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

DOI:
https://doi.org/10.1090/S0002-9947-1958-0097285-0

MathSciNet review:
0097285

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References | Similar Articles | Additional Information

**[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. 598-599.**[E-Z]**S. Eilenberg and J. A. Zilber,*Semi-simplicial complexes and singular homology*. Ann. of Math. 51 (1950) pp. 499-513. MR**0035434 (11:734e)****[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*, Journal of the Franklin Institute vol. 257 (1954) pp. 161-190. MR**0062648 (15:1009c)****[J]**G. T. Jacobi, unpublished paper.**[K]**M. Karnaugh,*The map method for synthesis of combinational logic circuits*, Trans.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. 593-598. MR**0069032 (16:979d)****[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]**W. S. McCulloch and W. Pitts,*A logical calculus of the ideas immanent in nervous activity*. Bulletin of Mathematical Biophysics vol. 5 (1943) pp. 115-134. 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. 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]**R. L. Nelson,*Simplest normal truth functions*, J. Symbolic Logic vol. 20 (1955) pp. 105-108. MR**0072073 (17:224g)****[N,R]**R. Z. Norman, unpublished paper.**[QO]**W. V. Quine,*Methods of logic*, New York, 1950.**[Q]**-,*The problem of simplifying truth functions*, Amer.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. 521-531. MR**0051191 (14:440e)****[Q1]**-,*A way to simplify truth functions*, Amer. Math. Monthly vol. 62 (1955) pp. 627-631. 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 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**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]**C. E. Shannon,*The synthesis of two-terminal switching circuits*, Bell System Technical Journal vol. 28 (1949) pp. 59-98. 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. 127-133.

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DOI:
https://doi.org/10.1090/S0002-9947-1958-0097285-0

Article copyright:
© Copyright 1958
American Mathematical Society