27,048 research outputs found
A Framework for Complexity Classes in Membrane Computing
The purpose of the present work is to give a general idea about the existing results and open problems
concerning the study of complexity classes within the membrane computing framework. To this aim,
membrane systems (seen as computing devices) are briefly introduced, providing the basic definition and
summarizing the key ideas, trying to cover the various approaches that are under investigation in this area
– of course, special attention is paid to the study of complexity classes. The paper concludes with some
final remarks that hint the reasons why this field (as well as other unconventional models of computation)
is attracting the attention of a growing community.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de AndalucÃa TIC-58
On the lexicographic representation of numbers
It is proven that, contrarily to the common belief, the notion of zero is not
necessary for having positional representations of numbers. Namely, for any
positive integer , a positional representation with the symbols for is given that retains all the essential properties of the usual
positional representation of base (over symbols for ).
Moreover, in this zero-free representation, a sequence of symbols identifies
the number that corresponds to the order number that the sequence has in the
ordering where shorter sequences precede the longer ones, and among sequences
of the same length the usual lexicographic ordering of dictionaries is
considered. The main properties of this lexicographic representation are proven
and conversion algorithms between lexicographic and classical positional
representations are given. Zero-free positional representations are relevantt
in the perspective of the history of mathematics, as well as, in the
perspective of emergent computation models, and of unconventional
representations of genomes.Comment: 15 page
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