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A new type of grammar, called a parallel leveled grammar, is introduced. The families of languages generated by such grammars with contextfree, linear or right-linear subrules are studied. Right-linear parallel finite-leveled languages can be displayed as nested vector expressions, which are extensions of regular expressions. Various hierarchy theorems for these families of languages are obtained...
In this paper, we have introduced a new style of formal grammars called String Adjunct Grammars (AG). The rules in an AG have a considerably different formal character as compared to the 'rewrite rule' in a Phrase Structure Grammar (PSG). Such a study of formal grammars of different styles (i.e., formal character of rules) is of great interest because each style is well suited for characterizing certain...
A superAFL is a family of languages closed under union with unitary sets, intersection with regular sets, and nested iterated substitution and containing at least one nonunitary set. Every superAFL is a full AFL containing all context-free languages. If L is a full principal AFL, then S∞(L, the least superAFL containing L, is full principal. If L is not substitution closed, the substitution closure...
A new model of abstract automata is presented employing the concept of finite automata on a network. Each normal network n provided with a one-way input tape determines a family of languages nl. A representation theorem, analogous to the Chomsky-Schützenberger representation theorem for context free languages1, is proved for the class nl. One consequence is that nl is a principal full AFL generated...
An n-dimensional bug-automation is generalization of a finite state acceptor to n-dimensions. With each bug B, we associate the language L(B) which is the set of top rows of the n-dimensional rectangular arrays accepted by B. One-dimensional bugs define trivially the regular sets. Twodimensional bugs define precisely the context-sensitive languages, while bugs of dimension 3 or greater define all...
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