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 - https://doi.org/10.1007/978-3-319-34171-2_27
DO - https://doi.org/10.1007/978-3-319-34171-2_27
M3 - منشور من مؤتمر
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.
T2 - 11th International Computer Science Symposium in Russia, CSR 2016
Y2 - 9 June 2016 through 13 June 2016
ER -