Further Results on P Systems with Promoters/Inhibitors

The paper gives several results regarding P systems with non-cooperative rules and promoters/inhibitors at the level of rules. For the class of P systems using inhibitors, generating families of sets of vectors of numbers, the equivalence with the family of Parikh sets of ET0L languages is presented. In case of P systems with non- cooperative promoted rules even if an upper bound was not given, the inclusion of the family PsET0L was proved. Moreover, a characterization of such systems by means of a particular form of random context grammars, therefore a sequential formal device, is proposed

On three variants of rewriting P systems

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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

Ogden's lemma for random permitting and forbidding context picture languages and table-driven context-free picture languages

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, February 16, 2015.Random context picture grammars are used to generate pictures through successive refinement. There are three important subclasses of random context picture grammars, namely random permitting context picture grammars, random forbidding context picture grammars and table-driven context-free picture grammars. These grammars generate the random permitting context picture languages, random forbidding context picture languages and table-driven context-free picture languages, respectively. Theorems exist which provide necessary conditions that have to be satisfied by a language before it can be classified under a particular subclass. Some of these theorems include the pumping and shrinking lemmas, which have been developed for random permitting context picture languages and random forbidding context picture languages respectively. Two characterization theorems were developed for the table-driven context-free picture languages. This dissertation examines these existing theorems for picture languages, i.e., the pumping and shrinking lemmas and the two characterisation theorems, and attempts to prove theorems, which will provide an alternative to the existing theorems and thus provide new tools for identifying languages that do not belong to the various classes. This will be done by adapting Ogden’s idea of marking parts of a word which was done for the string case. Our theorems essentially involve marking parts of a picture such that the pumping operation increases the number of marked symbols and the shrinking operation reduces it

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 rewriting in formal language theory

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2008.Context-free grammars are well-studied and well-behaved in terms of decidability, but many real-world problems cannot be described with context-free grammars. Grammars with regulated rewriting are grammars with mechanisms to regulate the applications of rules, so that certain derivations are avoided. Thus, with context-free rules and regulated rewriting mechanisms, one can often generate languages that are not context-free. In this thesis we study grammars with regulated rewriting mechanisms. We consider problems in which context-free grammars are insufficient and in which more descriptive grammars are required. We compare bag context grammars with other well-known classes of grammars with regulated rewriting mechanisms. We also discuss the relation between bag context grammars and recognizing devices such as counter automata and Petri net automata. We show that regular bag context grammars can generate any recursively enumerable language. We reformulate the pumping lemma for random permitting context languages with context-free rules, as introduced by Ewert and Van der Walt, by using the concept of a string homomorphism. We conclude the thesis with decidability and complexity properties of grammars with regulated rewriting

Maximally Parallel Multiset-Rewriting Systems: Browsing the Configurations

The aim of this research is to produce an algorithm for the software that would let a researcher to observe the evolution of maximally parallel multiset-rewriting systems with permitting and forbidding contexts, browsing the configuration space by following transitions like following hyperlinks in the World-Wide Web. The relationships of maximally parallel multiset-rewriting systems with other rewriting systems are investigated, such as Petri nets, different kinds of P systems, Lindenmayer systems, grammar systems, regulated grammars

Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes

We study cooperating distributed grammar systems working in hybrid modes in connection with the finite index restriction in two different ways: firstly, we investigate cooperating distributed grammar systems working in hybrid modes which characterize programmed grammars with the finite index restriction; looking at the number of components of such systems, we obtain surprisingly rich lattice structures for the inclusion relations between the corresponding language families. Secondly, we impose the finite index restriction on cooperating distributed grammar systems working in hybrid modes themselves, which leads us to new characterizations of programmed grammars of finite index.Comment: In Proceedings AFL 2014, arXiv:1405.527