Word recognition and generation is a fundamental part of the processing of natural language and it requires computationally effective morphological processors, especially for languages with rich morphology such as Modern Greek. Various models have been proposed for developing computerized systems to accomplish the task of recognition of morphosyntactic features of words In the work presented here, the lazy tagging approach was examined, in which taggers are expected to work in the simplest possible way. The model of functional decomposition was extended and adapted for Modern Greek as a target language, following the lazy word-parsing approach, in order to cover a number of morphological phenomena that are encountered in Modern Greek, namely inflection, affixation, and longdistance dependencies. To achieve a more efficient word recognition, several automata of different levels of computing power, based on the original model, were introduced and evaluated according to the criteria of complexity, recognition speed, and accuracy of the results. The proposed system was used for processing a large-scale corpus, and the results are presented and discussed. To accomplish their task, taggers can rely upon large lexical databases, which are expected to be organized in such a way as to provide rapid access to the stored data and efficient memory management. Directed graphs can be used to describe and organize a lexical database of large magnitude in a compact manner. These data structures are named here matrix lexica, where the letters are described as nodes of directed graphs and the lemmata as paths (set of edges). It is expected that matrix lexica will support a tagger efficiently by providing a high speed of resolution, sound mathematical foundation, low memory requirements, and ability to handle distorted input in future developments.