Tree Valence Controlled Grammars

Beyond a shadow of a doubt, the studying of context-free grammars with restricted derivationtrees known as tree controlled grammars have achieved plentiful remarkable results within formallanguage 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 theirderivation trees need to be satisfied by certain prescribed conditions. Our paper is a continuing of studyingof this kind of grammars, where we introduce a new variant of tree controlled grammar called a treevalence controlled grammar, which replaces regular sets with valences where every main production withcertain integer value will be derived into sub-productions with the value of combination of zero and one orzero 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 thegenerative capacity and structural properties of these grammars.