Algorithm: SiGN Move Coalescing

[lgarron]

alg.cubing.net currently does this, but it might be nice to define certain simplifications. The most useful one:

• Coalesce adjacent repeated-units moves with the same repeatable by adding the repetition amounts. Drop them if the amount becomes 0.
• Repeat until there are no adjacent repeated-units with the same repeatable.

For example: F R U U2' U R2 → F R R2 → F R3

[lgarron]

There are other forms of "simplification", e.g. distributing primes or coalescing over groups:

• replacing (X')' with X
• replacing ((A B C)')' with A B C
• replacing (A B C)' with C' B' A'
• replacing (A B) (B' C) with (A C)
• replacing [A: B]' with [A: B']
• replacing [A, B]' with [B', A']

I would definitely like to define something for coalescing; not sure if the others need standards too.

SiGN Canonicalization (#8) can already handle things like removing groups and distributing primes, albeit at a coarser granularity. Maybe it would be sufficiently useful to give names to all the production rules behind the canonicalization algorithm.

[lgarron]

Also note: move coalescing may not preserve the ability to execute an alg on a physical puzzle that doesn't allow undoing moves, like the Latch Cube.