Variants Of Array-Rewriting P Systems For Generating Picture Arrays
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Date
2015-10
Authors
Pradeep, Isawasan
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Inspired by the structure and functioning of the living cells, the field of membrane
computing was initiated around the year 2000. Since then the theoretical model introduced
in this area, called P system has been intensively investigated for properties and
applications. One such P system known as array-rewriting P systems provides a link
between two dimensional formal language theory and membrane computing. In formal
language theory, one of the main studies is on the language generating capability of the
grammars, referred to as the generative capacity, which depends on the types of rules.
Also a standard technique to increase the generative capacity is to endow the rules with
additional features. Here the array-rewriting P system is investigated by endowing the
grammatical rules of the system with three such features, namely, permitting symbols,
parallel rewriting and grouping of rules. Thus this thesis introduces and develops three
such variants of the array-rewriting P system and brings out their advantages. First a
new variant, known as permitting array-rewriting P system is introduced, which enables
to reduce the number of membranes used in the constructions of P systems in
comparison with the original array-rewriting P system. Second variant, called parallel
array-rewriting P systems is introduced incorporating the parallel rewriting feature,
motivated by parallel rewriting in string-rewriting P systems. Again an advantage of
this feature is that the number of membranes is small in many constructions, besides enabling generation of geometric objects such as hollow rectangles and hollow squares,
known to be not generated even by context-free array grammars. A third variant, called
tabled parallel array-rewriting P system, is also introduced incorporating the technique
of grouping rules into tables of rules. This feature enables to generate picture patterns
that cannot be generated by parallel array-rewriting P systems. As an application of the
array-rewriting P system model, a structural property, namely region-based segmentation
of picture arrays is investigated, which differentiates the regions of a picture array
with each region sharing certain visual characteristics. P systems for region-based
segmentation of rectangular picture arrays, are known. On the other hand, hexagonal
picture array has been of interest in several studies due to its unambiguous connectivity
feature. Here extending the technique in the rectangular case, region-based segmentation
of hexagonal picture arrays is performed resulting in a reduction in the number of
rules. Finally, a general method is proposed with certain specific types of array rewriting
rules, thereby providing a uniform framework to handle arrays independent of the
size and improving the existing region-based segmentation method.
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Description
Keywords
Membrane computing