It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is (Formula presented.) [respectively, (Formula presented.) ] when using complete (respectively, incomplete) deterministic finite automata. We show that the state complexity of bipolar deletion has an upper bound (Formula presented.) [respectively (Formula presented.) ] when using complete (respectively, incomplete) deterministic finite automata. In both cases we give almost matching lower bounds.
Bibliographical noteFunding Information:
An earlier version of the paper was presented at the 18th International Conference Developments in Language Theory (Ekaterinburg, Russia, August 26?29, 2014) and an extended abstract appeared in the proceedings of the conference. Han and Ko were supported by the Basic Science Research Program through NRF funded by MEST?(2012R1A1A2044562), the International Cooperation Program managed by NRF of Korea?(2014K2A1A2048512) and Yonsei University future-leading research initiative of 2014, and Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.
© 2015, Springer-Verlag Berlin Heidelberg.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Networks and Communications