Summary
In this paper are considered incompletely specified sequential machines for which the only unspecified entries are those which occur because of a restriction on the input states which can directly follow each possible input state.
For these machines the minimum number of states is equal to the chromatic number of the graph of all pairs of incompatible states. A new method for determining a minimum-class partition of the set of states which is formed from compatible classes is given.
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References
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I. Tomescu, Sur un problème de partition avec un nombre minimal de classes,C. R. Acad. Sci. Paris 265 (1967), 645–648.
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Tomescu, I. A method for minimizing the number of states for a restricted class of incompletely specified sequential machines. Math. Systems Theory 6, 1–2 (1972). https://doi.org/10.1007/BF01706068
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DOI: https://doi.org/10.1007/BF01706068