Nonerasing, Counting, and Majority over the Linear Time Hierarchy

In this paper, we investigate several extensions of the linear time hierarchy (denoted by LTH). We first prove that it is not necessary to erase the oracle tape between two successive oracle calls, thereby lifting a common restriction on LTH machines. We also define a natural counting extension of L...

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Bibliographic Details
Published in:Information and computation Vol. 174; no. 2; pp. 132 - 142
Main Authors: Durand, Arnaud, More, Malika
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.05.2002
Elsevier
Subjects:
Applied sciences
Automata. Abstract machines. Turing machines
Computer science; control theory; systems
Exact sciences and technology
Theoretical computing
counting classes
rudimentary relations
logic in computer science
computational and structural complexity
Hierarchy
Turing machine
Linear time
Logic
Oracle
Computational complexity
Counting
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:In this paper, we investigate several extensions of the linear time hierarchy (denoted by LTH). We first prove that it is not necessary to erase the oracle tape between two successive oracle calls, thereby lifting a common restriction on LTH machines. We also define a natural counting extension of LTH and show that it corresponds to a robust notion of counting bounded arithmetic predicates. Finally, we show that the computational power of the majority operator is equivalent to that of the exact counting operator in both contexts.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.2001.3084