Skip to main content

Concatenation product: a survey

  • Problems Related To The Theory Of Automata
  • Conference paper
  • First Online:
Formal Properties of Finite Automata and Applications (LITP 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 386))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Barrington. Bounded-width polynomial-size branching programs recognize only those languages in NC 1, in Proc. 18th A.C.M. S.T.O.C., 1986, pp. 1–5.

    Google Scholar 

  2. D. Barrington, H. Straubing and D. Thérien. Survey article, draft.

    Google Scholar 

  3. D. Barrington and D. Thérien. Finite monoids and the fine structure of NC 1, in Proc. 19th A.C.M. S.T.O.C., 1987, pp. 101–109.

    Google Scholar 

  4. D. Barrington and D. Thérien. Non-uniform automata over groups, in Proc. 14th I.C.A.L.P., 1987, pp. 163–173.

    Google Scholar 

  5. J. Brzozowski. Hierarchies of aperiodic languages, in R.A.I.R.O. Informatique Théorique 10 (1976), pp. 35–49.

    Google Scholar 

  6. J. Brzozowski and R. Cohen. Dot-depth of star-free events, in J. Comput. System Sci. 5 (1971), pp. 1–16.

    Google Scholar 

  7. J. Brzozowski and R. Knast. The dot-depth hierarchy of star-free events is infinite, in J. Comput. System Sci. 16 (1978), pp. 37–55.

    Google Scholar 

  8. J.R. Büchi. Weak second-order arithmetic and finite automata, in Z. Math. Logik Grundlagen Math. 6 (1960), pp. 66–92.

    Google Scholar 

  9. J.R. Büchi. On a decision method in restricted second-order arithmetic, in Logic Methodology and Philosophy of Science (Proc. 1960 Internat. Congress), pp. 1–11, Stanford Univ. Press (Stanford), 1960.

    Google Scholar 

  10. S. Cook. A taxonomy of problems with fast parallel algorithms, in Infor. and Control 64 (1985), pp. 2–22.

    Article  Google Scholar 

  11. S. Eilenberg. Automata, Languages and Machines, vol. B, Academic Press (New-York), 1976.

    Google Scholar 

  12. M. Furst, J. Saxe and M. Sipser. Parity, circuits and the polynomial time hierarchy, in Math. Systems Theory 18 (1984), pp. 13–27.

    Article  Google Scholar 

  13. S. Kleene. Representation of events in nerve nets and finite automata, in Automata Studies (Shannon and McCarthy eds.), Princeton University Press, (Princeton) 1954, pp. 3–51.

    Google Scholar 

  14. R. Knast. A semigroup characterization of semigroups of dot-depth one, in R.A.I.R.O. Informatique Théorique 17 (1983), pp. 321–330.

    Google Scholar 

  15. G. Lallement. Semigroups and Combinatorial Applications, Wiley (New-York), 1979.

    Google Scholar 

  16. R. McNaughton and S. Papert. Counter-free automata, M.I.T. Press (Cambridge, Mass.), 1971.

    Google Scholar 

  17. P. Péladeau. NUDFA's over finite monoids, a presentation, preprint.

    Google Scholar 

  18. D. Perrin. Finite automata, draft.

    Google Scholar 

  19. D. Perrin and J.-E. Pin. First-order logic and star-free events, in J. Comput. System Sci. 32 (1986), pp. 393–406.

    Article  Google Scholar 

  20. J.-E. Pin. Concatenation hierarchies and decidability results, in Combinatorics on Words, Progress and Perspectives (L. Cummings ed.), Academic Press, 1983, pp. 195–228.

    Google Scholar 

  21. J.-E. Pin. Variétés de langages formels, Masson (Paris), 1984, and Varieties of formal languages, North Oxford Academic (London), 1986 and Plenum (New-York), 1986.

    Google Scholar 

  22. J.-E. Pin and H. Straubing. Monoids of upper-triangular matrices, in Colloquia Mathematica Societatis Janos Bolyai, Szeged, 1981, pp. 259–271.

    Google Scholar 

  23. J.-E. Pin, H. Straubing and D. Thérien. Locally trivial categories and unambiguous concatenation, to appear.

    Google Scholar 

  24. Ch. Reutenauer. Sur les variétés de languages et de monoïdes, in Theoretical Computer Science 4th GI Conference, Lecture Notes in Computer Science 67, Springer (1979), pp. 260–265.

    Google Scholar 

  25. M.-P. Schützenberger. On finite monoids having only trivial subgroups, in Information and Control 8 (1965), pp. 190–194.

    Article  Google Scholar 

  26. I. Simon. Hierarchies of events of dot-depth one, Ph.D. Thesis, University of Waterloo, 1972.

    Google Scholar 

  27. I. Simon. Piecewise testable events, in Proc. 2nd G.I. Conf., Lecture Notes in Computer Science 33, Springer (1975), pp.214–222.

    Google Scholar 

  28. M. Sipser. Borel sets and circuit complexity, in Proc. 15th A.C.M. S.T.O.C., 1983, pp. 61–69.

    Google Scholar 

  29. H. Straubing. Families of recognizable sets corresponding to certain varieties of finite monoids, in Journal of Pure and Applied Algebra 15 (1979), pp. 305–318.

    Google Scholar 

  30. H. Straubing. Aperiodic homomorphisms and the concatenation product of recognizable sets, in Journal of Pure and Applied Algebra 15 (1979), pp. 319–327.

    Article  Google Scholar 

  31. H. Straubing. A generalization of the Schützenberger product of finite monoids, in Theoretical Computer Science 13 (1981), pp. 137–150.

    Google Scholar 

  32. H. Straubing. Varieties of the form V*D, in Journal of Pure and Applied Algebra 36 (1985), pp. 53–94.

    Google Scholar 

  33. H. Straubing. Semigroups and languages of dot-depth two, in Proc. 13th I.C.A.L.P., Lecture Notes in Computer Science 226, Springer, Berlin (1986), pp. 416–423.

    Google Scholar 

  34. H. Straubing. Semigroups and languages of dot-depth two, in Theoretical Computer Science 58 (1988), pp. 361–378.

    Google Scholar 

  35. H. Straubing and P. Weil. to appear.

    Google Scholar 

  36. D. Thérien. Subword counting and nilpotent groups, in Combinatorics on Words, Progress and Perspectives (L. Cummings ed.), Academic Press, 1983, pp. 297–305.

    Google Scholar 

  37. D. Thérien. Catégories et languages de dot-depth un, preprint, Technical Report SOCS-85-22, McGill University, Montréal, 1985.

    Google Scholar 

  38. W. Thomas. Classifying regular events in symbolic logic, in J. Comput. System Sci. 25 (1982), pp. 360–376.

    Article  Google Scholar 

  39. W. Thomas. An application of the Ehrenfeucht-Fraïssé game in formal language theory, in Bulletin Soc. Math. France 16 (1984), pp. 11–21.

    Google Scholar 

  40. B. Tilson. Chapters XI and XII in

    Google Scholar 

  41. P. Weil. Products of languages with counter, to appear in Theoretical Computer Science.

    Google Scholar 

  42. P. Weil. Inverse monoids of dot-depth two, to appear in Theoretical Computer Science.

    Google Scholar 

  43. P. Weil. Inverse monoids and the dot-depth hierarchy, Ph.D. Thesis, University of Nebraska, Lincoln, 1988.

    Google Scholar 

  44. P. Weil. An extension of the Schützenberger product, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. E. Pin

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Weil, P. (1989). Concatenation product: a survey. In: Pin, J.E. (eds) Formal Properties of Finite Automata and Applications. LITP 1988. Lecture Notes in Computer Science, vol 386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013116

Download citation

  • DOI: https://doi.org/10.1007/BFb0013116

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51631-6

  • Online ISBN: 978-3-540-46721-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics