | x229)]
&
[(x226 | x228)
|
(x230 | x231)]
f227 =
[(x227 & x229)
&
(x231 & x233)]
&
[(x235 & x237)
&
(x239 & x241)]
f229 =
[(x229 & x231)
&
(x233 & x235)]
&
[(x237 & x239)
&
(x240 | x241)]
f231 =
[(x231 & x233)
&
(x234 | x235)]
&
[(x234 | x236)
|
(x237 & x238)]
f234 =
[(x234 | x236)
|
(x238 | x240)]
|
[(x242 | x244)
|
(x246 | x248)]
f240 =
[(x240 | x242)
|
(x243 & x244)]
|
[(x243 & x245)
&
(x246 | x247)]
f243 =
[(x243 & x245)
&
(x247 & x249)]
&
[(x251 & x253)
&
(x255 & x257)]
f247 =
[(x247 & x249)
&
(x250 | x251)]
&
[(x250 | x252)
|
(x253 & x254)]
f249 =
[(x249 & x251)
&
(x253 & x255)]
&
[(x254 | x256)
|
(x257 & x258)]
f249a =
[(x249 & x251)
&
(x253 & x255)]
&
[(x257 & x259)
&
(x260 | x261)]
f258 =
[(x258 | x260)
|
(x262 | x264)]
|
[(x266 | x268)
|
(x269 & x270)]
f259 =
[(x259 & x261)
&
(x263 & x265)]
&
[(x267 & x269)
&
(x271 & x273)]
f260 =
[(x260 | x262)
|
(x263 & x264)]
|
[(x263 & x265)
&
(x266 | x267)]
f269 =
[(x269 & x271)
&
(x272 | x273)]
&
[(x272 | x274)
|
(x275 & x276)]
f272 =
[(x272 | x274)
|
(x276 | x278)]
|
[(x280 | x282)
|
(x283 & x284)]
f275 =
[(x275 & x277)
&
(x278 | x279)]
&
[(x276 | x278)
|
(x280 | x281)]
f276 =
[(x276 | x278)
|
(x280 | x282)]
|
[(x284 | x286)
|
(x288 | x290)]
f278 =
[(x278 | x280)
|
(x282 | x284)]
|
[(x286 | x288)
|
(x290 | x292)]
f283 =
[(x283 & x285)
&
(x286 | x287)]
&
[(x284 | x286)
|
(x288 | x289)]
f287 =
[(x287 & x289)
&
(x291 & x293)]
&
[(x295 & x297)
&
(x298 | x299)]
f289 =
[(x289 & x291)
&
(x292 | x293)]
&
[(x292 | x294)
|
(x295 & x296)]
f291 =
[(x291 & x293)
&
(x295 & x297)]
&
[(x299 & x301)
&
(x303 & x305)]
f294 =
[(x294 | x296)
|
(x298 | x300)]
|
[(x302 | x304)
|
(x306 | x308)]
f298 =
[(x298 | x300)
|
(x301 & x302)]
|
[(x299 & x301)
&
(x303 & x304)]
f302 =
[(x302 | x304)
|
(x306 | x308)]
|
[(x310 | x312)
|
(x313 & x314)]
f304 =
[(x304 | x306)
|
(x307 & x308)]
|
[(x307 & x309)
&
(x310 | 311)]
f310 =
[(x310 | x312)
|
(x314 | x316)]
|
[(x318 | x320)
|
(x321 & x322)]
f313 =
[(x313 & x315)
&
(x316 | x317)]
&
[(x314 | x316)
|
(x318 | x319)]
f317 =
[(x317 & x319)
&
(x321 & x323)]
&
[(x325 & x327)
&
(x329 & x331)]
f319 =
[(x319 & x321)
&
(x323 & x325)]
&
[(x327 & x329)
&
(x330 | x331)]
f321 =
[(x321 & x323)
&
(x324 | x325)]
&
[(x324 | x326)
|
(x327 & x328)]
f328 =
[(x328 | x330)
|
(x332 | x334)]
|
[(x336 | x338)
|
(x339 & x340)]
f330 =
[(x330 | x332)
|
(x333 & x334)]
|
[(x333 & x335)
&
(x336 | x337)]
f333 =
[(x333 & x335)
&
(x337 & x339)]
&
[(x341 & x343)
&
(x345 & x347)]
f339 =
[(x339 & x341)
&
(x342 | x343)]
&
[(x342 | x344)
|
(x345 & x346)]
f346 =
[(x346 | x348)
|
(x349 & x350)]
|
[(x349 & x351)
&
(x352 | x353)]
f348 =
[(x348 | x350)
|
(x352 | x354)]
|
[(x353 & x355)
&
(x356 | x357)]
f348a =
[(x348 | x350)
|
(x352 | x354)]
|
[(x356 | x358)
|
(x359 & x360)]
f357 =
[(x357 & x359)
&
(x361 & x363)]
&
[(x365 & x367)
&
(x368 | x369)]
f359 =
[(x359 & x361)
&
(x362 | x363)]
&
[(x362 | x364)
|
(x365 & x366)]
f368 =
[(x368 | x370)
|
(x371 & x372)]
|
[(x369 & x371)
&
(x373 & x374)]
g0 =
[(f0 & f0a)
&
(f0b | f11)]
&
[(f0c | f16)
|
(f13 & f24)]
g0a =
[(f0c | f16a)
|
(f29 | f31)]
|
[(f31a & f42)
&
(f40 | f51)]
g0b =
[(f0c | f16a)
|
(f32 | f48)]
|
[(f64 | f80)
|
(f96 | f112)]
g1 =
[(f1 & f17)
&
(f33 & f49)]
&
[(f52 | f63)
|
(f61 & f72)]
g1a =
[(f1 & f17)
&
(f33 & f49a)]
&
[(f65 & f81b)
&
(f97 & f108)]
g50 =
[(f50 | f66)
|
(f79 | f81)]
|
[(f81a & f92)
&
(f90 | f101)]
g102 =
[(f102 | f115)
|
(f113 & f124)]
|
[(f117 & f130)
&
(f128 | f139)]
g104 =
[(f104 | f120)
|
(f136 | f147)]
|
[(f145 & f156)
&
(f154 | f165)]
g128 =
[(f128a | f144)
|
(f160 | f176)]
|
[(f192 | f203)
|
(f201 & f212)]
g143 =
[(f143 & f159)
&
(f172 & f174)]
&
[(f174a | f185)
|
(f183 & f194)]
g195 =
[(f195 & f211)
&
(f227 & f243)]
&
[(f259 & f275)
&
(f272 | f283)]
g203 =
[(f203a & f216)
&
(f214 | f225)]
&
[(f218 | f231)
|
(f229 & f240)]
g218 =
[(f218 | f234)
|
(f247 | f249)]
|
[(f249a & f260)
&
(f258 | f269)]
g276 =
[(f276 | f289)
|
(f287 & f298)]
|
[(f291 & f304)
&
(f302 | f313)]
g278 =
[(f278 | f294)
|
(f310 | f321)]
|
[(f319 & f330)
&
(f328 | f339)]
g317 =
[(f317 & f333)
&
(f346 & f348)]
&
[(f348a | f359)
|
(f357 & f368)]
h0 =
[(g0 & g0a)
|
(g1 & g50)]
|
[(g1a & g102)
&
(g104 | g143)]
h0a =
[(g0b | g128)
|
(g203 & g218)]
|
[(g195 & g276)
&
(g278 | g317)]
out =
h0 & h0a.