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.
Regular Language Winning Strategy Disjunctive Normal Form Boolean Combination Formal Language Theory
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