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This paper presents systematic synthesis procedures for Lupanov decoding networks. Decoding networks find applications in computer memories for the selection of a particular item of data addressed by a binary code, in counter circuits, in character-by-character code conversion circuits, in the synthesis of switching functions and also in the theoretical derivations of complexity bounds for arbitrary...
This paper describes an algorithm for minimizing the storage required of a Read Only Memory that is going to be used as the control element for a digital machine. The technique is based upon the fact that not all sub-commands are required in all words so that bits of the memory may be time shared between subcommands. The algorithm provides a means for determining what sub-commands should share a common...
Not all switching functions are realizable by a single cascade of 2- input, 1-output switching elements, even if repeated inputs are allowed. However, arrays of such cascades feeding a single collector cascade of AND or OR cells can be used to synthesize any function. This paper is concerned with optimal array realizations of this form. A procedure is given which allows one to generate rather efficiently...
The need for a measure different from the number of states in analyzing stochastic sequential machines is pointed out. Using the decomposition previously demonstrated in association with actual physical realization of stochastic sequential machines4, a particular measure of complexity C(M) for a given machine M is introduced. The computational aspect of C(M) is discussed and an example exhibiting...
This paper describes a new approach to the design of combinational logic using large-scale-integrated (LSI) circuit technology. A simple "prototype" logic function of n binary variables is imbedded within an array of at most (n+1) rows and columns. The cells of this array contain 2-input exclusive-OR gates, and its rows are fed by the input variables and logical "1". Its column...
Many machines can be decomposed into a linear cascade of identical sequential machines. We consider the problem of implementing fault detection experiments for such machines. Cascade equivalence and information lossless properties of cascade machines are studied. Sufficient conditions for efficient testing of these machines are derived. Procedures are presented for testing cascades of arbitrary length...
Program schemes are represented as directed, labeled graphs over some vocabulary. Such schemes are transformed to block form by obtaining a regular expression from the graph and translating it to block form by using a recursive correspondence. A necessary and sufficient condition is given for the transformed graph to be deterministic.
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