Showing papers by "Grzegorz Rozenberg published in 1974"

L Systems

Abstract: L systems are parallel rewriting systems which were originally introduced in 1968 to model the development of multicellular organisms, [L1]. The basic ideas gave rise to an abundance of language-theoretic problems, both mathematically challenging and interesting from the point of view of diverse applications. After an exceptionally vigorous initial research period (roughly up to 1975; in the book [RSed2], published in 1985, the period up to 1975 is referred to, [RS2], as \when L was young"), some of the resulting language families, notably the families of D0L, 0L, DT0L, E0L and ET0L languages, had emerged as fundamental ones in the parallel or L hierarchy. Indeed, nowadays the fundamental L families constitute a similar testing ground as the Chomsky hierarchy when new devices (grammars, automata, etc.) and new phenomena are investigated in language theory. L systems were introduced by Aristid Lindenmayer in 1968, [L1]. The original purpose was to model the development of simple lamentous organisms. The development happens in parallel everywhere in the organism. Therefore, parallelism is a built-in characteristic of L-systems. This means, from the point of view of rewriting, that everything has to be rewritten at each step of the rewriting process. This is to be contrasted to the \sequential" rewriting of phrase structure grammars: only a speci c part of the word under scan is rewritten at each step. Of course, the e ect of parallelism can be reached by several se-

Nonterminals, homomorphisms and codings in different variations of OL-systems

Abstract: The use of nonterminals versus the use of homomorphisms of different kinds in the basic types of deterministic OL-systems is studied. A rather surprising result is that in some cases the use of nonterminals produces a comparatively low generative capacity, whereas in some other cases the use of nonterminals gives a very high generative capacity. General results are obtained concerning the use of erasing productions versus the use of erasing homomorphisms. The paper contains a systematic classification of the effect of nonterminals, codings, weak codings, nonerasing homomorphisms and homomorphisms for all basic types of deterministic OL-languages, including table languages.

Description of developmental languages using recurrence systems

Abstract: Recurrence systems have been devised to describe formally certain types of biological developments. A recurrence system specifies a formal language associated with the development of an organism. The family of languages defined by recurrence systems is an extension of some interesting families of languages, including the family of context-free languages. Some normal-form theorems are proved and the equivalence of the family of recurrence languages to a previously studied family of developmental languages (EOL-languages) is shown. Various families of developmental and other formal languages are characterized using recurrence systems. Some closure properties are also discussed.

The equality of EOL languages and codings of ol languages

Abstract: It is proved that a language is a coding (a letter-to-letter homomorphism) of a OL language, if, and only if, it is an EOL language.

Nonterminals versus homomorphisms in defining languages for some classes of rewriting systems

Abstract: Given a rewriting system G (its alphabet, the set of productions and the axiom) one can define the language of G by The "trade-offs" between these two mechanisms for defining languages are discussed for both "parallel" rewriting systems from the developmental systems hierarchy and "sequential" rewriting systems from the Chomsky hierarchy.

A Relationship between ETOL and EDTOL Languages

Abstract: This paper provides a method of ''decomposing'' a subclass of ETOL languages into deterministic ETOL languages. This allows one to use every known example of a language which is not a deterministic ETOL language to produce languages which are not ETOL languages. To appear in Theoretical Computer Science.

On a family of acceptors for some classes of developmental languages

Abstract: A machine model, which consists essentially of a finite state control and an array of counters with first-in-last-out access, is formulated and it is proved that, under certain restrictions, the class of languages accepted is identical to the class of developmental languages without interactions.

The Number of Occurrences of Letters Versus Their Distribution in Some EOL Languages

Abstract: A characterization theorem is given for a class of developmental languages. The theorem binds together the number of occurrences of letters in the words of the given language with the distribution of these letters.

Developmental Systems with Fragmentation

Abstract: The paper introduces a new class of L systems, where it is possible to continue derivations from certain specified subwords of the words obtained. Such L systems (called L systems with fragmentation or just JL systems) are of interest both from biological and formal language theory point of view. The paper deals with JL systems without interactions, discusses the basic properties of the language families obtained, as well as their position in the L hierarchy. Finalhy, two infinite hierarchies of language families are obtained by limited fragmentation, the notions being analogous to those of ultralinearity and finiteness of index for context-free languages.

Trade-off between the Use of Nonterminals, Codings and Homomorphisms in Defining Languages for Some Classes of Rewriting Systems

Abstract: Given a rewriting system G consisting of an alphabet V, the set of productions P and the axiom ω, the most natural set of strings associated with G is the set of all strings one can “derive in G” starting with ω and using productions from P. Now, one can define “the language of G” in at least two different ways.

Generatively Deterministic L Languages. Subword Point of View

Abstract: "d t The notion of a "deterministic machine" or a e erministic language" (as opposed to their nondeterministic Counterparts) is one of the oldest and most investigated in the theory of computation and in formal language theory. One can however observe that whereas the notion of a deterministic machine is usually the natural one (in every situation there is at most one possible "move" the machine can make), the notion of a deterministic language is often not natural at all. In fact a deterministic language is almost always defined as a language which can be recognized by a deterministic machine, although in many cases the languages themselves are being defined by grammars rather than by machines. The typical situation is of the following kind: first a class of languages £ is defined by a class of grammars ~, then one finds an "equivalent" class of machines~, and then by considering ~ the deterministie subelass~ D of the class~one obtains the deterministic subclass £D of the class £. What subclass of ~ generates £D is mostly not understood at all, or, in the best case, it is the "translation" of~ D into the subclass of~, which could neither be called natural nor give any insight into the nature of the deterministic restriction. The basic difficulty lies in the fact that the notion of a deterministic language is defined via recognizers whereas the languages themselves are often defined in terms of generative devices. In this paper we want to point out several classes of languages for which the notion of "generative determinism" (deterministic restriction defined in terms of grammars rather than recognizers) is not only a very natural one but it also lends itself to mathamatical treatment. The theory of L systems and languages originated with the work of