Contextual partial commutations

Solving Word Equations modulo Partial Commutations

On the expected number of commutations in reduced words

We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that nearly all positions in the reduced word are expected to support commutations. Finally, we calculate the asymptotic frequencies of commutations, consecutive n...

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...

Transitive factorizations of free partially commutative monoids and Lie algebras

Let M(A, θ) be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet B ⊂ A such that the right factor of a bisection M(A, θ) = M(B, θB).T be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations of M(A, θ) and associated bases of LK(A, θ).

RCdex: An Index Structure for Tree Matching in the Presence of Commutations

Tree-structured data models and formats are increasingly being used in many applications to represent and store data objects. Since the structural information inherent in such data cannot be captured in conventional index structures, quick retrieval of tree-structured data necessitates special indexing techniques. A variety of algorithms, such as ViST and Data Guides, have been proposed to answ...