### 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 language | English (US) |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 300-311 |

Number of pages | 12 |

Volume | 4588 LNCS |

State | Published - 2007 |

Externally published | Yes |

Event | 11th International Conference on Developments in Language Theory, DLT 2007 - Turku, Finland Duration: Jul 3 2007 → Jul 6 2007 |

### Other

Other | 11th International Conference on Developments in Language Theory, DLT 2007 |
---|---|

Country | Finland |

City | Turku |

Period | 7/3/07 → 7/6/07 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

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

*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.

}

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 -