On the complexity of iterated shuffle

Manfred K. Warmuth, David Haussler
1984 Journal of computer and system sciences (Print)  
It is demonstrated that the following problems are NP complete: (1) Given words w and w" wz ,..., w" is w in the shuffle of w" w 2,-r w,? (2) Given words w and v, is w in the iterated shuffle of v? From these results we show that the languages {%w$w": WE {a,b)*)@, lJ""",.(%w)@, (ab"cde'f: n > O}@, and {a ""b"c"f": n 2 O)@ are NP complete, where @ denotes the iterated shuffle. By representing these languages in various ways using the operations shuffle, iterated shuffle, union, concatenation,
more » ... ersection, intersection with a regular set, non-erasing homomorphism and inverse homomorphism, results on the complexity of language classes generated using various subsets of these operations are obtained. Finally, it is shown that the iterated shume of a regular set can be recognized in deterministic polynomial time.
doi:10.1016/0022-0000(84)90018-7 fatcat:wmw4u3zri5ep5ctfc6xsc3qgdu