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Some applications of the theory of semigroups to automata

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Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 79))

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References

  1. Arbib, M.A. (ed.): Algebraic theory of machines, languages, and semigroups. New York, 1968.

    Google Scholar 

  2. Brauer, W.: Zu den Grundlagen einer Theorie topologischer sequentieller Systeme und Automaten. GMD, Bericht 31, Bonn, 1970.

    Google Scholar 

  3. Brzozowski, J.A., K. Culik II, and A. Gabrielian:Classification of non-counting, events. J.Comp.Syst.Sci. 5 (1971), 41–53.

    Google Scholar 

  4. Brzozowski, J.A.: Run languages. Seminarbericht 87, Inst. f. Rechner-u. Programmstrukturen, GMD, 1975.

    Google Scholar 

  5. Brzozowski, J.A.: On aperiodic I-monoids. Res. report CS-7S-28, Univ. of Waterloo.

    Google Scholar 

  6. Brzozowski, J.A.: Hierarchies of aperiodic languages. RAIRO, Inf. théor. 10 (1976), 33–49.

    Google Scholar 

  7. Brzozowski, J.A., and R. Knast: The dot depth hierarchy of star free languages is infinite. Res. report CS-76-23, Univ. of Waterloo.

    Google Scholar 

  8. Deussen, P.: Krohn-Rhodes-decomposition revised universally. Fak. f. Informatik, Univ. Karlsruhe, Bericht 9, 1975.

    Google Scholar 

  9. Deussen, P.: Halbgruppen und Automaten. Berlin, 1971.

    Google Scholar 

  10. Dilger, E.: On permutation-reset automata. Inform. and Contr. 30 (1976), 86–95.

    Google Scholar 

  11. Dilger, E.: Zur Strukturtheorie abstrakter Automaten. Diss. Tübingen, 1977.

    Google Scholar 

  12. Dubreil, P.: Endomorphismes. Sém. Dubreil-Pisot (algèbre et théor. des nombres) 18 (1964/65), No.23.

    Google Scholar 

  13. Eichner, L.: Die Obergangshalbgruppen linear realisierbarer endlicher Automaten. To appear.

    Google Scholar 

  14. Eilenberg, S.: Automata, languages, and machines, A,B. New York, 1974, 1976.

    Google Scholar 

  15. Gécseg, F., and I. Peák: Algebraic theory of automata. Budapest, 1972.

    Google Scholar 

  16. Hotzel, E.: Der Kaskadenzerlegungssatz für Halbautomaten. In: GI, 1. Fachtagung über Automatentheorie und formale Sprachen, Bonn, 1973 (K.-H. Böhling and K. Indermark, eds.), Berlin, 1973 (= Lect. Notes in Comp. Sci. 2), 54–63.

    Google Scholar 

  17. Johansen, P.: An algebraic normal form for regular events. Lyngby, 1972.

    Google Scholar 

  18. Jürgensen, H.: Einige Eigenschaften der Monoide von Akzeptoren und Ereignissen. EIK 11 (1975), S4S–SS6.

    Google Scholar 

  19. Jürgensen, H.: Syntaktische Halbgruppen. Proc. 1st workshop-meeting on categorical and algebraic methods in computer science and system theory, 1976. Bericht 37, Abt. Informatik, Univ. Dortmund, 1976, 37–43.

    Google Scholar 

  20. Jürgensen, H.: Inf-Halbverbände als syntaktische Halbgruppen. To appear in Acta Math. Acad. Sci. Hung.

    Google Scholar 

  21. Kleene, S.C.: Introduction to metamathematics. Amsterdam, 1952.

    Google Scholar 

  22. Krohn, K., and J.L. Rhodes: Algebraic theory of machines, I. Prime decomposition theorem for finite semigroups and machines. Trans.AMS 116 (1965), 450–464.

    Google Scholar 

  23. Lallement, G.: The rôle of regular and inverse semigroups in the theory of finite state machines and languages. Proc. sympos. on inverse semigroups, De Kalb, 1973, 44–63.

    Google Scholar 

  24. Lallement, G.: On the prime decomposition theorem for finite monoids. Math. Syst. Theor. 3 (1969), 110–118.

    Google Scholar 

  25. Lallement, G., and E. Milito: Recognizable languages and finite semilattices of groups. Semigroup Forum 11 (1975), 181–184.

    Google Scholar 

  26. Mapкoв, A.A.: Hepeкyppeнтoe кoдиpoвaниe. Пpoблeмы кибepкeтики 8 (1962), 168–186.

    Google Scholar 

  27. Maxson, C.J., and M. Zeller: Elementary Γ-languages and finite semilattices of groups. Semigroup Forum 13 (1976/77), 385–386.

    Google Scholar 

  28. McNaughton, R., and S.Papert: Counter-free automata. Cambr., Mass., 1971.

    Google Scholar 

  29. Novotný, M.: Einführung in die algebraische Linguistik. Rhein.-Westf. Inst. f. Instrum. Math., Bonn, IIM-Skript 40/67, 1967.

    Google Scholar 

  30. Paz, A.: Introduction to probabilistic automata. New York, 1971.

    Google Scholar 

  31. Perrin, D.: Codes bipréfixes et groupes de permutations. Thèse, Paris, 1975.

    Google Scholar 

  32. Perrot, J.-F.: Monoides syntactiques des langages algébriques. Acta Inform. 7 (1977), 399–413.

    Google Scholar 

  33. Perrot, J.-F., and J. Sakarovitsch: A theory of syntactic monoids for context-free languages. Proc. IFIP, Toronto,1977.

    Google Scholar 

  34. Perrot, J.-F.: Une théorie algébrique des automats finis monogénes. Sympos. Math. 15, 201–244.

    Google Scholar 

  35. Perrot, J.-F.: Contribution à l'étude des monoides syntactiques et de certains groupes associés aux automates finis. Thèse, Paris, 1972.

    Google Scholar 

  36. Perrot, J.-F.: Groupes de permutations associés aux codes préfixes finis. In: Permutations, Paris, 1972 (A. Lentin, ed.), Paris, 1974, 19–35.

    Google Scholar 

  37. Perrot, J.-F.: Informatique et algébre — la théorie des codes à longueur variable. In: Theoretical computer science, 3rd GI conference,Darmstadt, 1977 (H. Tzschach, H. Waldschmidt, H.K.-G. Walter, eds.), Berlin, 1977, 27–44.

    Google Scholar 

  38. Reusch, B.: Lineare Automaten. Mannheim, 1969.

    Google Scholar 

  39. Sakarovitch, J.: Monoides syntactiques et langages algébriques. Thèse 3éme cycle, Paris, 1976.

    Google Scholar 

  40. Schein, B.M.: Stationary subsets, stabilizers, and transitive representations of semigroups. Dissertationes Math. (Rozprawy Mat.) 77 (1970).

    Google Scholar 

  41. Schützenberger, M.P.: On a question concerning certain free submonoids. J. Comb. Theor. 1 (1966), 437–442.

    Google Scholar 

  42. Schützenberger, M.P.: Sur les monoides finis n'ayant que des sous-groupes triviaux. Sém. Dubreil-Pisot (alg. et théor. des nombres) 18 (1964/65), No. 10.

    Google Scholar 

  43. Schützenberger, M.P.: Sur le produit de concaténation non ambigu. Semigroup Forum 13 (1976), 47–75.

    Google Scholar 

  44. Schützenberger, M.P.: Une théorie algébrique du codage. Sém. Dubreil-Pisot (algébre et théor. des nombres) 1955/56, No. 15.

    Google Scholar 

  45. Schützenberger, M.P.: On the synchronizing properties of certain prefix codes. Inform. and control 7 (1964), 23–36.

    Google Scholar 

  46. Schwarz, St.: On the structure of the semigroup of stochastic matrices. Publ.Math.Inst.Hung. Acad. Sci. A 9,3 (1964), 297–311.

    Google Scholar 

  47. Simon, I.: Piecewise testable events. In: GI, 2nd conf. on automata theory and formal languages, Kaiserslautern, 1975 (H. Brakhage, ed.), Berlin, 1975 (=Lect. Notes in Comp. Sci. 33), 214–222.

    Google Scholar 

  48. Valkema, E.: Zur Charakterisierung formaler Sprachen durch Halbgruppen. Diss., Kiel, 1974.

    Google Scholar 

  49. Valkema, E.: Syntaktische Monoide und Hypercodes. Semigroup Forum 13 (1976/77), 119–126.

    Google Scholar 

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  1. Technische Hochschule Darmstadt, Institut für theoretische Informatik, 6100, Darmstadt

    H. Jürgensen

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  1. H. Jürgensen
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P. Kramer A. Rieckers

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© 1978 Springer-Verlag

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Jürgensen, H. (1978). Some applications of the theory of semigroups to automata. In: Kramer, P., Rieckers, A. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08848-2_16

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  • DOI: https://doi.org/10.1007/3-540-08848-2_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08848-6

  • Online ISBN: 978-3-540-35813-8

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