On commutative languages

On Commutative Context-Free Languages

Let C = {a,, a2, . . . . a,} be an alphabet and let LcZ* be the commutative image of FP* where F and P are finite subsets of Z*. If, for any permutation c of { 1,2, . . . . n}, L n a&) a%, 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 conjectur...

Learning Commutative Regular Languages

Commutative Positive Varieties of Languages

We study the commutative positive varieties of languages closed under various operations: shuffle, renaming and product over one-letter alphabets. Most monoids considered in this paper are finite. In particular, we use the term variety of monoids for variety of finite monoids. Similarly, all languages considered in this paper are regular languages and hence their syntactic monoid is finite.

Partially-commutative context-free languages

The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (pc CFL), where non-terminal symbols are commutative according to a binary independence relation, very much like in trace theory. The class has been recently proposed as a robust class subsuming CFL ...

A Note on the Commutative Closure of Star-Free Languages

We show that the commutative closure of a star-free language is either star-free or not regular anymore. Actually, this property is shown to hold exactly for the closure with respect to a partial commutation corresponding to a transitive dependence relation. Moreover, the question whether the closure of a star-free language remains star-free is decidable precisely for transitive partial commuta...