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Abstract?Autonomous sequential networks are represented by transformation graphs, i.e., finite directed graphs, each vertex of which has outdegree one. A network that can be realized by a set of simpler, parallel networks corresponds to a transformation graph representable as a Cartesian product of simpler graphs. An algorithm for obtaining the various decompositions of a given transformation graph into irreducible factors is presented. The particular decomposition into a minimum number of factors is directly reached by the method. Decompositions into a greater number of factors are also obtained so that a balance may be struck between number and complexity of factors.
Index Terms:
Index terms?Automata decompositions, autonomous sequential networks, network decomposition algorithm, parallel decomposition lgorithm, transformation graph, unary algebra.
Citation:
C.M. Ablow, M. Yoeli, J. Turner, "Irreducible Decompositions of Transformation Graphs by Assignment Techniques," IEEE Transactions on Computers, vol. 17, no. 4, pp. 325-329, April 1968, doi:10.1109/TC.1968.229384
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