Speedsolving Post: "Shortest" PLL Algs?

From an October 2013 discussion at http://www.speedsolving.com/forum/showthread.php?44398:

What are the shortest possible PLL algs, in terms of how long they are when written down? This should be more interesting than just finding move-optimal stuff, and I think there's a lot of room for creativity. The most common algs may not be the shortest!

To start with, the following notations are OK:
- [P,Q] is a commutator (that is, P Q P' Q')
- [P:Q] is a setup move/conjugate (that is, P Q P')
- (P)n is P repeated n times; parentheses are unnecessary if it's clear what P is
- Any face or slice moves, rotations, or lowercase moves.
Also, the algorithm can do the PLL on any face, and you do not have to include any adjustment at the end, or rotations at the very start/end.






And the shortest algs we found:


A: L'[F,R'B2R]L, L'[R'd2R,U]L (thanks to Stefan Pochmann)
E: [[RU'L:D2],U2] (thanks to TDM)
F: R'URU'R2F'U'FU[R,F]R2
G: [RL:U2][F'UB':d2], [R'UL',d2][BF:U2], L'R'U2LR[FU'B,d2], [LU'R,d2]B'F'U2BF
H: (M2U)6
J: [[RU'L:d2],U], [[R'UL':d2],U]
N: (r'DrU2)5, (rDr'U2)5
R: R[U2R'U2,UR'F'R]R', R'[U2RU2,U'RBR']R
T: [R2D':F2][B2D:L2]
U: M2uMu2MuM2, B2UMU2M'UB2
V: [F'UBU'F:U][U2,B]
Y: F2[DR2:U][R'U'R:F2]
Z: (UF2)6M'U2M (thanks to Moritz Karl)

Speedsolving Posts: Almost-2gen LL Algs

From http://www.speedsolving.com/forum/showthread.php?18539 (January 2010):

From any ZBLL we can easily get to PLL using only 2gen moves. All PLLs are a U, Z, or H perm away from either solved, R perm, or Y perm. Therefore, if we can do R and Y perm with at most 2 D-layer moves, we can do any ZBLL with at most 2 D-layer moves.

So, here is an R perm with exactly 2 D-layer moves:
R U2 R D R' U R D' R' U' R' U R U R' U
And here is a Y perm (but not an efficient one):
R' U' D (R' U' R U)3 D' U R (R U R' U R U2 R')2 U'

I imagine these algs could be very useful for OH - everyone loves 2gen moves, and keeping D turns to a minimum is very helpful. Unfortunately, I don't know of any way to generate optimal algs of this type. Does anyone have an idea?

P.S. You can also do every ZBLL with and at most two F moves, although it's less useful IMO. You can prove this with the T perm and this Y perm:
F (R U R' U')3 F' U (R U R' U R U2 R')2 U2 

From http://www.speedsolving.com/forum/showthread.php?708&p=680961#post680961 (December 2011):

Dumping some optimal 2-F-move PLLs (there are probably a few optimal ones I missed but the optimal lengths should be accurate):

A-perm a
HTM-optimal: 11f
 R U' R F2 R' U R' U' R2 F2 R2

QTM-optimal: 15q
 R U' R F2 R' U R' U' R2 F2 R2

A-perm a
HTM-optimal: 11f
 R2 F2 R2 U R U' R F2 R' U R'

QTM-optimal: 15q
 R2 F2 R2 U R U' R F2 R' U R'
 

E-perm

HTM-optimal: 18f
 R' U2 R U' F' R' U R' U2 R U R' U R2 F R' U' R
 R' U R F' R2 U' R U' R' U2 R U' R F U R' U2 R
 R U R' U R' F U' R2 U' R2 U2 R' U' R F' R' U R2
 R2 U F' U R' U' R U R' U' R U R' U' R F U' R2
 R2 U F' R' U R U' R' U R U' R' U R U' F U' R2
 R2 U' R F R' U R U2 R2 U R2 U F' R U' R U' R'
 R2 U2 F' U' R' U R U' R' U R U' R' U R F U2 R2
 R2 U2 F' R' U' R U R' U' R U R' U' R U F U2 R2
 F U R2 U' R U R' U R2 U' R' U R' U' R U' R F'
 F U' R U' R U R' U R U2 R' U R' U' R U2 R' F'
 F U' R U' R' U2 R U' R' U R' U2 R U R' U R F'
 F U' R' U R' U' R2 U R' U R U' R2 U R U' R F'
 F R U2 R' U R U' R U2 R' U' R U' R' U R' U F'
 F R' U R' U R U' R U R2 U' R U' R' U R2 U' F'
 F R' U R' U' R2 U R' U' R U' R2 U R U' R U F'
 F R' U' R U' R' U2 R U' R U R' U2 R U R' U F'

QTM-optimal: 20q
 R2 U F' U R' U' R U R' U' R U R' U' R F U' R2
 R2 U F' R' U R U' R' U R U' R' U R U' F U' R2
 F U R2 U' R U R' U R2 U' R' U R' U' R U' R F'
 F U' R U' R U R' U R U2 R' U R' U' R U2 R' F'
 F U' R U' R' U2 R U' R' U R' U2 R U R' U R F'
 F U' R' U R' U' R2 U R' U R U' R2 U R U' R F'
 F R U2 R' U R U' R U2 R' U' R U' R' U R' U F'
 F R' U R' U R U' R U R2 U' R U' R' U R2 U' F'
 F R' U R' U' R2 U R' U' R U' R2 U R U' R U F'
 F R' U' R U' R' U2 R U' R U R' U2 R U R' U F'
 

F-perm
HTM-optimal: 15f
 R2 U R2 U2 F2 U R2 U2 R2 U R2 U' R2 U2 F2
 R2 U R2 U' R2 U2 R2 U' F2 U2 R2 U' R2 U' F2
 F2 U R2 U R2 U2 F2 U R2 U2 R2 U R2 U' R2
 F2 U2 R2 U R2 U' R2 U2 R2 U' F2 U2 R2 U' R2
 R2 U' F2 U2 R2 U' R2 U2 R2 U R2 U F2 U2 R2
 R2 U2 F2 U' R2 U' R2 U2 R2 U R2 U2 F2 U R2

QTM-optimal: 19q
 R U R' U' R' U R U F' U R' U R U2 F R U' R'
 R U R' F' U2 R' U' R U' F U' R' U' R U R U' R'
 R U R U F' U' R U R' U' R' U2 F U' R' U2 R'
 R U2 R U F' U2 R U R U' R' U F U' R' U' R'
 R' U' R U' R' U R U R2 F' R U R U' R' F U R
 R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R
 

G-perm a
HTM-optimal: 15f
 F2 U R U2 R' U' R' U2 R2 U R' F2 R' U R
 R' U' F2 U R U2 R U2 R' U F2 U2 R U' R'

QTM-optimal: 18q
 R U R' U' R' U F R U R U' R' F' U R' U2 R
 

G-perm b
HTM-optimal: 15f
 R' U' R F2 R U' R2 U2 R U R U2 R' U' F2
 R U R' U2 F2 U' R U2 R' U2 R' U' F2 U R

QTM-optimal: 18q
 R' U2 R U' F R U R' U' R' F' U' R U R U' R'
 

G-perm c

HTM-optimal: 14f
 R2 U2 R2 F2 U' R2 U R2 U F2 U2 R2 U' R2

QTM-optimal: 17q
 R2 U' R U' R U R' U R' F' R' U R U' F R'
 

G-perm d
HTM-optimal: 14f
 R2 U R2 U2 F2 U' R2 U' R2 U F2 R2 U2 R2

QTM-optimal: 17q
 R F' U R' U' R F R U' R U' R' U R' U R2
 

J-perm a
HTM-optimal: 13f
 R' F R' U' R2 U' R2 U R' F' R U R2
 R2 U' R' F R U' R2 U R2 U R F' R

QTM-optimal: 16q
 R' F R' U' R2 U' R2 U R' F' R U R2
 R2 U' R' F R U' R2 U R2 U R F' R
 F R' U R U' F' U R' U2 R U' R' U2 R
 R' U2 R U R' U2 R U' F U R' U' R F'
 R' U' R U F R U' R' U' R' U R2 U R' F'
 R' U' R U' R' U F U R' U' R F' R' U R2
 R2 U' R F R' U R U' F' U' R U R' U R
 F R U' R2 U' R U R U R' F' U' R' U R
 

J-perm b
HTM-optimal: 11f
 R U' F U' R' U' R U F' U2 R'
 R U2 F U' R' U R U F' U R'

QTM-optimal: 12q
 R U' F U' R' U' R U F' U2 R'
 R U2 F U' R' U R U F' U R'
 

N-perm a
HTM-optimal: 15f
 R2 U R2 U' R2 U' F2 U' R2 U R2 U F2 U2 R2
 R2 U2 F2 U' R2 U' R2 U F2 U R2 U R2 U' R2

QTM-optimal: 21q
 R U2 R2 U' R2 F' R U R' U' R' F R' U R U2 R'
 R U2 R' U' R F' R U R U' R' F R2 U R2 U2 R'
 R U R' U R U' F U' R' U' R U F' U2 R' U2 R U' R'
 R U R' U2 R U2 F U' R' U R U F' U R' U' R U' R'
 

N-perm b
HTM-optimal: 15f
 R2 U F2 U2 R2 U R2 U2 R2 U' R2 U2 F2 U' R2
 R2 U' R2 U2 F2 U' R2 U2 R2 U F2 U2 R2 U R2

QTM-optimal: 23q?
 R U' R' U R' U2 R2 U R2 F2 U R U R U' R' U' F2
 F2 U R U R' U' R' U' F2 R2 U' R2 U2 R U' R U R'
 R' U2 R' U' R2 U F' U' R U R' U' R2 U2 R F R' U R
 R' U2 F U R2 U2 R' U' R U R' F' R U2 R' U' R' U R
 R' U' R U R U2 R' F R U' R' U R U2 R2 U' F' U2 R
 R' U' R F' R' U2 R2 U R U' R' U F U' R2 U R U2 R
 

R-perm a
HTM-optimal: 13f
 R2 F2 U R U R' U' R' U' F2 R' U R'
 R U' R F2 U R U R U' R' U' F2 R2

QTM-optimal: 16q
 R2 F2 U R U R' U' R' U' F2 R' U R'
 R U' R F2 U R U R U' R' U' F2 R2
 

R-perm b

HTM-optimal: 13f
 R2 F R U R U' R' F' R U2 R' U2 R
 R' U2 R U2 R' F R U R' U' R' F' R2

QTM-optimal: 16q
 R2 F R U R U' R' F' R U2 R' U2 R
 R' U2 R U2 R' F R U R' U' R' F' R2
 

T-perm

HTM-optimal: 14f
 R U R' U' R' F R2 U' R' U' R U R' F'
 F R U' R' U R U R2 F' R U R U' R'

QTM-optimal: 15q
 R U R' U' R' F R2 U' R' U' R U R' F'
 F R U' R' U R U R2 F' R U R U' R'
 

V-perm
HTM-optimal: 15f
 R2 U2 R2 U R2 U2 F2 U R2 U R2 U2 F2 U' R2
 R2 U2 R2 U' F2 U2 R2 U' R2 U' F2 U2 R2 U R2
 R2 U F2 U2 R2 U' R2 U' F2 U2 R2 U' R2 U2 R2
 R2 U' R2 U2 F2 U R2 U R2 U2 F2 U R2 U2 R2

QTM-optimal: 19q
 R U' R' U R F R' U' R2 U R U' R U R2 F' R'
 R F R2 U' R' U R' U' R2 U R F' R' U' R U R'
 

Y-perm

HTM-optimal: 14f
 R2 U' R2 U F2 U' R2 U' R2 U F2 R2 U R2
 R2 U' R2 F2 U' R2 U R2 U F2 U' R2 U R2

QTM-optimal: 19q
 R2 U' R2 U' R2 U R' F' R U R2 U' R' F R
 R' F' R U R2 U' R' F R U' R2 U R2 U R2
 R' U' R U' R U' F U' R' U' R U F' U2 R2 U R
 R' U' R2 U2 F U' R' U R U F' U R' U R' U R