Jürgen Dassow

Grammar Systems: A Grammatical Approach to Distribution and Cooperation

From the Publisher: This book investigates two major systems: firstly, cooperating distributed grammar systems, where the grammars work on one common sequential form and the cooperation is realized by the control of the sequence of active grammars; secondly, parallel communicating grammar systems, where each grammar works on its own sequential form and cooperation is done by means of communicating between grammars. The investigation concerns hierarchies with respect to different variants of cooperation, relations with classical formal language theory, syntactic parameters such as the number of components and their size, power of synchronization, and general notions generated from artificial intelligence.

Grammars with Controlled Derivations

In [13], N. Chomsky says that “the main problem of immediate relevance to the theory of language is that of determining where in the hierarchy of devices the grammars of natural languages lie.” Formulated in other terms, the question is “where are the natural languages placed in the Chomsky hierarchy?” The debate started in 1959 and is not yet settled. Various arguments over English [4], Mohawk [92], Swiss German [112], Bambara [16], Chinese [95], etc., were given, refuted, rehabilitated — see pro and con arguments as well as further bibliographical information in [38] and [70]. The main difficulty is not a mathematical one but a linguistic one: what is English, what is a natural language, can we separate the syntax and the morphology from semantics or pragmatics? Whatever is or will be the position with respect to these questions, the linguists seem to agree (see again [70]) that “all” natural languages contain constructions which cannot be described by context-free grammars. Three basic such features of natural languages are: reduplication, leading to languages of the form {xx | x ∈ V*} multiple agreements, modeled by languages of the form {a n b n c n | n ≥ 1}, {a n b n c n d n | n ≥ 1}, etc. crossed agreements, as modeled by {a n b m c n d m | n, m ≥ 1}.

Language-theoretic problems arising from Richelieu cryptosystems

Abstract Classical cryptosystems of the type “Richelieu” or “garbage-in-between” give rise to ideas and notions so far neglected in the theory of formal languages. This paper investigates such notions, mainly from the point of view of decidability.

COOPERATING ARRAY GRAMMAR SYSTEMS

The aim of this paper is to elaborate the power of cooperation in generating pictures by array grammars. As it is expected, the generative capacity of cooperating array grammar systems (with a fixed number, with a number greater than a given threshold, or with the maximal number of derivation steps in each component when it is enabled) is strictly greater than that of context-free array grammars. Yet the same result is also obtained in the case of systems with regular components, which contradicts the corresponding result for string grammar systems. In fact, some more results for array grammar systems are obtained which either contradict the results for the corresponding string grammar systems or are not even known for these string grammar systems. Various non-context-free sets of arrays which can be generated in a simple way by cooperating array grammar systems are presented and show the power of the mechanism of cooperation for picture descritpion.

On Networks of Evolutionary Processors with Nodes of Two Types

We discuss the power of networks of evolutionary processors where only two types of nodes are allowed. We prove that (up to an intersection with a monoid) every recursively enumerable language can be generated by a network with one deletion and one insertion node. Networks with an arbitrary number of deletion and substitution nodes only produce finite languages, and for each finite language one deletion node or one substitution node is sufficient. Networks with an arbitrary number of insertion and substitution nodes only generate context-sensitive languages, and (up to an intersection with a monoid) every context-sensitive language can be generated by a network with one substitution node and one insertion node. All results are optimal with respect to the number of nodes.

Grammars With Regulated Rewriting

Context-free grammars are not able to cover all linguistic phenomena. Thus we define some types of grammars where context-free rules are used and restriction imposed on the derivations. We illustrate the concepts by examples, compare the generative power, give some closure and decidability properties and basic facts on syntactic complexity.

Decision problems and regular chain code picture languages

Abstract By interpretation of the letters u, d, r, l, ↑, ↓ as “move u p, ( d own, r ight, l eft)” with the pen, “lift” and “sink” the pen of a plotter we can associate a picture with a word. The set of pictures associated with the words in a regular (context-free) string language is called a regular (context-free) picture language or chain code picture language. In this paper we discuss the decidability status of the following problems for regular and context-free picture languages: • Is some picture a subpicture of all pictures of the language? • Does the language contain a picture with a given property? • Have all pictures of the language a given property?

Context-free evolutionary grammars and the structural language of nucleic acids.

This paper introduces and investigates a generative mechanism based on some operations inspired by the large-scale mutations in genomes (deletion, inversion, transposition, duplication). Basic questions regarding these devices and their generated languages are investigated: generative capacity, closure properties, decidability. We also briefly discuss a few problems concerning our model with respect to some structural features of the nucleic acids.

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.