Given a grammar for a Context Free language $ L$ , we can augment it by "shuffling" the right hand side of each production, e.g.:
$ A \to BCD$ is expanded to $ A \to BCD \; | \; BDC \; | \; CBD \; | CDB \; | \; DBC \; | \; DCB$
It may happen that the resulting language $ L’$ is equal to $ L$
For example:
Source Shuffled S -> XA | YB S -> XA | AX | YB | BY A -> YS | SY A -> YS | SY B -> XS | SX B -> XS | SX X -> 1 X -> 1 Y -> 0 Y -> 0 Is there a name for such class of CF languages ($ L = \text{shuffled}(L)$ ?
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