## On commutative context-free languages.(English)Zbl 0627.68063

Let $$\Sigma =\{a_ 1,a_ 2,...,a_ n\}$$ be an alphabet and let $$L\subset \Sigma^*$$ be the commutative image of $$FP^*$$ where F and P are finite subsets of $$\Sigma^*$$. If, for any permutation $$\sigma$$ of $$\{$$ 1,2,...,n$$\}$$, $$L\cap a^*_{\sigma (1)}...a^*_{\sigma (n)}$$ is context-free, then L is context-free. This theorem provides a solution to the Fliess conjecture in a restricted case. If the result could be extended to finite unions of the $$FP^*$$ above, the Fliess conjecture could be solved.

### MSC:

 68Q45 Formal languages and automata

### Keywords:

Fliess conjecture
Full Text:

### References:

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