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A bifix code is a prefix code which is also a suffix code. The family of all bifix codes is the most important family of all codes. This family has been split into subfamilies such as the family of comma codes, the family of comma-free codes and the families of strict intercodes of index m, m ≥ 2. This paper is a study of the properties of the annihilators of a given bifix code. The types of annihilators we will consider are comma code, comma-free code and strict intercode of index m annihilators. We present the existence of each kind of annihilators we considered. We obtained several interesting properties together with two-word comma codes and strict intercodes of index 2.

A code $A$ over a finite alphabet $X$ is a comma-free code if $A^2\cap X^+AX^+=\emptyset$, where $X$ is a finite alphabet containing more than one letter. This paper is a study of some algebraic properties of finite maximal comma-free codes. We give several characterizations on two-element comma-free codes and maximal comma-free codes. Let $X_n^m= X^n\cup X^{n+1}\cup \cdots \cup X^m$. We prove that for $n \ge 3$ , a maximal comma-free code in $X^n$ is a maximal comma-free code in the region $X_1^m\cup X^n$, $m < n/2$. We also obtain that for $X = \{a,b\}$, a maximal comma-free code in $X^3$ is a maximal comma-free code; a maximal comma-free code in $X^4$ is a maximal comma-free code in $X_1^4$; for every $n\ge 4$, there is a maximal comma-free code in $X^n$ which is not a maximal comma-free code.

Every infinite regular language contains a regular subset of the formuv+w for some words u, v, w, where v is not the empty word. The regularsubsets of the above form are called regular components. Some well-knowncontext-free languages, such as the Dyck language and the balanced language(over an alphabet X with |X| = 2), are decomposed as disjointunions of disjunctive languages. In this paper, we investigate thedecompositions of some of the regular languages and the context-freelanguages as disjoint unions of regular components. An infinite language iscalled regular component splittable if it can be expressed as a disjointunion of regular components and a finite set. We show that the Dycklanguage, the balanced language and some disjunctive context-free splittablelanguages are regular component splittable. We also present an example toshow that there is a disjunctive context-free language which is not regularcomponent splittable.

In this paper, a solid code is introduced and disjunctive domain is defined as a language by which one can determined whether a given language is disjunctive or not. Some properties of solid codes were investigated. We show that a solid code consists of only primitive words. A characterization of disjunctive domains is obtained.

Soit X, un alphabet fini qui contient strictement plus d'une lettre. Soit X* le monoide libre genere par X et soit X + =X*-{1} ou 1 est le mot vide. Tout sous-ensemble de X* est appele un langage. Le propos de ces articles est de montrer qu'un langage est dijonctif separable si et seulement si il est dense

It is known that both the class of all (n,k)-languages and the class of all time-variant languages over a finite alphabet contain the class of all regular languages. In this paper we show that in general neither one of these two classes of languages contains the other by constructing an infinite sequence of strongly primitive words over an alphabet with four letters.

LeA be an automaton whose set of inputs equalsX (|X|≧2) and whose cardinality of the set of states equalsn (n≧2), and letQ be the set of all primitive words overX. ByT(A) we denote the language accepted byA. In this paper, we give the following results: Moreover, we deal with the case |T(A)⋔Q

Let X be an alphabet contains more than one letter and let X* be the free monoid generated by X. A language S≤X* is right dense if uX*∩S≠ϕ for all u∈X*. The purpose of this paper is to give characterizations of right dense languages.

A language L is f-disjunctive if every class of its syntactic congruence is finite. The family of f-disjunctive languages is a natural generalization of the family of disjunctive languages and both families are anti-AFL. Every f-disjunctive language is dense and every class (≠ 1) of its syntactic congruence is an infix code. Five different classes of f-disjunctive languages are considered and it is shown that they form a strict hierarchy. Also some properties of the syntactic monoid of a f-disjunctive language are established, in particular its decomposition as a subdirect product of nil monoids.

The combinatorial structure of n-prefix-suffix languages, called n-ps-codes in this paper, is investigated. An n-ps-code is a language, each of whose subsets of cardinality at most n is a prefix code or a suffix code.