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The problem of simplifying logical expressions1

Published online by Cambridge University Press:  12 March 2014

B. Dunham  and
R. Fridshal
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Extract

By quite elementary means, one can find “large” examples difficult, if not (for practical purposes) impossible, to be managed by that host of methods, after Quine, for minimizing expressions in alternational normal form. Because the workability rather than existence of an algorithm for minimizing logical formulae is generally critical, it may be pertinent to outline briefly the derivation of these “large” examples. Some more general insight may also be gained about simplification techniques.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 24 , Issue 1 , March 1959 , pp. 17 - 19
Copyright
Copyright © Association for Symbolic Logic 1959

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Footnotes

1

The material of this paper was presented by R. Fridshal in July, 1957, at the Summer Institute of Symbolic Logic, Cornell University. The authors wish to thank the referee for several helpful comments.

References

2 Quine, W. V., The problem of simplifying truth functions, The American mathematical monthly, vol. 59 (1952), pp. 521–531CrossRefGoogle Scholar, and A way to simplify truth functions, ibid., vol. 62 (1955), pp. 627–631. Familiarity with these papers is assumed. The following are among the more notable papers, exclusive of the ones listed in other footnotes, dealing with these problems:

J. P. Roth, Algebraic topological methods for the synthesis of switching circuits in variables, The Institute for Advanced Study Electronic Computer Project technical report No. 56–02 (April, 1956), and Combinatorial topological methods in the synthesis of switching circuits, to appear in the Proceedings of the International Symposium on the Theory of Switching, Harvard University (April, 1957).

Nelson, R. J., Simplest normal truth functions, this Journal, vol. 20 (1955), pp. 105–108Google Scholar, and Weak simplest normal truth functions, ibid., pp. 232–234.

Ghazala, M. J. (Gazale), Irredundant disjunctive and conjunctive forms of a Boolean function, International Business Machines journal of research and development, vol. 1 (1957), pp. 171–176.Google Scholar

B. Harris, A n algorithm for determining minimal representations of a logic function, Institute of Radio Engineers transactions on electronic computers, EC-b, no. 2 (June, 1957), pp. 103–107.

A series of papers by E. W. Samson, B. E. Mills, R. K. Mueller, R. H. Urbano and S. R. Petrick appearing as Air Force Cambridge Research Center technical reports in 1954–1956.

3 See, for example, McCluskey, E. J. Jr., Detection of group invariance or total symmetry of a boolean function, The Bell System technical journal, vol. 35 (1956), pp. 1445–1453.CrossRefGoogle Scholar

4 See, for example, McCluskey, E. J. Jr., Minimization of boolean functions, The Bell System technical journal, vol. 35 (1956), pp. 1417–1444.CrossRefGoogle Scholar