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

Published online by Cambridge University Press:  15 April 2002

Viliam Geffert  and
Norbert Popély
Viliam Geffert
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04154 Košice, Slovakia; ([email protected])
Norbert Popély
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04154 Košice, Slovakia; ([email protected])
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Abstract

We show that one-way Π2-alternating Turing machines cannotaccept unary nonregular languages in o(log n) space. This holdsfor an accept mode of space complexity measure, defined asthe worst cost of any accepting computation. This lower boundshould be compared with the corresponding bound for one-wayΣ2-alternating machines, that are able to accept unarynonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternationfor space bounded one-way machines with unary inputs.

Keywords

Alternationlower boundsnonregular languagesspace complexityTuring machine.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 5 , September 2000 , pp. 357 - 372
Copyright
© EDP Sciences, 2000

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