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

Membrane systems with limited parallelism

Membrane computing is an emerging research field that belongs to the more general area of molecular computing, which deals with computational models inspired from bio-molecular processes. Membrane computing aims at defining models, called membrane systems or P systems, which abstract the functioning and structure of the cell. A membrane system consists of a hierarchical arrangement of membranes delimiting regions, which represent various compartments of a cell, and with each region containing bio-chemical elements of various types and having associated evolution rules, which represent bio-chemical processes taking place inside the cell. This work is a continuation of the investigations aiming to bridge membrane computing (where in a compartmental cell-like structure the chemicals to evolve are placed in compartments defined by membranes) and brane calculi (where one considers again a compartmental cell-like structure with the chemicals/proteins placed on the membranes themselves). We use objects both in compartments and on membranes (the latter are called proteins), with the objects from membranes evolving under the control of the proteins. Several possibilities are considered (objects only moved across membranes or also changed during this operation, with the proteins only assisting the move/change or also changing themselves). Somewhat expected, computational universality is obtained for several combinations of such possibilities. We also present a method for solving the NP-complete SAT problem using P systems with proteins on membranes. The SAT problem is solved in O(nm) time, where n is the number of boolean variables and m is the number of clauses for an instance written in conjunctive normal form. Thus, we can say that the solution for each given instance is obtained in linear time. We succeeded in solving SAT by a uniform construction of a deterministic P system which uses rules involving objects in regions, proteins on membranes, and membrane division. Then, we investigate the computational power of P systems with proteins on membranes in some particular cases: when only one protein is placed on a membrane, when the systems have a minimal number of rules, when the computation evolves in accepting or computing mode, etc. This dissertation introduces also another new variant of membrane systems that uses context-free rewriting rules for the evolution of objects placed inside compartments of a cell, and symport rules for communication between membranes. The strings circulate across membranes depending on their membership to regular languages given by means of regular expressions. We prove that these rewriting-symport P systems generate all recursively enumerable languages. We investigate the computational power of these newly introduced P systems for three particular forms of the regular expressions that are used by the symport rules. A characterization of ET0L languages is obtained in this context

A Characterization of ETOL Tree Languages by Cooperating Regular Tree Grammars

In this paper we show that the class of tree languages generated by ETOL tree systems is equal to the class of tree languages generated by distributed regular tree grammars cooperating with terminal strategy. 1 Introduction In theoretical computer science the classical theory of automata and formal languages was generalized to that of tree automata and tree languages. The base of this generalization is that an alphabet is generalized to a ranked alphabet, in which every symbol has a rank in the set of nonnegative integers. (An ordinary alphabet is considered as a ranked alphabet of which all symbols have rank 1.) Then, having a ranked alphabet, one can build up terms (called trees) from its symbols. A set of trees is called a tree language. Grammars generating tree languages are called tree grammars and automata recognizing tree languages are called tree automata. Devices that define transductions over trees, and thus generalize sequential machines, are called tree transducers. Regula..