First of all, it's a project initiated by Guillaume Erbibou who explained his idea to me and we worked together to find a relatively good set of algorithm.
As said in the title, PLLEF stands for "Permute Last Layer and Edge Flip" , in reference to CLLEF. Basically, it's simply PLL but with all edges flipped. He had this idea when he learned CLLEF and keeping in mind VH-system.
Further explanation now. When we do VH and there is OCLL skip, we often do a PLL (which is totally natural) but when we use CLLEF and there is OCLL skip, we tend to do OLL/PLL or CPEOLL/EPLL. If we think a bit further, we realize there is only 22 PLLEF and 8 are probably known because it's just skip, the 5 ELLs and the 2 CPEOLLs 4-flip. We can also see that one of the CPEOLL is actually the A-perm PLLEF so if we include the symmetry, we almost have half of the set.
Here is the set :
The most difficult will probably be recognition which is radically different from PLL. At first, we have been trying to recognize cases just like PLLs but we soon realized it's pretty hard and we lost the advantage of a CFCE method where this set can be part of.
So, we will first check the configuration of the corners and then the configuration of the edges in order to determine which PLLEF we get.
I'll let you check the guide to really understand what I/we mean :
(By the way, I'm only translating what Guillaume explained on the French forum and please note that this is his original idea. I've only helped him to develop the set because I liked the idea )