Gheorghe Păun

Dynamically controlled cooperating/distributed grammar systems

Abstract Motivated by systems of artificial intelligence with distributed knowledge bases, we introduce the concept of a cooperating/distributing grammar system. In this paper, we study the effect of different conditions for starting and stopping of the components of the grammar system. If the start condition is of random context type, we obtain at most all matrix languages; if conditional or semiconditional start conditions are used, we get the family of context-sensitive languages. Time limitations have no further effect in these cases.

On parallelism in colonies

Colonies (basically, grammar systems with the components generating finite languages) with parallel activity (all the components that can work must work) in two variants are defined here and their generative capacity is investigated. It is found that the (strong) parallelism increases the power of colonies, but subfamilies of matrix languages are obtained.

On the generative capacity of conditional grammars

A conditional grammar is a Chomsky grammar with languages associated to its rules such that each rule is applicable only to words in the corresponding language. In this paper the generative capacity of type 0, 1, 2, 2 — λ , 3 grammars with associated type 0, 1, 2, 3 languages will be characterized in terms of the Chomsky hierarchy. We shall prove that the generative capacity of context-free and of regular grammars is increased in this way, while for type-0 and type-1 grammars the generative capacity is not modified. Two other variants of these grammars are shown to be equivalent with them.

On the index of grammars and languages

We prove the following results concerning the index of grammars and languages. (1) Any context-free grammar with the terminal vocabulary containing only one letter has a finite index. (2) Any type-O grammar of finite index such that any rule is of the form αAβ → αγβ , generates a context-free language of finite index. (3) The family of matrix languages of finite index is a full AFL.

A homomorphic representation of simple matrix languages

In this paper we given a homomorphic representation of simple matrix languages similar in form to those of context-free languages, namely: Any simple matrix language L can be written as the homomorphic image of the intersection of the Dyck context-free language and an equal matrix language. We do not obtain a characterization, because the converse is not true.

Modelling economic processes by means of formal grammars: A survey of results at the middle of 1981

This paper briefly presents the topics of research and the results obtained by using formal language techniques (mainly Chomsky grammars) in modelling economic processes. This ‘grammatical approach’ to economics is a fairly new way of applying a very modern mathematical theory, and most of the results in this field were obtained by the Roumanian School of Mathematical Linguistics. The survey covers the results reported before the summer of 1981 (those summarized in the monograph [44]). A later survey will present more recent results, some of which are still developing.