TY - GEN

T1 - On expressive power of regular expressions over infinite orders

AU - Rabinovich, Alexander

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - 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 secondorder logic. Hence, the weak monadic logic and regular expressions are expressively equivalent over finite words. We generalize this to words over arbitrary linear orders.

AB - 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 secondorder logic. Hence, the weak monadic logic and regular expressions are expressively equivalent over finite words. We generalize this to words over arbitrary linear orders.

UR - http://www.scopus.com/inward/record.url?scp=84977492818&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-34171-2_27

DO - 10.1007/978-3-319-34171-2_27

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AN - SCOPUS:84977492818

SN - 9783319341705

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 382

EP - 393

BT - Computer Science - Theory and Applications - 11th International Computer Science Symposium in Russia, CSR 2016, Proceedings

A2 - Woeginger, Gerhard J.

A2 - Kulikov, Alexander S.

PB - Springer Verlag

T2 - 11th International Computer Science Symposium in Russia, CSR 2016

Y2 - 9 June 2016 through 13 June 2016

ER -