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Completely specified functions


In the following, all completely specified functions including their realizations are listed. If you want to download all specifications at once, click on this link.



1 Name Type vars. const. garb. File Notes
   toffoli complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 EQ proven as minimal 5 5 realization was verified Download realization Show realization Tof:80 n/a
2 MCT proven as minimal 1 5 realization was verified Download realization Show realization Tof:80 n/a
 
2 Name Type vars. const. garb. File Notes
   toffoli_double complete 4 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 EQ proven as minimal 7 7 realization was verified Download realization Show realization GWDD:2008 n/a
2 MCT proven as minimal 2 10 realization was verified Download realization Show realization RevLib n/a
 
3 Name Type vars. const. garb. File Notes
   fredkin complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 EQ proven as minimal 7 7 realization was verified Download realization Show realization GWDD:2008 n/a
2 MCT proven as minimal 3 15 realization was verified Download realization Show realization WG:2007 n/a
3 MCF proven as minimal 1 7 realization was verified Download realization Show realization FT:82 n/a
 
4 Name Type vars. const. garb. File Notes
   peres complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 EQ proven as minimal 4 4 realization was verified Download realization Show realization GWDD:2008 n/a
2 MCT proven as minimal 2 6 realization was verified Download realization Show realization WG:2007 n/a
3 P proven as minimal 1 4 realization was verified Download realization Show realization Per:85 n/a
 
5 Name Type vars. const. garb. File Notes
   miller complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT proven as minimal 5 17 realization was verified Download realization Show realization WG:2007 n/a
2 EQ proven as minimal 8 8 realization was verified Download realization Show realization GWDD:2008 n/a
 
6 Name Type vars. const. garb. File Notes
   3_17 complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 6 14 realization was verified Download realization Show realization MMD:2003 n/a
2 MCT proven as minimal 6 14 realization was verified Download realization Show realization WG:2007 n/a
3 EQ proven as minimal 10 10 realization was verified Download realization Show realization GWDD:2008 n/a
 
7 Name Type vars. const. garb. File Notes
   4_49 complete 4 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 16 60 realization was verified Download realization Show realization MMD:2003 n/a
2 MCT not proven as minimal 12 16 realization was verified Download realization Show realization MDS:2005 n/a
 
8 Name Type vars. const. garb. File Notes
   graycode6 complete 6 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 NCT proven as minimal 5 5 realization was verified Download realization Show realization MDS:2005 n/a
2 EQ proven as minimal 5 5 realization was verified Download realization Show realization MDS:2005 n/a
 
9 Name Type vars. const. garb. File Notes
   hwb4 complete 4 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 17 65 realization was verified Download realization Show realization MDS:2005 n/a
2 MCT+P not proven as minimal 16 63 realization was verified Download realization Show realization   Optimized by hand from previous found realization
3 MCF not proven as minimal 11 81 realization was verified Download realization Show realization MDS:2005 n/a
4 MCT proven as minimal 11 23 realization was verified Download realization Show realization WLDG:2008 n/a
 
10 Name Type vars. const. garb. File Notes
   hwb5 complete 5 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 55 315 realization was verified Download realization Show realization MDS:2005 n/a
2 MCF not proven as minimal 24 248 realization was verified Download realization Show realization MDS:2005 n/a
3 MCT not proven as minimal 24 104 realization was verified Download realization Show realization MDS:2005 n/a
 
11 Name Type vars. const. garb. File Notes
   hwb6 complete 6 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 126 1530 realization was verified Download realization Show realization MDS:2005 n/a
2 MCF not proven as minimal 65 1171 realization was verified Download realization Show realization MDS:2005 n/a
3 MCT not proven as minimal 42 142 realization was verified Download realization Show realization MDS:2005 n/a
 
12 Name Type vars. const. garb. File Notes
   hwb7 complete 7 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 289 5236 realization was verified Download realization Show realization MDS:2005 n/a
2 MCF not proven as minimal 166 4170 realization was verified Download realization Show realization MDS:2005 n/a
3 MCT not proven as minimal 236 3876 realization was verified Download realization Show realization MDS:2005 n/a
4 MCT not proven as minimal 331 2611 realization was verified Download realization Show realization MDS:2005 n/a
 
13 Name Type vars. const. garb. File Notes
   mod5d1 complete 5 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT proven as minimal 7 11 realization was verified Download realization Show realization WG:2007 n/a
 
14 Name Type vars. const. garb. File Notes
   mod5d2 complete 5 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT proven as minimal 8 20 realization was verified Download realization Show realization WG:2007 n/a
2 MCT not proven as minimal 8 16 realization was verified Download realization Show realization MDM:2005 n/a
 
15 Name Type vars. const. garb. File Notes
   mod5mils complete 5 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT proven as minimal 5 13 realization was verified Download realization Show realization WG:2007 n/a
2 MCT not proven as minimal 5 13 realization was verified Download realization Show realization MDM:2005 n/a
 
16 Name Type vars. const. garb. File Notes
   ham3 complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT proven as minimal 5 9 realization was verified Download realization Show realization MDS:2005 Has been proven as minimal (wrt number of gates) by WG:2007
2 MCT+MCF not proven as minimal 4 10 realization was verified Download realization Show realization MDS:2005 n/a
 
17 Name Type vars. const. garb. File Notes
   ham7 complete 7 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 23 83 realization was verified Download realization Show realization MDS:2005 n/a
2 MCT not proven as minimal 21 65 realization was verified Download realization Show realization MDS:2005 n/a
3 NCT not proven as minimal 25 49 realization was verified Download realization Show realization MDS:2005 n/a
 
18 Name Type vars. const. garb. File Notes
   ham15 complete 15 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 132 1831 realization was verified Download realization Show realization MDS:2005 n/a
2 MCT not proven as minimal 70 453 realization was verified Download realization Show realization MDS:2005 n/a
3 MCT not proven as minimal 109 206 realization was verified Download realization Show realization MDS:2005 n/a
 
19 Name Type vars. const. garb. File Notes
   cycle10_2 complete 12 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 19 1202 realization was verified Download realization Show realization MDS:2005 n/a
 
20 Name Type vars. const. garb. File Notes
   not_spec complete Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 48 6063 realization was verified Download realization Show realization MDS:2005 cycle17_3
2 NCT not proven as minimal 32 96 realization was verified Download realization Show realization D. Michael Miller An 8-bit adder
3 EQ not proven as minimal 48 48 realization was verified Download realization Show realization D. Michael Miller An 8-bit adder
4 NCT not proven as minimal 64 192 realization was verified Download realization Show realization D. Michael Miller A 16-bit adder
5 EQ not proven as minimal 96 96 realization was verified Download realization Show realization D. Michael Miller A 16-bit adder
6 NCT not proven as minimal 116 368 realization was verified Download realization Show realization MDS:2005 A form of integer adder.
7 EQ not proven as minimal 305 305 realization was verified Download realization Show realization MDS:2005 A form of integer adder.
8 NCT not proven as minimal 128 384 realization was verified Download realization Show realization D. Michael Miller A 32-bit adder
9 NCT not proven as minimal 256 768 realization was verified Download realization Show realization D. Michael Miller A 64-bit adder
10 EQ not proven as minimal 192 192 realization was verified Download realization Show realization D. Michael Miller A 32-bit adder
11 EQ not proven as minimal 384 384 realization was verified Download realization Show realization D. Michael Miller A 64-bit adder
 
21 Name Type vars. const. garb. File Notes
   hwb8 complete 8 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 637 16530 realization was verified Download realization Show realization MDS:2005 n/a
2 MCT not proven as minimal 614 14699 realization was verified Download realization Show realization MDS:2005 n/a
3 MCT+P not proven as minimal 610 14691 realization was verified Download realization Show realization MDS:2005 Same as the previous circuit, with explicit Peres gates.
4 MCT not proven as minimal 749 7015 realization was verified Download realization Show realization MDS:2005 n/a
5 MCT+P not proven as minimal 748 7013 realization was verified Download realization Show realization MDS:2005 Same as the previous circuit, with explicit Peres gates.
6 MCT+P not proven as minimal 633 16522 realization was verified Download realization Show realization MDS:2005 Same as the first circuit, with explicit Peres gates.
 
22 Name Type vars. const. garb. File Notes
   hwb9 complete 9 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 1544 44714 realization was verified Download realization Show realization MDS:2005 n/a
2 MCT+P not proven as minimal 1538 44702 realization was verified Download realization Show realization MDS:2005 Same as the previous circuit, with explicit Peres gates.
3 MCT not proven as minimal 1541 44665 realization was verified Download realization Show realization MDS:2005 n/a
4 MCT+P not proven as minimal 1535 44653 realization was verified Download realization Show realization MDS:2005 Same as the previous circuit, with explicit Peres gates.
5 MCT not proven as minimal 1959 22510 realization was verified Download realization Show realization MDS:2005 n/a
 
23 Name Type vars. const. garb. File Notes
   mod5adder complete 6 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 21 125 realization was verified Download realization Show realization MDS:2005 n/a
2 MCT not proven as minimal 15 83 realization was verified Download realization Show realization MDS:2005 n/a
3 MCT not proven as minimal 17 77 realization was verified Download realization Show realization MDS:2005 n/a
 
24 Name Type vars. const. garb. File Notes
   urf1 complete 9 0 9 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 11554 57770 realization was verified Download realization Show realization Sae:2008 n/a
2 MCT not proven as minimal 1517 48952 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 without template application.
3 MCT not proven as minimal 1487 45855 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 with template application.
 
25 Name Type vars. const. garb. File Notes
   urf2 complete 8 0 8 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 5030 25150 realization was verified Download realization Show realization Sae:2008 n/a
2 MCT not proven as minimal 638 17027 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 without template application.
3 MCT not proven as minimal 620 16152 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 with template application.
4 MCT not proven as minimal 3250 20465 realization was verified Download realization Show realization   Templates from MDM:2005 were applied to the first realization.
 
26 Name Type vars. const. garb. File Notes
   urf3 complete 10 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 26468 132340 realization was verified Download realization Show realization Sae:2008 n/a
2 MCT not proven as minimal 2732 128172 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 without template application.
3 MCT not proven as minimal 2674 121716 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 with template application.
 
27 Name Type vars. const. garb. File Notes
   urf5 complete 9 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 10276 51380 realization was verified Download realization Show realization Sae:2008 n/a
2 MCT not proven as minimal 499 24253 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 without template application.
 
28 Name Type vars. const. garb. File Notes
   urf6 complete 15 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 10740 53700 realization was verified Download realization Show realization Sae:2008 n/a
 
29 Name Type vars. const. garb. File Notes
   plus127mod8192 complete 13 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 910 73357 realization was verified Download realization Show realization   n/a
 
30 Name Type vars. const. garb. File Notes
   plus63mod4096 complete 12 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 429 32539 realization was verified Download realization Show realization   n/a
 
31 Name Type vars. const. garb. File Notes
   plus63mod8192 complete 13 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 492 45025 realization was verified Download realization Show realization   n/a
 
32 Name Type vars. const. garb. File Notes
   aj-e11 complete 4 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 13 45 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 with template application.
2 MCT proven as minimal 10 30 realization was verified Download realization Show realization   n/a
 
33 Name Type vars. const. garb. File Notes
   ex-1 complete 3 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 4 8 realization was verified Download realization Show realization   The function was minimized using the algorithm from MDM:2005 with template application.
 
34 Name Type vars. const. garb. File Notes
   0410184 complete 14 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 NCT not proven as minimal 46 90 realization was verified Download realization Show realization MDS:2005 n/a
2 EQ not proven as minimal 74 74 realization was verified Download realization Show realization MDS:2005 n/a
 
35 Name Type vars. const. garb. File Notes
   urf4 complete 11 0 0 Download specification n/a

Realizations:
    Lib. min. gates costs ver. File Pic. Ref. Notes
1 MCT not proven as minimal 32004 160020 realization was verified Download realization Show realization Sae:2008 n/a
 

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