Abstract
Two fundamental results of classical automata theory are the Kleene theorem and the Büchi-Elgot-Trakhtenbrot theorem. Kleene’s theorem states that a language of finite words is definable by a regular expression iff it is accepted by a finite state automaton. Büchi-Elgot-Trakhtenbrot’s theorem states that a language of finite words is accepted by a finite-state automaton iff it is definable in the weak monadic second-order logic. Hence, the weak monadic logic and regular expressions are expressively equivalent over finite words. We generalize this to words over arbitrary linear orders.
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Notes
- 1.
In algebraic framework to formal languages the concatenation of \(w_1\) and \(w_2\) is called “the product” and is denoted by \(w_1\cdot w_2\).
- 2.
Hintikka formulas made their first appearance in [6], in the framework of first-order logic.
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Rabinovich, A. (2016). On Expressive Power of Regular Expressions over Infinite Orders. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_27
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