Watson-crick petri net and place-labelled petri net controlled grammar using formal language theory

Abstract

formal language theory is a branch of applied discrete mathematics and theoretical computer science. a watson-crick automaton is an automaton that works on tapes which are double-stranded sequences of symbols related by watson-crick complementarity that are similar to the dna molecules. a petri net is a model of information flow in systems that provides a useful mathematical formalism for modelling concurrent systems. in this thesis, the relation between watson-crick automata and petri nets is investigated to consider the massive parallelism in watson- crick automata. thus, a new concept called watson-crick petri net is introduced. besides that, the structural properties of watson-crick petri net are found, namely a single start place, a run place and the stop transition. also, the generative power of watson-crick petri net is determined. besides using watson-crick complementarity in petri nets, a context-free grammar is also considered in this research. a petri net controlled grammar is a type of a context-free grammar equipped with petri nets, where the successful derivation of the grammar can be simulated by the sequence of occurrences of the net. the production rules of a grammar, for all variants of petri net controlled grammars that have been introduced, are associated only with transitions of a petri net. therefore, a place-labelled petri net controlled grammar is introduced in this research. the place labelling enables the parallel application of production rules in petri net controlled grammars to be considered. the effects of labelling strategies and the set of final markings, along with lower and upper bounds are chosen in order to increase the generative power of place-labelled petri net controlled grammar. besides that, the structural properties and structural subclass of place-labelled petri net controlled grammar are also found in this thesis.