### Abstract

A pushdown automaton is said to make a turn at a given instant if it changes at that instant from stack increasing to stack decreasing. Let NPDA-TURN(f(n)) and DPDA-TURN(f(n)) denote the classes of languages accepted by nondeterministic and deterministic pushdown automata respectively that make at most f(n) turns for any input of length n. In this paper the following inclusions that express the space complexity of turn bounded pushdown automata are given: DPDA-TURN(f(n)) ⊆ DSPACE(log f(n) log n), and NPDA-TURN(f(n)) ⊆ NSPACE (log f(n) log n). In particular, it follows that finite-turn pushdown automata are logarithmic space bounded: DPDA-TURN(O(1)) ⊆ DL and NPDA-TURN(O(1)) ⊆ NL, from which two corollaries follow: one is that the class of metalinear context-free languages is complete for NL, and the other is that a more tight inclusion NPDA-TURN(f(n)) ⊆ DSPACE(log^{2} f(n) log n) cannot be derived unless DL = NL, though NPDA-TURN (f(n)) ⊆ DSPACE(log^{2} f(n) log^{2} n) holds.

Original language | English |
---|---|

Pages (from-to) | 295-304 |

Number of pages | 10 |

Journal | International Journal of Computer Mathematics |

Volume | 80 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2003 Mar |

### Fingerprint

### Keywords

- Pushdown automaton
- Space complexity
- Turn (head reversal)

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*International Journal of Computer Mathematics*,

*80*(3), 295-304. https://doi.org/10.1080/0020716022000005564

**On the space complexity of turn bounded pushdown automata.** / Moriya, Etsuro; Tada, Takemaru.

Research output: Contribution to journal › Article

*International Journal of Computer Mathematics*, vol. 80, no. 3, pp. 295-304. https://doi.org/10.1080/0020716022000005564

}

TY - JOUR

T1 - On the space complexity of turn bounded pushdown automata

AU - Moriya, Etsuro

AU - Tada, Takemaru

PY - 2003/3

Y1 - 2003/3

N2 - A pushdown automaton is said to make a turn at a given instant if it changes at that instant from stack increasing to stack decreasing. Let NPDA-TURN(f(n)) and DPDA-TURN(f(n)) denote the classes of languages accepted by nondeterministic and deterministic pushdown automata respectively that make at most f(n) turns for any input of length n. In this paper the following inclusions that express the space complexity of turn bounded pushdown automata are given: DPDA-TURN(f(n)) ⊆ DSPACE(log f(n) log n), and NPDA-TURN(f(n)) ⊆ NSPACE (log f(n) log n). In particular, it follows that finite-turn pushdown automata are logarithmic space bounded: DPDA-TURN(O(1)) ⊆ DL and NPDA-TURN(O(1)) ⊆ NL, from which two corollaries follow: one is that the class of metalinear context-free languages is complete for NL, and the other is that a more tight inclusion NPDA-TURN(f(n)) ⊆ DSPACE(log2 f(n) log n) cannot be derived unless DL = NL, though NPDA-TURN (f(n)) ⊆ DSPACE(log2 f(n) log2 n) holds.

AB - A pushdown automaton is said to make a turn at a given instant if it changes at that instant from stack increasing to stack decreasing. Let NPDA-TURN(f(n)) and DPDA-TURN(f(n)) denote the classes of languages accepted by nondeterministic and deterministic pushdown automata respectively that make at most f(n) turns for any input of length n. In this paper the following inclusions that express the space complexity of turn bounded pushdown automata are given: DPDA-TURN(f(n)) ⊆ DSPACE(log f(n) log n), and NPDA-TURN(f(n)) ⊆ NSPACE (log f(n) log n). In particular, it follows that finite-turn pushdown automata are logarithmic space bounded: DPDA-TURN(O(1)) ⊆ DL and NPDA-TURN(O(1)) ⊆ NL, from which two corollaries follow: one is that the class of metalinear context-free languages is complete for NL, and the other is that a more tight inclusion NPDA-TURN(f(n)) ⊆ DSPACE(log2 f(n) log n) cannot be derived unless DL = NL, though NPDA-TURN (f(n)) ⊆ DSPACE(log2 f(n) log2 n) holds.

KW - Pushdown automaton

KW - Space complexity

KW - Turn (head reversal)

UR - http://www.scopus.com/inward/record.url?scp=28244495061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28244495061&partnerID=8YFLogxK

U2 - 10.1080/0020716022000005564

DO - 10.1080/0020716022000005564

M3 - Article

AN - SCOPUS:28244495061

VL - 80

SP - 295

EP - 304

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 3

ER -