We initiate a study of languages of partial words related to regular languages of full words. First, we study the possibility of expressing a regular language of full words as the image of a partial-wordslanguage through a substitution that only replaces the hole symbols of the partial words with a finite set of letters. Results regarding the structure, uniqueness and succinctness of such a rep...

A language L is the orthogonal catenation of languages L1 and L2 if every word of L can be written in a unique way as a catenation of a word in L1 and a word in L2. We establish a tight bound for the state complexity of orthogonal catenation of regular languages. The bound is smaller than the bound for arbitrary catenation.

For a cylindric set algebra A with (base U and) unit U ω and , U X ⊆ let X A be the subalgebra of ( ) U ω ℘ generated by {{ } }. : X u U u A ∈ × ω ∪ D At denotes the set of atoms of . D It is shown that, there exists a simple and countable ω ∈ Lf A such that A Nrn is atomic for every n and the following hold. For every A C C ≅ ∈ ω ω , reg Cs Lf ∩ and C has base U, there is a non-empty U V ⊆ suc...

The relationship between the family SH of simple splicing languages, which was recently introduced by A. Mateescu and coauthors, and the family SLT of strictly locally testable languages is clariied by establishing an ascending hierarchy of families fSiH : i ?1g of splicing languages for which SH = S1H and the union of the families is the family SLT. A procedure is given which, for an arbitrary...

A mathematical procedure used to convert an element in the universe of discourse into the membership value of the fuzzy set is termed as fuzzification. In this paper we propose a new technique Vague-Fuzzification to implement fuzzification using vague sets. The proposed technique is designed that is using two methods to implement the same. First method includes a positive ordered transforming f...

Various attempts have been made by researchers on the study of vagueness of data through intuitionistic fuzzy sets and vague sets, and also it was shown that vague sets are intuitionistic fuzzy sets. But there are algebraic and graphical differences between vague sets and intuitionistic fuzzy sets. In this paper an attempt is made to define the correlation coefficient of interval vague sets lyi...

In this paper, we study the power of internal contextual grammars with selection languages from subfamilies of the family of regular languages. If we consider families Fn which are obtained by restriction to n states or nonterminals or productions or symbols to accept or to generate regular languages, we obtain four infinite hierarchies of the corresponding families of languages generated by in...

Using a genealogically ordered infinite regular language, we know how to represent an interval ofR. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language. The syntactical properties of these words...

In this paper, we study the state complexities of union and intersection combined with star and reversal, respectively. We obtain the state complexities of these combined operations on regular languages and show that they are less than the mathematical composition of the state complexities of their individual participating operations.

In this paper we propose a condition for rejecting the input word by an accepting splicing system which is defined by a finite set of forbidding words. More precisely, the input word is accepted as soon as a permitting word is obtained provided that no forbidding word has been obtained so far, otherwise it is rejected. Note that in the new variant of accepting splicing system the input word can...