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
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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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