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In order to understand natural languages, we have to be able to determine the relations between words, in other words we have to be able to 'parse' the input text. This is a difficult task, especially for Arabic, which has a number of properties that make it particularly difficult to handle. There are two approaches to parsing natural languages: grammar-driven and data-driven. Each of these approaches poses its own set of problems, which we discuss in this paper. The goal of our work is to produce a hybrid parser, which retains the advantages of the data-driven approach but is guided by grammar rules in order to produce more accurate output. This work consists of two stages: the first stage is to develop a baseline data-driven parser, which is guided by a machine learning algorithm for establishing dependency relations between words. The second stage is to integrate grammar rules into the baseline parser. In this paper, we describe the first stage of our work, which is now implemented, and a number of experiments that have been conducted on this parser. We also discuss the result of these experiments and highlight the different factors that are affecting parsing speed and the correctness of the parser results.