Recursive Matrix Systems (RMS) and TAG

Introduction We define Recursive Matrix Systems (RMS), a highly parameterizable formalism that allows for a clear separation of various kinds of recursion. One instance of RMS, namely context--free RMS with two rows and a specific reading interpretation turns out to be weakly equivalent to TAG. This allows for the transfer of results from TAGs to this class of RMS. Furthermore, the equivalence proof is constructive and exhibits a very close relationship between the structures of the two formalism, namely trees and matrices. This allows to transfer interesting restrictions which can easily be defined in RMS to TAG. In particular, the obvious restriction of context-- free RMS to regular RMS results in a restricted form of TAG which appears sufficient for natural language processing, albeit being less complex than regular TAG. Recursive Matrix Systems A Recursive Matrix is a finite matrix whose elements are either terminal symbols or again recursive matrices (see Figure 1). Recursive