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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...
Some new techniques for finding minimal set of tests which detect faults in combinational logic networks are described. A systematic procedure which can be programmed on a digital computer is given. Moreover, a new approach to the design of fault detection experiments for sequential machines which takes into account the actual construction of the sequential network is described.
The automata roots of path sensitizing fault diagnosis are discussed. It is demonstrated that the path sensitizing diagnosis method is equivalent to a Moore type "machine identification" experiment for a machine class which contains good and faulty copies of a transmission path submachine of a complete machine. The maximum length of a complete set of path sensitizing tests for a machine...
This paper continues investigations pertaining to recursive bounds on computing resources (such as time or memory) and the amount by which these bounds must be increased if new computations are to occur within the new bound. The paper proves that no recursive operator can increase every recursive bound enough to reach new computations. In other words, given any general recursive operator F[ ], there...
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...
This paper develops techniques for establishing a lower bound on the number of arithmetic operations necessary for sets of simple expressions. The techniques are applied to matrix multiplication. A modification of Strassen's algorithm is developed for multiplying n × p matrices by p × q matrices. The techniques are used to prove that this algorithm minimizes the number of multiplications for a few...
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