Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Algebraic topological methods for the synthesis of switching systems. I

Author: J. Paul Roth
Journal: Trans. Amer. Math. Soc. 88 (1958), 301-326
MSC: Primary 93.00; Secondary 06.00
MathSciNet review: 0097285
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [A] Synthesis of Electronic Computing and Control Circuits, Harvard University Press, Cambridge, Mass., 1951. By the Staff of the Computation Laboratory. MR 0044916
  • [C] S. H. Caldwell, Discussion of Karnaugh's paper, AIEE vol. 72 Part I (1953) pp. 598-599.
  • [E-Z] Samuel Eilenberg and J. A. Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. (2) 51 (1950), 499–513. MR 35434,
  • [G] H. H. Goldstine, On the relation between machine developments and numerical analysis, paper presented at Bonn Colloquium, October 20-22, 1955.
  • [H] D. A. Huffman, The synthesis of sequential switching circuits. I, II, J. Franklin Inst. 257 (1954), 161–190, 275–303. MR 62648,
  • [J] G. T. Jacobi, unpublished paper.
  • [K] M. Karnaugh, The map method for synthesis of combinational logic circuits, Commun. and Electronics 1953 (1953), 593–599. MR 0069032
  • [K-R-W] W. Keister, A. E. Ritchie and S. H. Washburn, The design of switching circuits, Chapter 5, New York, D. Van Nostrand Co., 1951.
  • [M-P] Warren S. McCulloch and Walter Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5 (1943), 115–133. MR 0010388,
  • [M] G. A. Montgomerie, Sketch for an algebra of relay and contactor circuits, J. IEE vol. 95, Part III (1948) pp. 303-312.
  • [M,E] E. F. Moore, A table of four-relay two-terminal contact networks--case 22108, Bell Telephone Laboratory Technical Memo. MM-52-180-45.
  • [N-H ] A. Nakasima and M. Hanzawa, The theory of the equivalent transformation of simple partial paths in relay circuits. J. Inst. Elec. Comm. Engrs. Japan, 1936-1938.
  • [N] Raymond J. Nelson, Review of Quine's paper, J. Symbolic Logic vol. 18 (1953) pp. 280-283.
  • [N1] Raymond J. Nelson, Simplest normal truth functions, J. Symbolic Logic 20 (1955), 105–108. MR 72073,
  • [N,R] R. Z. Norman, unpublished paper.
  • [QO] W. V. Quine, Methods of logic, New York, 1950.
  • [Q] W. V. Quine, The problem of simplifying truth functions, Amer. Math. Monthly 59 (1952), 521–531. MR 51191,
  • [Q1] W. V. Quine, A way to simplify truth functions, Amer. Math. Monthly 62 (1955), 627–631. MR 75886,
  • [R1] J. P. Roth, A combinatorial topological method for the synthesis of switching systems in $ n$ variables, Bull. Amer. Math. Soc. Abstract 62-2-281.
  • [R2] -, An algorithm for the problem of Quine, Bull. Amer. Math. Abstract 62-3-367.
  • [R3] -, A function-space formulation of the switching circuit synthesis problem, Bull. Amer. Math. Soc. Abstract 62-3-392.
  • [R4] -, Algebraic topological methods for the synthesis of switching systems in $ n$ variables, The Institute for Advanced Study, Princeton, ECP 56-02, April 1956.
  • [S] C. E. Shannon, A symbolic analysis of relay and switching circuits, Trans. AIEE vol. 57 (1938) pp. 713-723.
  • [S1] Claude E. Shannon, The synthesis of two-terminal switching circuits, Bell System Tech. J. 28 (1949), 59–98. MR 29860,
  • [V] E. W. Veitch, A chart method for simplifying truth functions, Proceedings of the Association for Computing Machinery, Richard Rimbach Associates, Pittsburgh, 1952, pp. 127-133.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 93.00, 06.00

Retrieve articles in all journals with MSC: 93.00, 06.00

Additional Information

Article copyright: © Copyright 1958 American Mathematical Society