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

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.

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© 1988 Springer-Verlag

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Lippert, D., Thomas, W. (1988). Relativized star-free expressions, first-order logic, and a concatenation game. In: Jürgensen, H., Lallement, G., Weinert, H.J. (eds) Semigroups Theory and Applications. Lecture Notes in Mathematics, vol 1320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083433

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  • DOI: https://doi.org/10.1007/BFb0083433

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19347-0

  • Online ISBN: 978-3-540-39225-5

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