SILVA, A. da.; SILVA, ANDRESSO DA.; DA SILVA, ANDRESSO.; http://lattes.cnpq.br/5104871861245226; SILVA, Andresso da.
Resumo:
Most applications of information theory are based on the use of alphabets with a total
order. When the systems considered present events with partial order (e.g. concurrent
systems), conventional information theory provides incomplete tools due to the nature
of the processes. This becomes a relevant issue when considering that the number of
concurrent systems has been growing more and more. When there is a partial order, the
main tools for analysis are commutativity graphs and equivalence classes, induced by these
graphs. It is aimed, in this dissertation, to develop new information measures for alphabets
with partial order and apply these measures in the analysis and development of algorithms
that use these alphabets. As a result, estimation methods and limits for the number of
equivalence classes were obtained. Besides, it was proposed a new definition of entropy
for alphabets with a partial order, called commutativity entropy. It is shown that this
definition allows overcoming some of the limitations of similar entropies proposed before.
Furthermore, a new optimal compression algorithm is presented that considers the partial
order between symbols in the sequence to be compressed. When partial order relations
are considered, it is shown that higher sequence compression rates can be obtained.
