Reversible Circuit Classification
This page lists the benchmarks for the reversible reciprocal circuits reported in
Mathias Soeken, Nabila Abdessaied, and Giovanni De Micheli:
Enumeration of reversible functions and its application to circuit complexity,
Conference on Reversible Computation,
2016, 255–270.
2-variable functions
NPNP-equivalence
LL-equivalence
AA-equivalence
Representative |
Size |
Min |
Max |
0,1,2,3
|
24 |
0 |
3 |
3-variable functions
NPNP-equivalence
Representative |
Size |
Min |
Max |
0,1,2,3,4,5,6,7
|
48 |
0 |
6 |
0,1,2,3,5,4,7,6
|
288 |
1 |
5 |
0,1,2,3,4,5,7,6
|
576 |
1 |
5 |
0,1,3,2,7,6,4,5
|
288 |
2 |
5 |
0,1,3,2,5,4,6,7
|
144 |
2 |
4 |
0,1,3,2,6,7,5,4
|
288 |
2 |
5 |
0,1,2,3,7,6,5,4
|
144 |
2 |
5 |
0,1,2,7,5,4,3,6
|
576 |
2 |
5 |
0,1,2,3,5,6,7,4
|
1152 |
2 |
5 |
0,1,2,5,6,7,4,3
|
576 |
2 |
5 |
0,1,2,3,4,6,7,5
|
2304 |
2 |
6 |
0,1,2,7,5,4,6,3
|
1152 |
2 |
5 |
0,3,5,6,7,4,2,1
|
144 |
3 |
4 |
0,1,3,2,5,6,4,7
|
576 |
3 |
5 |
0,1,3,6,7,2,4,5
|
576 |
3 |
4 |
0,1,2,7,3,6,5,4
|
576 |
3 |
5 |
0,1,2,3,4,6,5,7
|
288 |
3 |
5 |
0,1,2,5,7,6,3,4
|
288 |
3 |
6 |
0,1,2,5,3,6,7,4
|
1152 |
3 |
5 |
0,1,2,7,5,6,3,4
|
1152 |
3 |
5 |
0,1,3,2,5,7,6,4
|
576 |
3 |
5 |
0,1,3,4,6,7,5,2
|
576 |
3 |
4 |
0,1,2,7,3,4,5,6
|
1152 |
3 |
5 |
0,1,2,4,7,6,5,3
|
576 |
3 |
5 |
0,1,2,5,7,6,4,3
|
1152 |
3 |
5 |
0,1,2,4,5,6,7,3
|
1152 |
3 |
5 |
0,1,2,4,7,3,5,6
|
1152 |
3 |
5 |
0,1,2,5,4,6,7,3
|
2304 |
3 |
6 |
0,1,2,3,5,7,4,6
|
288 |
3 |
5 |
0,1,2,4,5,6,3,7
|
1152 |
3 |
6 |
0,1,2,4,3,6,7,5
|
2304 |
3 |
6 |
0,1,2,7,5,6,4,3
|
2304 |
3 |
6 |
0,1,2,5,3,6,4,7
|
1152 |
3 |
6 |
0,1,3,6,7,4,5,2
|
384 |
3 |
6 |
0,1,3,4,7,6,2,5
|
288 |
4 |
5 |
0,1,3,4,5,6,2,7
|
1152 |
4 |
5 |
0,1,3,4,5,2,6,7
|
288 |
4 |
5 |
0,1,3,7,6,2,5,4
|
288 |
4 |
5 |
0,1,2,5,3,4,7,6
|
576 |
4 |
5 |
0,1,2,4,5,3,7,6
|
576 |
4 |
5 |
0,1,2,5,4,3,7,6
|
576 |
4 |
6 |
0,1,2,4,5,3,6,7
|
576 |
4 |
6 |
0,1,2,4,3,5,7,6
|
576 |
4 |
6 |
0,1,2,4,7,3,6,5
|
1152 |
4 |
6 |
0,1,3,6,5,7,2,4
|
576 |
4 |
5 |
0,1,2,4,3,6,5,7
|
576 |
4 |
5 |
0,1,2,4,7,5,6,3
|
576 |
4 |
6 |
0,1,3,4,5,7,6,2
|
1152 |
4 |
5 |
0,1,2,5,4,6,3,7
|
384 |
4 |
6 |
0,1,2,4,5,7,3,6
|
1152 |
4 |
6 |
0,1,2,5,3,7,4,6
|
1152 |
4 |
6 |
0,1,2,4,3,5,6,7
|
192 |
5 |
6 |
LL-equivalence
Representative |
Size |
Min |
Max |
0,1,2,3,4,5,6,7
|
168 |
0 |
6 |
1,0,2,3,4,5,7,6
|
1176 |
1 |
6 |
0,1,2,3,4,5,7,6
|
1176 |
1 |
6 |
1,0,2,3,4,5,6,7
|
1176 |
1 |
6 |
1,0,2,3,4,6,7,5
|
7056 |
2 |
6 |
0,1,2,3,4,6,7,5
|
2352 |
2 |
6 |
1,0,2,3,4,6,5,7
|
7056 |
2 |
6 |
1,0,2,4,3,6,7,5
|
9408 |
3 |
6 |
0,1,2,4,3,6,7,5
|
1344 |
3 |
6 |
1,0,2,4,3,6,5,7
|
9408 |
3 |
6 |
AA-equivalence
Representative |
Size |
Min |
Max |
0,1,2,3,4,5,6,7
|
1344 |
0 |
6 |
0,1,2,3,4,5,7,6
|
9408 |
1 |
6 |
0,1,2,3,4,6,7,5
|
18816 |
2 |
6 |
0,1,2,4,3,6,7,5
|
10752 |
3 |
6 |