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Previous papers have shown that for any given n-input synchronous sequential machine there exists a circuit realization in which the circuit consists of a finite number of identical copies of one module and in which the modules are interconnected in a uniform manner. This paper shows that additionally the signal fan-in to every module and the signal fan-out from every module and from the input can...
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...
A context-sensitive grammar G is said to be CS(k) iff a particular kind of table-driven parser, Jk(G), exists. Corresponding to each Jk(G), we define a class of parsers Jk(G). Jk(G) is itself a Jk(G). The main results are: 1. Any processor Jk(G) for a CS(k) grammar G accepts exactly the sentences of G. 2. The set of languages generable by CS(k) grammars is exactly the set of languages accepted by...
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