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Analysis by Reduction of D-trees

The goal of this study is to introduce and ob- serve analysis by reduction of dependency trees. We focus on formalization of certain minimalistic properties of anal- ysis by reduction of dependency trees, and its complexity issues. We introduce analysis by reduction of D-trees (ARDT) in order to give a new formal tool for study of individual de- pendency trees in tree-banks, namely for the study of their structural complexity. In this way we give at the same time a tool for observations of properties of the whole tree- banks, and their interesting subsets. We work in a way which is close to the formal languages theory. We should be able to study complexity issues of formal D-tree lan- guages. 1.1 Analysis by Reduction Based on D-Trees Analysis by reduction on D-trees is derived from analysis by reduction of natural language sentences (AR), see (3), helps one to study AR, and to identify a sentence depen- dency structure and the corresponding grammatical cat- egories of an analyzed language. ARDT is based upon a stepwise simplification of a correctly composed D-tree (e.g, correctly composed to a correct Czech sentence). It defines possible sequences of reductions in the D-tree - each step of ARDT consists in some cuts of some sub- trees from the input D-tree; here, we allow the cuts of to be accompanied by some shifts of (a) word(s) (node(s)) to another horizontal position(s) in the D-tree. Let us stress the basic constraints imposed on reduction steps of surface ARDT: (i) individual words (word forms), their morphological characteristics and/or their syntactic categories must be preserved in the course of ARDT;