A Space Lower Bound for Acceptance by One-Way Π2-Alternating Machines

Viliam Geffert; Norbert Popély

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 34, Issue: 5, page 357-372
  • ISSN: 0988-3754

Abstract

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We show that one-way Π2-alternating Turing machines cannot accept unary nonregular languages in o(log n) space. This holds for an accept mode of space complexity measure, defined as the worst cost of any accepting computation. This lower bound should be compared with the corresponding bound for one-way Σ2-alternating machines, that are able to accept unary nonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternation for space bounded one-way machines with unary inputs.

How to cite

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Geffert, Viliam, and Popély, Norbert. " A Space Lower Bound for Acceptance by One-Way Π2-Alternating Machines." RAIRO - Theoretical Informatics and Applications 34.5 (2010): 357-372. <http://eudml.org/doc/222025>.

@article{Geffert2010,
abstract = { We show that one-way Π2-alternating Turing machines cannot accept unary nonregular languages in o(log n) space. This holds for an accept mode of space complexity measure, defined as the worst cost of any accepting computation. This lower bound should be compared with the corresponding bound for one-way Σ2-alternating machines, that are able to accept unary nonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternation for space bounded one-way machines with unary inputs. },
author = {Geffert, Viliam, Popély, Norbert},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Alternation; lower bounds; nonregular languages; space complexity; Turing machine.; -alternating Turing machines},
language = {eng},
month = {3},
number = {5},
pages = {357-372},
publisher = {EDP Sciences},
title = { A Space Lower Bound for Acceptance by One-Way Π2-Alternating Machines},
url = {http://eudml.org/doc/222025},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Geffert, Viliam
AU - Popély, Norbert
TI - A Space Lower Bound for Acceptance by One-Way Π2-Alternating Machines
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 357
EP - 372
AB - We show that one-way Π2-alternating Turing machines cannot accept unary nonregular languages in o(log n) space. This holds for an accept mode of space complexity measure, defined as the worst cost of any accepting computation. This lower bound should be compared with the corresponding bound for one-way Σ2-alternating machines, that are able to accept unary nonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternation for space bounded one-way machines with unary inputs.
LA - eng
KW - Alternation; lower bounds; nonregular languages; space complexity; Turing machine.; -alternating Turing machines
UR - http://eudml.org/doc/222025
ER -

References

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