Rule matrices for syntactic deep structure

Syntactic deep structure may be simplified and systematized according to rule matrices. Rule matrices provide an effective tool for structural analysis by uniting the functions of parsing trees with rewriting rules. A production grammar employing rule matrices may be defined as the quadruple P=composed of VN and VT, two disjoint nonnull finite sets, the non-terminal and terminal vocabularies of P, SeVN and is the initial symbol of P, and M a finite set of rule matrices where alpha and beta are elements of the free monoid over the vocabulary, and alpha contains at least one element from VN. K1,...,Kn provide for (possibly null) contextual, expansion, and transformation constraints. By assertion, a rule matrix realizes it's upper-row entry string, excluding K1,...,Kn, as the lower-row entry string, and the converse, subject to explicit constraints. Thus it has the effect of a bidirectional rewriting rule in the form of a left-adjusted parsing tree. This greatly simplifies expansion, transformation, and bracketing. AA