Advertisement

A concatenation game and the dot-depth hierarchy

  • Wolfgang Thomas
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 270)

Abstract

We introduce a variant of the Ehrenfeucht Fraïssé game which is appropriate for an analysis of the expressive power of star-free regular expressions. As an application we present a simple proof showing that the dot-depth hierarchy of star-free languages is strict.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrington DA, Thérien D (1986) Finite monoids and the fine structure of NC, draft.Google Scholar
  2. Brzozowski JA, Knast R (1978) The dot-depth hierarchy of star-free languages is infinite, J Comput System Sci 16, 37–55.Google Scholar
  3. Cohen RS, Brzozowski JA (1971) Dot-Depth of Star-free events, J Comput System Sci 5, 1–16.Google Scholar
  4. McNaughton R, Papert S (1971) Counter-Free Automata, MIT-Press.Google Scholar
  5. Pin JE (1984) Hierarchies de concatenation, RAIRO Inform Théor 18, 23–46.Google Scholar
  6. Perrin D, Pin JE (1986) First-order logic and star-free sets, J Comput System Sci 32, 393–406.Google Scholar
  7. Sistla AP, Clarke EM, Francez N, Meyer AR (1984) Can message buffers be axiomatized in linear temporal logic? Inform Contr 63, 88–112.Google Scholar
  8. Straubing H (1981) A generalization of the Schützenberger product of finite monoids, Theor Comput Sci 13, 107–110.Google Scholar
  9. Thomas W (1982) Classifying regular events in symbolic logic, J Comput System Sci 25, 360–376.Google Scholar
  10. Thomas W (1984) An application of the Ehrenfeucht Fraïssé game in formal language theory, Bull Soc Math France, Mem 16, 11–21.Google Scholar
  11. Thomas W, Lippert D (1986) Relativized star-free expressions, first-order logic, and a concatenation game, Schriften zur angew. Math. u. Informatik Nr. 121, RWTH Aachen.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Wolfgang Thomas
    • 1
  1. 1.Lenrstuhl für Informatik IIAachen

Personalised recommendations