Tree Valence Controlled Grammars

Abstract

Beyond a shadow of a doubt, the studying of context-free grammars with restricted derivation
trees known as tree controlled grammars have achieved plentiful remarkable results within formal
language theory as demonstrated in a number of publications on this subject for the past forty five years.
In principle, these grammars generate their languages as an ordinary context-free grammar except their
derivation trees need to be satisfied by certain prescribed conditions. Our paper is a continuing of studying
of this kind of grammars, where we introduce a new variant of tree controlled grammar called a tree
valence controlled grammar, which replaces regular sets with valences where every main production with
certain integer value will be derived into sub-productions with the value of combination of zero and one or
zero and minus represented in matrices form with the permutations of each matrix row yield a zero value
(at every level of tree derivation, the summation of valence value is zero). We also investigate the
generative capacity and structural properties of these grammars.