Simple-Semi-Conditional Versions of Matrix Grammars with a Reduced Regulating Mechanism

This paper discusses some conditional versions of matrix grammars. It establishes several characterizations of the family of the recursively enumerable languages based on these grammars. In fact, making use of the Geffert Normal forms, the present paper demonstrates these characterizations based on matrix grammars with conditions of a limited length, a reduced number of nonterminals, and a reduced number and size of matrices

Reduction of simple semi-conditional grammars with respect to the number of conditional productions

The present paper discusses the descriptional complexity of simple semiconditional grammars with respect to the number of conditional productions. More specifically, it demonstrates that for every phrase-structure grammar, there exists an equivalent simple semi-conditional grammar that has no more than twelve conditional productions

Accepting grammars and systems

We investigate several kinds of regulated rewriting (programmed, matrix, with regular control, ordered, and variants thereof) and of parallel rewriting mechanisms (Lindenmayer systems, uniformly limited Lindenmayer systems, limited Lindenmayer systems and scattered context grammars) as accepting devices, in contrast with the usual generating mode. In some cases, accepting mode turns out to be just as powerful as generating mode, e.g. within the grammars of the Chomsky hierarchy, within random context, regular control, L systems, uniformly limited L systems, scattered context. Most of these equivalences can be proved using a metatheorem on so-called context condition grammars. In case of matrix grammars and programmed grammars without appearance checking, a straightforward construction leads to the desired equivalence result. Interestingly, accepting devices are (strictly) more powerful than their generating counterparts in case of ordered grammars, programmed and matrix grammars with appearance checking (even programmed grammarsm with unconditional transfer), and 1lET0L systems. More precisely, if we admit erasing productions, we arrive at new characterizations of the recursivley enumerable languages, and if we do not admit them, we get new characterizations of the context-sensitive languages. Moreover, we supplement the published literature showing: - The emptiness and membership problems are recursivley solvable for generating ordered grammars, even if we admit erasing productions. - Uniformly limited propagating systems can be simulated by programmed grammars without erasing and without appearance checking, hence the emptiness and membership problems are recursively solvable for such systems. - We briefly discuss the degree of nondeterminism and the degree of synchronization for devices with limited parallelism

Cooperating distributed grammar systems with random context grammars as components

In this paper, we discuss cooperating distributed grammar systems where components are (variants of) random context grammars. We give an overview of known results and open problems, and prove some further results

Regulated Formal Models and Their Reduction

Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult