We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. We consider two kind of problems depending on representation of regular language. If a regular language on input is represented by a DFA, then we obtain (deterministic) regular realizability...

This paper introduce two types of edge degrees (line degree and near line degree) total (total an in a fuzzy semigraph, where semigraph is defined as (V, σ, μ, η) on G* which σ : V → [0, 1], μ VxV 1] η X satisfy the conditions that for all vertices u, v vertex set, μ(u, v) ≤ σ(u) ᴧ σ(v) η(e) = μ(u1, u2) μ(u2, u3) … μ(un-1, un) σ(u1) σ(un), if e (u1, u2, …, un), n ≥ 2 G*, pair sets X) set non - ...

The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic meta-language for the definition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions, although only regular expressions that denote words unambiguously, in the sense of the ISO standard, are allowed. In general, a word that is denoted by a regula...

In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class of accepting automata and, using this characterisation, establish several decidability and closu...

We define a language to be overlap-free if any two distinct strings in the language do not overlap with each other. We observe that overlap-free languages are a proper subfamily of infix-free languages and also a proper subfamily of comma-free languages. Based on these observations, we design a polynomial-time algorithm that determines overlapfreeness of a regular language. We consider two case...

The main goal of this paper is to introduce and study fuzzy multiset regular grammar to show that fuzzy multiset finite automata and fuzzy multiset regular grammars are equivalent. We also study fuzzy multiset linear grammars and fuzzy multiset regular grammars in normal form. Furthermore, we show the equivalence of fuzzy multiset regular grammars, fuzzy multiset left linear grammars, fuzzy mul...

Given a strictly increasing sequence s of non-negative integers, filtering a word a0a1 · · · an by s consists in deleting the letters ai such that i is not in the set {s0, s1, . . .}. By a natural generalization, denote by L[s], where L is a language, the set of all words of L filtered by s. The filtering problem is to characterize the filters s such that, for every regular language L, L[s] is ...

Intercodes are a generalization of comma-free codes. Using the structural properties of finite-state automata recognizing an intercode we develop a polynomial-time algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yields also the smallest index k such that L is a k-intercode. Furthermore, we examine the prime intercode decom...

We provide an algorithm for learning an unknown regular set of infinite words, using membership and equivalence queries. Three variations of the algorithm learn three different canonical representations of omega regular languages, using the notion of families of dfas. One is of size similar to L$, a dfa representation recently learned using L ∗ [7]. The second is based on the syntactic forc, in...