Scattered deletion and commutativity

On Iterated Scattered Deletion

In this note, we solve an open problem of Ito et al. 2] on iterated scattered deletion. Note: Since this note has appeared in Bull. EATCS, I have been informed that this problem has been previously solved; see Ito and Silva 1], where the authors show that there exists a regular language R such that (;) + (R) is not a CFL. I am grateful to Masami Ito for pointing me to this reference. is the set...

Shuffle and scattered deletion closure of languages

We introduce and study the notion of shu e residual of a language L: the set containing the words whose shu e with L is completely included in L. Several properties and a characterization of the shu e residual of a language are obtained. The shu e closure of a language L (the smallest language that is shu e closed and contains L) is investigated. Moreover, conditions for the existence of maxima...

Medial commutativity

It is shown that all the assumptions for symmetric monoidal categories flow out of a unifying principle involving natural isomorphisms of the type (A ∧B) ∧ (C ∧D) → (A ∧ C) ∧ (B ∧D), called medial commutativity. Medial commutativity in the presence of the unit object enables us to define associativity and commutativity natural isomorphisms. In particular, Mac Lane’s pentagonal and hexagonal coh...

On Multiple Left-Branch Dislocation: Multiple Extraction and/or Scattered Deletion?

Generalized J-Rings and Commutativity

A J-ring is a ring R with the property that for every x in R there exists an integer n(x)>1 such that x x x n = ) ( , and a well-known theorem of Jacobson states that a Jring is necessarily commutative. With this as motivation, we define a generalized Jring to be a ring R with the property that for all x, y in R0 there exists integers 1 ) ( , 1 ) ( > = > = y m m x n n such that m n xy y x − is ...