State complexity of inversion operations

Da Jung Cho; Yo Sub Han; Sang Ki Ko; Kai Salomaa

doi:10.1007/978-3-319-09704-6_10

State complexity of inversion operations

Da Jung Cho, Yo Sub Han, Sang Ki Ko, Kai Salomaa

College of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2ⁿ (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings ux^R v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n ³). We establish that the deterministic state complexity of the inversion is 2^Ω(n·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.

Original language	English
Title of host publication	Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings
Publisher	Springer Verlag
Pages	102-113
Number of pages	12
ISBN (Print)	9783319097039
DOIs	https://doi.org/10.1007/978-3-319-09704-6_10
Publication status	Published - 2014
Event	16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014 - Turku, Finland Duration: 2014 Aug 5 → 2014 Aug 8

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8614 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014
Country/Territory	Finland
City	Turku
Period	14/8/5 → 14/8/8

Bibliographical note

Funding Information:
Cho, 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 the Yonsei University Future-leading Research Initiative of 2014. Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224 .

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-09704-6_10

Cite this

Cho, D. J., Han, Y. S., Ko, S. K., & Salomaa, K. (2014). State complexity of inversion operations. In Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings (pp. 102-113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8614 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-09704-6_10

@inproceedings{1f7ad21f8ae748489e6983c0f598edc4,

title = "State complexity of inversion operations",

abstract = "The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings uxR v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n 3). We establish that the deterministic state complexity of the inversion is 2Ω(n·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.",

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

note = "Funding Information: Cho, 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 the Yonsei University Future-leading Research Initiative of 2014. Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224 . ; 16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014 ; Conference date: 05-08-2014 Through 08-08-2014",

year = "2014",

doi = "10.1007/978-3-319-09704-6_10",

language = "English",

isbn = "9783319097039",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "102--113",

booktitle = "Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings",

address = "Germany",

}

Cho, DJ, Han, YS, Ko, SK & Salomaa, K 2014, State complexity of inversion operations. in Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8614 LNCS, Springer Verlag, pp. 102-113, 16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014, Turku, Finland, 14/8/5. https://doi.org/10.1007/978-3-319-09704-6_10

State complexity of inversion operations. / Cho, Da Jung; Han, Yo Sub; Ko, Sang Ki et al.

Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings. Springer Verlag, 2014. p. 102-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8614 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - State complexity of inversion operations

AU - Cho, Da Jung

AU - Han, Yo Sub

AU - Ko, Sang Ki

AU - Salomaa, Kai

N1 - Funding Information: Cho, 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 the Yonsei University Future-leading Research Initiative of 2014. Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224 .

PY - 2014

Y1 - 2014

N2 - The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings uxR v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n 3). We establish that the deterministic state complexity of the inversion is 2Ω(n·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.

AB - The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings uxR v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n 3). We establish that the deterministic state complexity of the inversion is 2Ω(n·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.

UR - http://www.scopus.com/inward/record.url?scp=84905395541&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905395541&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-09704-6_10

DO - 10.1007/978-3-319-09704-6_10

M3 - Conference contribution

AN - SCOPUS:84905395541

SN - 9783319097039

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

SP - 102

EP - 113

BT - Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings

PB - Springer Verlag

T2 - 16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014

Y2 - 5 August 2014 through 8 August 2014

ER -

Cho DJ, Han YS, Ko SK, Salomaa K. State complexity of inversion operations. In Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings. Springer Verlag. 2014. p. 102-113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-09704-6_10

State complexity of inversion operations

Abstract

Publication series

Other

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this