Families Of Formal Languages Research Articles

Formel Ontolojiler ve Betimleyici Mantıklar

The history of ontology reveals various methodologies that examine being. Traditional ontology studies being qua being and categorizes it. Formal ontology determines the categories that are common to all entities and classifies them with formal languages using these categories as well. However, for over thirty years, formal ontologies have been studied and built outside of philosophy. The reason why ontology is separated from philosophy and becomes an interdisciplinary study is due to our need to make classifications and standardization in data and information management in accordance with reality. What lies behind this requirement is the exponential growth of data and the impossibility of analyzing it neither by humans nor by existing methods. For instance, dozens of studies are published every minute, and then scientists cannot follow all these developments with classical techniques. Therefore, the desire that machines should be involved in the processes of sharing and producing knowledge is far higher than ever. This desire, thus, has led us to develop new models for knowledge production. It has been experienced that the standardization of knowledge is essential in the construction of models; for, significant differences were found between taxonomic structures, concept definitions, and different granularity levels in the knowledge representations of various working groups, and even the integration of data was not possible. At this point, the selection, classification, and standardization of knowledge have been guaranteed by using ontological principles and methods. In this article, within information systems, we will introduce the formal ontologies, the formal theory covering the broadest knowledge of the field by selecting, classifying and standardizing it by using the principles and methods of philosophical ontologies. We will mention that we use description logics, a family of formal languages with the expressive power of natural language and high-performance reasoning algorithms, to represent this theory in machines. In essence, this article will introduce formal ontologies and description logics in the realm of knowledge representation.

On language equations with concatenation and various sets of Boolean operations

Systems of equations of the form X i = ϕ i (X 1 , ... , X n ), for 1 ⩽ i ⩽ n , in which the unknowns X i are formal languages, and the right-hand sides ϕ i may contain concatenation and union, are known for representing context-free grammars. If, instead of union only, another set of Boolean operations is used, the expressive power of such equations may change: for example, using both union and intersection leads to conjunctive grammars [A. Okhotin, J. Automata, Languages and Combinatorics 6 (2001) 519–535], whereas using all Boolean operations allows all recursive sets to be expressed by unique solutions [A. Okhotin, Decision problems for language equations with Boolean operations, Automata, Languages and Programming, ICALP 2003, Eindhoven, The Netherlands, 239–251]. This paper investigates the expressive power of such equations with any possible set of Boolean operations. It is determined that different sets of Boolean operations give rise to exactly seven families of formal languages: the recursive languages, the conjunctive languages, the context-free languages, a certain family incomparable with the context-free languages, as well as three subregular families.

Language equations with complementation: Expressive power

Consider a system of language equations of the form X i = φ i ( X 1 , … , X n ) ( 1 ⩽ i ⩽ n ) , where every φ i may contain the operations of concatenation and complementation. These systems have been studied in “Language equations with complementation: Decision problems” [A. Okhotin, O. Yakimova, Theoretical Computer Science 376 (2007) 112–126]. This paper investigates the family of languages representable by unique solutions of such systems. A method for proving nonrepresentability of particular languages is developed. Several natural subfamilies of this family are compared to each other and to the main known families of formal languages. Their position in the hierarchy is established.

On sets of numbers accepted by P/T systems composed by join

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow.Here we continue this line of research by introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only by join. Moreover, we study how J languages relate to other families of formal languages.

On Languages Accepted by P/T Systems Composed of joins

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow. Here we continue this line of research introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only of joins. Moreover, we investigate how J languages relate to other families of formal languages. In particular, we show that every J language can be accepted by a log n space-bounded non-deterministic Turing machine with a one-way read-only input. We also show that every J language has a semilinear Parikh map and that J languages and context-free languages (CFLs) are incomparable.

COMPLEXITY AND STRUCTURE IN FORMAL LANGUAGE THEORY

The following survey reviews some connections between formal languages and complexity theory. Families of formal languages are treated with complexity theoretical methods. In particular, the concept of unambiguity, common to both areas, is treated in detail. Some complexity theoretical aspects of operations on formal languages are indicated. This picture is completed by taking parallel models into account.

Closure properties of certain families of formal languages with respect to a generalization of cyclic closure

Closure properties of certain families of formal languages with respect to a generalization of cyclic closure

Weakly context-sensitive languages as model for programming languages

An abstract family of formal languages containing context-free languages and properly contained in (deterministic) context-sensitive languages is introduced. This family is comprehensive enough to contain e.g. Algol 60 without admitting too complex recursive constructions possible in the frame of general context-sensitive languages. This family is essentially a family of property-languages, whereby the considered properties are restricted to properties which are constructively definable from a finite number of context-free sets.