On Expressive Power of Regular Expressions over Infinite Orders

  • Alexander RabinovichEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)


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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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The Blavatnik School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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