scholarly journals Arithmetization: A new method in structural complexity theory

1991 ◽  
Vol 1 (1) ◽  
pp. 41-66 ◽  
Author(s):  
L�szl� Babai ◽  
Lance Fortnow
Keyword(s):  
Complexity Theory ◽  
Structural Complexity ◽  
New Method

A proof of Beigel's cardinality conjecture

1992 ◽  
Vol 57 (2) ◽  
pp. 677-681 ◽  
Author(s):  
Martin Kummer
Keyword(s):  
Complexity Theory ◽  
Structural Complexity ◽  
Halting Problem ◽  
Parallel Queries

In 1986, Beigel [Be87] (see also [Od89, III.5.9]) proved the nonspeedup theorem: if A, B ⊆ ω, and as a function of 2n variables can be computed by an algorithm which makes at most n queries to B, then A is recursive (informally, 2n parallel queries to a nonrecursive oracle A cannot be answered by making n sequential (or “adaptive”) queries to an arbitrary oracle B). Here, 2n cannot be replaced by 2n − 1. In subsequent papers of Beigel, Gasarch, Gill, Hay, and Owings the theory of “bounded query classes” has been further developed (see, for example, [BGGOta], [BGH89], and [Ow89]). The topic has also been studied in the context of structural complexity theory (see, for example, [AG88], [Be90], and [JY90]).If A ⊆ ω and n ≥ 1, let . Beigel [Be87] stated the powerful “cardinality conjecture” (CC): if A, B ⊆ ω, and can be computed by an algorithm which makes at most n queries to B, then A is recursive. Owings [Ow89] verified CC for n = 1, and, for n 1, he proved that A is recursive in the halting problem. We prove that CC is true for all n.

scholarly journals Structural complexity theory: Recent surprises

1990 ◽  
pp. 1-12 ◽  
Author(s):  
Juris Hartmanis ◽  
Richard Chang ◽  
Desh Ranjan ◽  
Pankaj Rohatgi
Keyword(s):  
Complexity Theory ◽  
Structural Complexity

scholarly journals Development of a Rapid and Precise Method of Digital Image Analysis to Quantify Canopy Density and Structural Complexity

ISRN Ecology ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Anne E. Goodenough ◽  
Andrew S. Goodenough
Keyword(s):  
Image Analysis ◽  
Digital Image ◽  
Digital Image Analysis ◽  
Complex Analysis ◽  
Interobserver Variability ◽  
Structural Complexity ◽  
New Method ◽  
Canopy Density ◽  
Direct Light ◽  
Manual Methods

Estimation of canopy density is necessary for ecological research and woodland management. However, traditional manual methods are time consuming and subject to interobserver variability, while existing photographic methods usually require expensive fish-eye lenses and complex analysis. Here we introduce and test a new method of digital image analysis, CanopyDigi. This allows user-defined threshold to polarise the 256 grey shades of a standard monochrome bitmap into dark “canopy” and light “sky” pixels (the threshold being selected using false-colour images to ensure its suitability). Canopy density data are calculated automatically and rapidly, and, unlike many other common methods, aggregation data are obtainable using Morisita’s index to differentiate closed (diffuse light) and open (direct light) canopies. Results were highly repeatable in both homogeneous and heterogeneous woodland. Estimates correlated strongly with existing (nondigital) canopy techniques, but quicker and with significantly lower interobserver variability (CV = 3.74% versus 20.73%). We conclude that our new method is an inexpensive and precise technique for quantifying canopy density and aggregation.

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