Roth, J. Paul Algebraic topological methods for the synthesis of switching systems. I. (English) Zbl 0083.13103 Trans. Am. Math. Soc. 88, 301-326 (1958). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 Documents Keywords:numerical analysis PDF BibTeX XML Cite \textit{J. P. Roth}, Trans. Am. Math. Soc. 88, 301--326 (1958; Zbl 0083.13103) Full Text: DOI References: [1] Synthesis of Electronic Computing and Control Circuits, Harvard University Press, Cambridge, Mass., 1951. By the Staff of the Computation Laboratory. [2] S. H. Caldwell, Discussion of Karnaugh’s paper, AIEE vol. 72 Part I (1953) pp. 598-599. [3] Samuel Eilenberg and J. A. Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. (2) 51 (1950), 499 – 513. · Zbl 0036.12601 [4] H. H. Goldstine, On the relation between machine developments and numerical analysis, paper presented at Bonn Colloquium, October 20-22, 1955. · Zbl 0078.30506 [5] D. A. Huffman, The synthesis of sequential switching circuits. I, II, J. Franklin Inst. 257 (1954), 161 – 190, 275 – 303. [6] G. T. Jacobi, unpublished paper. [7] M. Karnaugh, The map method for synthesis of combinational logic circuits, Commun. and Electronics 1953 (1953), 593 – 599. [8] W. Keister, A. E. Ritchie and S. H. Washburn, The design of switching circuits, Chapter 5, New York, D. Van Nostrand Co., 1951. · Zbl 0053.40303 [9] Warren S. McCulloch and Walter Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5 (1943), 115 – 133. · Zbl 0063.03860 [10] G. A. Montgomerie, Sketch for an algebra of relay and contactor circuits, J. IEE vol. 95, Part III (1948) pp. 303-312. [11] E. F. Moore, A table of four-relay two-terminal contact networks–case 22108, Bell Telephone Laboratory Technical Memo. MM-52-180-45. [12] 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. [13] Raymond J. Nelson, Review of Quine’s paper, J. Symbolic Logic vol. 18 (1953) pp. 280-283. [14] Raymond J. Nelson, Simplest normal truth functions, J. Symb. Logic 20 (1955), 105 – 108. · Zbl 0066.25602 [15] R. Z. Norman, unpublished paper. [16] W. V. Quine, Methods of logic, New York, 1950. · Zbl 0038.14811 [17] W. V. Quine, The problem of simplifying truth functions, Amer. Math. Monthly 59 (1952), 521 – 531. · Zbl 0048.24503 [18] W. V. Quine, A way to simplify truth functions, Amer. Math. Monthly 62 (1955), 627 – 631. · Zbl 0068.24209 [19] J. P. Roth, A combinatorial topological method for the synthesis of switching systems in \( n\) variables, Bull. Amer. Math. Soc. Abstract 62-2-281. [20] -, An algorithm for the problem of Quine, Bull. Amer. Math. Abstract 62-3-367. [21] -, A function-space formulation of the switching circuit synthesis problem, Bull. Amer. Math. Soc. Abstract 62-3-392. [22] -, Algebraic topological methods for the synthesis of switching systems in \( n\) variables, The Institute for Advanced Study, Princeton, ECP 56-02, April 1956. [23] C. E. Shannon, A symbolic analysis of relay and switching circuits, Trans. AIEE vol. 57 (1938) pp. 713-723. [24] Claude E. Shannon, The synthesis of two-terminal switching circuits, Bell System Tech. J. 28 (1949), 59 – 98. [25] 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.