Algebraic tools for the concatenation product

Algebraic Tools for the Concatenation Product

Theme and Variations on the Concatenation Product

The concatenation product is one of the most important operations on regular languages. Its study requires sophisticated tools from algebra, finite model theory and profinite topology. This paper surveys research advances on this topic over the last fifty years. The concatenation product plays a key role in two of the most important results of automata theory: Kleene’s theorem on regular langua...

Schützenberger Products in a Category

The Schützenberger product of monoids is a key tool for the algebraic treatment of language concatenation. In this paper we generalize the Schützenberger product to the level of monoids in an algebraic category D , leading to a uniform view of the corresponding constructions for monoids (Schützenberger), ordered monoids (Pin), idempotent semirings (Klíma and Polák) and algebras over a field (Re...

Collared Cospans , Cohomotopy and Tqft ( Cospans in Algebraic Topology , Ii )

Topological cospans and their concatenation, by pushout, appear in the theories of tangles, ribbons, cobordisms, etc. Various algebraic invariants have been introduced for their study, which it would be interesting to link with the standard tools of Algebraic Topology, (co)homotopy and (co)homology functors. Here we introduce collarable (and collared) cospans between topological spaces. They ge...

Dense packings from algebraic number fields and codes

We introduce a new method from number fields and codes to construct dense packings in the Euclidean spaces. Via the canonical Q-embedding of arbitrary number field K into R, both the prime ideal p and its residue field κ can be embedded as discrete subsets in R. Thus we can concatenate the embedding image of the Cartesian product of n copies of p together with the image of a length n code over ...