Advertisement

Relativized star-free expressions, first-order logic, and a concatenation game

  • D. Lippert
  • W. Thomas
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1320)

Abstract

Star-free expressions with an additional constant for some fixed language are considered. In contrast to the well-known equivalence between star-free expressions and first-order logic (over finite orderings), it is shown here that in the relativized version star-free expressions are strictly weaker than the corresponding first-order formulas. For the proof, a concatenation game is introduced which captures the expressive power of the relativized star-free expressions.

Keywords

Regular Language Winning Strategy Disjunctive Normal Form Boolean Combination Formal Language Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BrzK 78]
    J.A. Brzozowski, R. Knast, The dot depth hierarchy of star-free languages is infinite, J.Comput.System Sci. 16 (1978), 37–55.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [CBrz 71]
    R.S. Cohen, J.A. Brzozowski, Dot depth of star-free events, J.Comput.System Sci. 5(1971), 1–16.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [Lip 86]
    D. Lippert, Ausdrucksstärke der Intervall-Temporallogik: Eine Untersuchung mit spieltheoretischen Methoden. Diplomarbeit, RWTH Aachen 1986.Google Scholar
  4. [MoMa 84]
    B. Moszkowski, Z. Manna, Reasoning in interval temporal logic, In: Logic of Programs (E. Clarke, D. Kozen, Eds.), Springer Lecture Notes in Computer Science 164 (1984), 371–384.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [Mo 83]
    B.C. Moszkowski, Reasoning about digital circuits, PhD Dissertation, Stanford University 1983.Google Scholar
  6. [McNP 71]
    R. McNaughton, S. Papert, Counter-Free Automata, MIT Press, Cambridge, Mass. 1971.zbMATHGoogle Scholar
  7. [P 84]
    J.E. Pin, Variétés de langages formels, Masson, Paris 1984.zbMATHGoogle Scholar
  8. [PP 86]
    D. Perrin, J.E. Pin, First-order logic and star-free sets, J.Comput. System Sci. 32 (1986), 393–406.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [Sch 65]
    M.P. Schützenberger, On monoids having only trivial subgroups, Inf. Contr. 8 (1965), 190–194.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [Str 81]
    H. Straubing, A generalization of the Schützenberger product, Theor. Comput. Sci. 25 (1982), 107–110.Google Scholar
  11. [Th 82]
    W. Thomas, Classifying regular events in symbolic logic, J. Comput. System Sci. 25 (1982), 360–376.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [Th 84]
    W. Thomas, An application of the Ehrenfeucht-Fraissé game in formal language theory, Mem. Soc. Math. France 16 (1984), 11–21.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • D. Lippert
  • W. Thomas

There are no affiliations available

Personalised recommendations