Lattice-Ordered Semigroups, Graphs, and Automata
Michael Yoeli · Journal of the Society for Industrial and Applied Mathematics · 1965
Previous article Next article Lattice-Ordered Semigroups, Graphs, and AutomataMichael YoeliMichael Yoelihttps://doi.org/10.1137/0113023PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, revised edition, American Mathematical Society, New York, N. Y., 1948xiii+283 MR0029876 0033.10103 Google Scholar[2] Janusz A. Brzozowski, A survey of regular expressions and their applications, IRE Trans., EC-11 (1962), 324–335 MR0146026 0129.26202 Google Scholar[3] J. A. Brzozowski, Properties of regular expressions and state diagrams, Tech. Rep., 15, Department of Electrical Engineering, Digital Systems Laboratory, Princeton University, 1962 Google Scholar[4] J. A. Brzozowski and , J. McCluskey, Jr., Signal flow graph techniques for sequential circuit state diagrams, IEEE Trans. Electronic Computers, EC-12 (1963), 67–76 0119.12903 CrossrefGoogle Scholar[5] Noam Chomsky and , George A. Miller, Finite state languages, Information and Control, 1 (1958), 91–112 10.1016/S0019-9958(58)90082-2 MR0108417 0158.25302 CrossrefGoogle Scholar[6] M. L. Dubreil-Jacotin, , L. Lesieur and , R. Croisot, Leçons sur la théorie des treillis des structures algébriques ordonnées et des treillis géométriques, Gauthier-Villars, Paris, 1953viii+385 MR0057838 0051.26005 Google Scholar[7] C. C. Elgot and , J. E. Mezei, Two-sided finite-state transductions, Research Paper, RC-1017, IBM Research Center, Yorktown Heights, New York, 1963 Google Scholar[8] C. C. Elgot and , J. D. Rutledge, Operations on finite automata, extended summary, Proc. Second Ann. Symp. on Switching Circuit Theory and Logical Design, AIEE Publication S-134, 1961, 129–132 Google Scholar[9] Seymour Ginsburg, An introduction to mathematical machine theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1962ix+147 MR0145693 0102.33804 Google Scholar[10] Seymour Ginsburg and , Edwin H. Spanier, Quotients of context-free languages, J. Assoc. Comput. Mach., 10 (1963), 487–492 MR0163808 0148.00803 CrossrefISIGoogle Scholar[11] Ju. I. Janov, On identical transformations of regular expressions, Dokl. Akad. Nauk SSSR, 147 (1962), 327–330, transl. Soviet Math. Dokl., 3, pp. 1630–1634 MR0142460 0129.26201 Google Scholar[12] S. C. Kleene, Representation of events in nerve nets and finite automataAutomata studies, Annals of mathematics studies, no. 34, Princeton University Press, Princeton, N. J., 1956, 3–41 MR0077478 CrossrefGoogle Scholar[13] Arthur E. Laemmel, Application of lattice-ordered semigroups to codes and finite-state transducers, Proc. Sympos. Math. Theory of Automata (New York, 1962), Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, N.Y., 1963, 241–256 MR0175714 0122.12801 Google Scholar[14] R. McNaughton and , H. Yamada, Regular expressions and state graphs for automata, IRE Trans. Electronic Computers, EC-9 (1960), 39–47 0156.25501 CrossrefGoogle Scholar[15] J. Myhill, Finite automata and representation of events, Fundamental Concepts in the Theory of Systems, Astia Document AD 155741, 1957 Google Scholar[16] Gene Ott and , Neil H. Feinstein, Design of sequential machines from their regular expressions, J. Assoc. Comput. Mach., 8 (1961), 585–600 MR0141549 0171.27505 CrossrefGoogle Scholar[17] M. O. Rabin and , D. Scott, Finite automata and their decision problems, IBM J. Res. Develop., 3 (1959), 114–125 MR0103795 0158.25404 CrossrefISIGoogle Scholar[18] Alfonso Shimbel, Structure in communication nets, Proceedings of the symposium on information networks, New York, April, 1954, Polytechnic Institute of Brooklyn, Brooklyn, N.Y., 1955, 199–203 MR0076719 Google Scholar[19] R. E. Stearns and , J. Hartmanis, Regularity preserving modifications of regular expressions, Information and Control, 6 (1963), 55–69 10.1016/S0019-9958(63)90110-4 MR0160694 0112.11307 CrossrefGoogle Scholar[20] M. Yoeli, The theory of switching nets, Trans. 1959 International Symp. on Circuit and Information Theory, Vol. CT-6, IRE Trans. Circuit Theory, 1959, 152–157 Google Scholar[21] Michael Yoeli, A note on a generalization of Boolean matrix theory, Amer. Math. Monthly, 68 (1961), 552–557 MR0126472 0115.02103 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 13, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:20 April 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113023Article page range:pp. 411-422ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics