Compressão de Sequências Individuais e Fontes Parcialmente Ordenadas.

Abstract

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.