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Languages under concatenation and shuffling. (English) Zbl 0829.68077

Summary: A class of generalized shuffling operations on languages is defined in terms of partial orders. The operations generated from concatenation and shuffling correspond to a special class of these partial orders, the class of series-parallel partial orders. The question of what identities hold for these operations is solved by showing that series-parallel partial orders give rise to the same operation on languages iff they are isomorphic (a result that does not hold for the whole class of generalized shuffling operations). That leaves open the question of what other identities might hold between these generalized shuffling operations.

MSC:

68Q45 Formal languages and automata
68R15 Combinatorics on words
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[1] DOI: 10.1016/0304-3975(88)90124-7 · Zbl 0669.68015 · doi:10.1016/0304-3975(88)90124-7
[2] DOI: 10.1137/0211023 · Zbl 0478.68065 · doi:10.1137/0211023
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