For eachbasic language operationwedefine its ‘‘unique’’ counterpart as being the operation that results in a language whose words can be obtained uniquely through the given operation. These unique operations can arguably be viewed as combined basic operations, placing thiswork in the popular area of state complexity of combined operations on regular languages. We study the state complexity of u...

Let L be a set of regular languages of A∗. An L-polynomial is a finite union of products of the form L0a1L1 · · · anLn, where each ai is a letter of A and each Li is a language of L. We give an explicit formula for computing the intersection of two L-polynomials. Contrary to Arfi’s formula (1991) for the same purpose, our formula does not use complementation and only requires union, intersectio...

Although there exists a multitude of different approaches to vagueness in linguistics, there seems to be a general agreement that vagueness involves one or another kind of context dependence. E.g. Lewis [17] gives a high level overview of the use of contexts in natural language and illustrates that they are essential for modeling the shifting of vague standards. Therefore a vague sentence canno...

This article presents a translation of the Property formalism of [2] into the XFST regular expression formalism [6]. Besides offering at no cost a platform to use Properties in natural language processing, this operation allows us to clarify the interpretation of the Property formalism, which may be interpreted as strictly limited either to regular languages or to context-free languages, depend...

In this paper, a general expression of the Shapley value for fuzzy games on vague sets is proposed, where the player participation levels are vague sets. The existence and uniqueness of the given Shapley value are showed by establishing axiomatic system. When the fuzzy games on vague sets are convex, the given Shapley value is a vague population monotonic allocation function (VPMAF) and an elem...

In the theory of formal languages, the understanding of concatenation hierarchies of regular languages is one of the most fundamental and challenging topic. In this paper, we survey progress made in the comprehension of this problem since 1971, and we establish new generic statements regarding this problem.

This paper focuses on the basic operations of Chomsky’s languages. The validity and the effectiveness of some closure operations, such as union operator, product operator and Kleene Closure operator, are discussed in detail. The crosstalk problems in Context-Sensitive Languages (CSL) and Phrase Structure Languages (PSL) are analyzed, and a valuable method to solve this problem is presented by s...

Recently, Augmented Regular Expressions (AREs) have been proposed as a formalism to describe, recognize and learn a non-trivial class of context-sensitive languages (CSLs) 1, 2]. AREs augment the expressive power of Regular Expressions (REs) by including a set of constraints, that involve the number of instances in a string of the operands of the star operations of an RE. Although it is demonst...

This paper studies the problem of predicting occurrences of a significant event in a discrete-event system. The predictability of occurrences of an event in a system is defined in the context of formal languages. The predictability of a language is a stronger condition than the diagnosability of the language. An implementable necessary and sufficient condition for predictability of occurrences ...