Functions computable in polynomial space

Consider nondeterministic polynomial- time Turing machine that on input x outputs a 3 × 3 matrix with entries from {−1, 0, 1} on each of its paths. Define the function f where f ( x) is the upper left entry in the product of all these matrices (in an order of the paths to be made precise below). We...

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Bibliographic Details
Published in:Information and computation Vol. 198; no. 1; pp. 56 - 70
Main Authors: Galota, Matthias, Vollmer, Heribert
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 10.04.2005
Elsevier
Subjects:
68Q05
68Q10
68Q15
Algorithmics. Computability. Computer arithmetics
Applied sciences
Arithmetic circuits
Automata. Abstract machines. Turing machines
Bottleneck machines
Complexity class of functions
Computer science; control theory; systems
Exact sciences and technology
Leaf languages
Polynomial space
Straight-line programs
Theoretical computing
68Q15
Straight-line programs
68Q05
Arithmetic circuits
Polynomial space
Bottleneck machines
68Q10
Complexity class of functions
Leaf languages
Bottleneck
Arithmetic circuit
68Q05 Polynomial space; Complexity class of functions; Bottleneck machines; Leaf languages; Arithmetic circuits; Straight-line programs
Computer theory
Turing machine
Straight line program
Leaf language
Polynomial time
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:Consider nondeterministic polynomial- time Turing machine that on input x outputs a 3 × 3 matrix with entries from {−1, 0, 1} on each of its paths. Define the function f where f ( x) is the upper left entry in the product of all these matrices (in an order of the paths to be made precise below). We show that the class of functions f computable as just described is exactly the class FPSPACE of integer-valued functions computable by polynomial-space Turing machines. Along the way we obtain characterizations of FPSPACE in terms of arithmetic circuits and straight-line programs.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2005.02.002