State complexity of deletion and bipolar deletion

Yo Sub Han; Sang Ki Ko; Kai Salomaa

doi:10.1007/s00236-015-0245-y

State complexity of deletion and bipolar deletion

Yo Sub Han, Sang Ki Ko, Kai Salomaa

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	67-85
Number of pages	19
Journal	Acta Informatica
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s00236-015-0245-y
Publication status	Published - 2016 Feb 1

Bibliographical note

Funding 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.

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

Software
Information Systems
Computer Networks and Communications

Access to Document

10.1007/s00236-015-0245-y

Cite this

@article{f03d8c4f10154807866b731db313cc7a,

title = "State complexity of deletion and bipolar deletion",

abstract = "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.",

author = "Han, {Yo Sub} and Ko, {Sang Ki} and Kai Salomaa",

note = "Funding 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. Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

year = "2016",

month = feb,

day = "1",

doi = "10.1007/s00236-015-0245-y",

language = "English",

volume = "53",

pages = "67--85",

journal = "Acta Informatica",

issn = "0001-5903",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - State complexity of deletion and bipolar deletion

AU - Han, Yo Sub

AU - Ko, Sang Ki

AU - Salomaa, Kai

N1 - Funding 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. Publisher Copyright: © 2015, Springer-Verlag Berlin Heidelberg.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84958167092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958167092&partnerID=8YFLogxK

U2 - 10.1007/s00236-015-0245-y

DO - 10.1007/s00236-015-0245-y

M3 - Article

AN - SCOPUS:84958167092

VL - 53

SP - 67

EP - 85

JO - Acta Informatica

JF - Acta Informatica

SN - 0001-5903

IS - 1

ER -

State complexity of deletion and bipolar deletion

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this