A Study Of Multiset Ordering For Constructing Alternative P Systems And Their Applications

In this thesis, basic ingredients of partially ordered multisets were employed in which some of its formalisms were further developed and a set of rules formulated which explicitly characterize the chemical and physical functions, among others, of the processes taking place in a biological cell. In the sequel, a grid form of the Jouannaud-Lescanne set-based and submultiset-based multiset orderings have been developed. Relatively, more applicable definitions of the multiset orderings and some of their systematic relationships were presented. A possibility of extending the set-based multiset ordering to simple multisets of incomparable objects has also been observed. A consequence of partial ordering – a partial ordering which is restricted to incomparable element – was studied and a number of its examples presented. By using this concept, a variant of alternative P system using specialized rules was developed, and was shown to adequately simulate the activities of the biological cells as opposed to the conventional P systems whose rules represent the activities of the biological cells in an unspecialized manner. It is shown that with only one membrane and three rules, a nondeterministic alternative P system based on ideal ordering is able to characterize the family of recursively enumerable languages. Finally, some deterministic P systems based on weak rule priority were defined to carry out arithmetic operations and exemplified.

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