scholarly journals Low complexity classes of multidimensional cellular automata

2006 ◽  
Vol 369 (1-3) ◽  
pp. 142-156 ◽  
Author(s):  
Véronique Terrier
Keyword(s):  
Cellular Automata ◽  
Low Complexity ◽  
Complexity Classes ◽  
Multidimensional Cellular Automata

scholarly journals Examining conifer canopy structural complexity across forest ages and elevations with LiDAR data

2010 ◽  
Vol 40 (4) ◽  
pp. 774-787 ◽  
Author(s):  
Van R. Kane ◽  
Jonathan D. Bakker ◽  
Robert J. McGaughey ◽  
James A. Lutz ◽  
Rolf F. Gersonde ◽  
...  
Keyword(s):  
Pacific Northwest ◽  
Canopy Structure ◽  
Structural Complexity ◽  
Low Complexity ◽  
Primary Forest ◽  
Complexity Classes ◽  
High Complexity ◽  
Development Models ◽  
Management Actions ◽  
The Pacific

LiDAR measurements of canopy structure can be used to classify forest stands into structural stages to study spatial patterns of canopy structure, identify habitat, or plan management actions. A key assumption in this process is that differences in canopy structure based on forest age and elevation are consistent with predictions from models of stand development. Three LiDAR metrics (95th percentile height, rumple, and canopy density) were computed for 59 secondary and 35 primary forest plots in the Pacific Northwest, USA. Hierarchical clustering identified two precanopy closure classes, two low-complexity postcanopy closure classes, and four high-complexity postcanopy closure classes. Forest development models suggest that secondary plots should be characterized by low-complexity classes and primary plots characterized by high-complexity classes. While the most and least complex classes largely confirmed this relationship, intermediate-complexity classes were unexpectedly composed of both secondary and primary forest types. Complexity classes were not associated with elevation, except that primary Tsuga mertensiana (Bong.) Carrière (mountain hemlock) plots were complex. These results suggest that canopy structure does not develop in a linear fashion and emphasize the importance of measuring structural conditions rather than relying on development models to estimate structural complexity across forested landscapes.

Entropy of multidimensional cellular automata

2006 ◽  
Vol 42 (1) ◽  
pp. 38-45
Author(s):  
E. L. Lakshtanov ◽  
E. S. Langvagen
Keyword(s):  
Cellular Automata ◽  
Multidimensional Cellular Automata

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

scholarly journals Multidimensional cellular automata and generalization of Fekete's lemma

2008 ◽  
Vol Vol. 10 no. 3 (Automata, Logic and Semantics) ◽  
Author(s):  
Silvio Capobianco
Keyword(s):  
Growth Rate ◽  
Cellular Automata ◽  
New Variant ◽  
Number Sequences ◽  
Combinatorial Result ◽  
International Audience ◽  
Multidimensional Cellular Automata

Automata, Logic and Semantics International audience Fekete's lemma is a well-known combinatorial result on number sequences: we extend it to functions defined on d-tuples of integers. As an application of the new variant, we show that nonsurjective d-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.

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