Complexity theory for splicing systems

Remco Loos, Mitsunori Ogihara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes a notion of time complexity in splicing systems and presents fundamental properties of SPLTIME, the class of languages with splicing system time complexity t(n). Its relations to classes based on standard computational models are explored. It is shown that for any function t(n), SPLTIME[t(n)] is included in 1-NSPACE[t(n)]. Expanding on this result, 1-NSPACE[t(n)] is characterized in terms of splicing systems: it is the class of languages accepted by a t(n)-space uniform family of extended splicing systems having production time O(t(n)) with regular rules described by finite automata with at most a constant number of states. As to lower bounds, it is shown that for all functions t(n) > log n, all languages accepted by a pushdown automaton with maximal stack height t(|x|) for a word x are in SPLTIME[t(n)]. From this result, it follows that the regular languages are in SPLTIME[O(log(n))] and that the context-free languages are in SPLTIME[O(n)].

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages300-311
Number of pages12
Volume4588 LNCS
StatePublished - 2007
Externally publishedYes
Event11th International Conference on Developments in Language Theory, DLT 2007 - Turku, Finland
Duration: Jul 3 2007Jul 6 2007

Other

Other11th International Conference on Developments in Language Theory, DLT 2007
CountryFinland
CityTurku
Period7/3/077/6/07

Fingerprint

Complexity Theory
Language
Context free languages
Formal languages
Finite automata
Time Complexity
Pushdown Automata
Uniform Space
Context-free Languages
Regular Languages
Finite Automata
Computational Model
Standard Model
Lower bound
Class

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Loos, R., & Ogihara, M. (2007). Complexity theory for splicing systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4588 LNCS, pp. 300-311)

Complexity theory for splicing systems. / Loos, Remco; Ogihara, Mitsunori.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4588 LNCS 2007. p. 300-311.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Loos, R & Ogihara, M 2007, Complexity theory for splicing systems. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4588 LNCS, pp. 300-311, 11th International Conference on Developments in Language Theory, DLT 2007, Turku, Finland, 7/3/07.
Loos R, Ogihara M. Complexity theory for splicing systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4588 LNCS. 2007. p. 300-311
Loos, Remco ; Ogihara, Mitsunori. / Complexity theory for splicing systems. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4588 LNCS 2007. pp. 300-311
@inproceedings{9f8636e489404929aaef270744a38eee,
title = "Complexity theory for splicing systems",
abstract = "This paper proposes a notion of time complexity in splicing systems and presents fundamental properties of SPLTIME, the class of languages with splicing system time complexity t(n). Its relations to classes based on standard computational models are explored. It is shown that for any function t(n), SPLTIME[t(n)] is included in 1-NSPACE[t(n)]. Expanding on this result, 1-NSPACE[t(n)] is characterized in terms of splicing systems: it is the class of languages accepted by a t(n)-space uniform family of extended splicing systems having production time O(t(n)) with regular rules described by finite automata with at most a constant number of states. As to lower bounds, it is shown that for all functions t(n) > log n, all languages accepted by a pushdown automaton with maximal stack height t(|x|) for a word x are in SPLTIME[t(n)]. From this result, it follows that the regular languages are in SPLTIME[O(log(n))] and that the context-free languages are in SPLTIME[O(n)].",
author = "Remco Loos and Mitsunori Ogihara",
year = "2007",
language = "English (US)",
isbn = "3540732071",
volume = "4588 LNCS",
pages = "300--311",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - Complexity theory for splicing systems

AU - Loos, Remco

AU - Ogihara, Mitsunori

PY - 2007

Y1 - 2007

N2 - This paper proposes a notion of time complexity in splicing systems and presents fundamental properties of SPLTIME, the class of languages with splicing system time complexity t(n). Its relations to classes based on standard computational models are explored. It is shown that for any function t(n), SPLTIME[t(n)] is included in 1-NSPACE[t(n)]. Expanding on this result, 1-NSPACE[t(n)] is characterized in terms of splicing systems: it is the class of languages accepted by a t(n)-space uniform family of extended splicing systems having production time O(t(n)) with regular rules described by finite automata with at most a constant number of states. As to lower bounds, it is shown that for all functions t(n) > log n, all languages accepted by a pushdown automaton with maximal stack height t(|x|) for a word x are in SPLTIME[t(n)]. From this result, it follows that the regular languages are in SPLTIME[O(log(n))] and that the context-free languages are in SPLTIME[O(n)].

AB - This paper proposes a notion of time complexity in splicing systems and presents fundamental properties of SPLTIME, the class of languages with splicing system time complexity t(n). Its relations to classes based on standard computational models are explored. It is shown that for any function t(n), SPLTIME[t(n)] is included in 1-NSPACE[t(n)]. Expanding on this result, 1-NSPACE[t(n)] is characterized in terms of splicing systems: it is the class of languages accepted by a t(n)-space uniform family of extended splicing systems having production time O(t(n)) with regular rules described by finite automata with at most a constant number of states. As to lower bounds, it is shown that for all functions t(n) > log n, all languages accepted by a pushdown automaton with maximal stack height t(|x|) for a word x are in SPLTIME[t(n)]. From this result, it follows that the regular languages are in SPLTIME[O(log(n))] and that the context-free languages are in SPLTIME[O(n)].

UR - http://www.scopus.com/inward/record.url?scp=34548079575&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548079575&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:34548079575

SN - 3540732071

SN - 9783540732075

VL - 4588 LNCS

SP - 300

EP - 311

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

ER -