Finitely generated biω-languages

Finitely Generated Ideal Languages and Synchronizing Automata

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2 states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.

On Message Sequence Graphs and Finitely Generated Regular MSC Languages

Message Sequence Charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. A standard method to describe multiple communication scenarios is to use message sequence graphs (MSGs). A message sequence graph allows the protocol designer to write a finite specification which combines MSCs...

A Note on Finitely Generated Semigroups of Regular Languages∗

Let E = {E1, . . . , Ek} be a set of regular languages over a finite alphabet Σ. Consider morphism φ : ∆ → (S, ·) where ∆ is the semigroup over a finite set ∆ and (S, ·) = 〈E〉 is the finitely generated semigroup with E as the set of generators and language concatenation as a product. We prove that the membership problem of the semigroup S, the set [u] = {v ∈ ∆ | φ(v) = φ(u)}, is a regular langu...

Ring With All Finitely Generated Modules Retractable

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...