Algebraic topological methods for the synthesis of switching systems. I
Author:
J. Paul Roth
Journal:
Trans. Amer. Math. Soc. 88 (1958), 301326
MSC:
Primary 93.00; Secondary 06.00
MathSciNet review:
0097285
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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V. Quine, A way to simplify truth functions, Amer. Math.
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J. P. Roth, A combinatorial topological method for the synthesis of switching systems in variables, Bull. Amer. Math. Soc. Abstract 622281.
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, An algorithm for the problem of Quine, Bull. Amer. Math. Abstract 623367.
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, A functionspace formulation of the switching circuit synthesis problem, Bull. Amer. Math. Soc. Abstract 623392.
 [R4]
, Algebraic topological methods for the synthesis of switching systems in variables, The Institute for Advanced Study, Princeton, ECP 5602, April 1956.
 [S]
C. E. Shannon, A symbolic analysis of relay and switching circuits, Trans. AIEE vol. 57 (1938) pp. 713723.
 [S1]
Claude
E. Shannon, The synthesis of twoterminal switching circuits,
Bell System Tech. J. 28 (1949), 59–98. MR 0029860
(10,671c)
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E. W. Veitch, A chart method for simplifying truth functions, Proceedings of the Association for Computing Machinery, Richard Rimbach Associates, Pittsburgh, 1952, pp. 127133.
 [A]
 H. H. Aiken (editor), Synthesis of electronic computing and control circuits, Harvard University Press (1951). MR 0044916 (13:497e)
 [C]
 S. H. Caldwell, Discussion of Karnaugh's paper, AIEE vol. 72 Part I (1953) pp. 598599.
 [EZ]
 S. Eilenberg and J. A. Zilber, Semisimplicial complexes and singular homology. Ann. of Math. 51 (1950) pp. 499513. MR 0035434 (11:734e)
 [G]
 H. H. Goldstine, On the relation between machine developments and numerical analysis, paper presented at Bonn Colloquium, October 2022, 1955.
 [H]
 D. A. Huffman, The synthesis of sequential switching circuits, Journal of the Franklin Institute vol. 257 (1954) pp. 161190. MR 0062648 (15:1009c)
 [J]
 G. T. Jacobi, unpublished paper.
 [K]
 M. Karnaugh, The map method for synthesis of combinational logic circuits, Trans. AIEE vol. 72, Part I (1953) pp. 593598. MR 0069032 (16:979d)
 [KRW]
 W. Keister, A. E. Ritchie and S. H. Washburn, The design of switching circuits, Chapter 5, New York, D. Van Nostrand Co., 1951.
 [MP]
 W. S. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics vol. 5 (1943) pp. 115134. MR 0010388 (6:12a)
 [M]
 G. A. Montgomerie, Sketch for an algebra of relay and contactor circuits, J. IEE vol. 95, Part III (1948) pp. 303312.
 [M,E]
 E. F. Moore, A table of fourrelay twoterminal contact networkscase 22108, Bell Telephone Laboratory Technical Memo. MM5218045.
 [NH ]
 A. Nakasima and M. Hanzawa, The theory of the equivalent transformation of simple partial paths in relay circuits. J. Inst. Elec. Comm. Engrs. Japan, 19361938.
 [N]
 Raymond J. Nelson, Review of Quine's paper, J. Symbolic Logic vol. 18 (1953) pp. 280283.
 [N1]
 R. L. Nelson, Simplest normal truth functions, J. Symbolic Logic vol. 20 (1955) pp. 105108. MR 0072073 (17:224g)
 [N,R]
 R. Z. Norman, unpublished paper.
 [QO]
 W. V. Quine, Methods of logic, New York, 1950.
 [Q]
 , The problem of simplifying truth functions, Amer. Math. Monthly vol. 59 (1952) pp. 521531. MR 0051191 (14:440e)
 [Q1]
 , A way to simplify truth functions, Amer. Math. Monthly vol. 62 (1955) pp. 627631. MR 0075886 (17:814o)
 [R1]
 J. P. Roth, A combinatorial topological method for the synthesis of switching systems in variables, Bull. Amer. Math. Soc. Abstract 622281.
 [R2]
 , An algorithm for the problem of Quine, Bull. Amer. Math. Abstract 623367.
 [R3]
 , A functionspace formulation of the switching circuit synthesis problem, Bull. Amer. Math. Soc. Abstract 623392.
 [R4]
 , Algebraic topological methods for the synthesis of switching systems in variables, The Institute for Advanced Study, Princeton, ECP 5602, April 1956.
 [S]
 C. E. Shannon, A symbolic analysis of relay and switching circuits, Trans. AIEE vol. 57 (1938) pp. 713723.
 [S1]
 C. E. Shannon, The synthesis of twoterminal switching circuits, Bell System Technical Journal vol. 28 (1949) pp. 5998. MR 0029860 (10:671c)
 [V]
 E. W. Veitch, A chart method for simplifying truth functions, Proceedings of the Association for Computing Machinery, Richard Rimbach Associates, Pittsburgh, 1952, pp. 127133.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947195800972850
PII:
S 00029947(1958)00972850
Article copyright:
© Copyright 1958 American Mathematical Society
