Algorithmic complexity

2001 ◽  
pp. 19-19
Author(s):  
Saul I. Gass ◽  
Carl M. Harris
Keyword(s):  
Algorithmic Complexity

scholarly journals The algorithmic complexity of mixed domination in graphs

2011 ◽  
Vol 412 (22) ◽  
pp. 2387-2392 ◽  
Author(s):  
Yancai Zhao ◽  
Liying Kang ◽  
Moo Young Sohn
Keyword(s):  
Algorithmic Complexity ◽  
Domination In Graphs

scholarly journals Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 778
Author(s):  
Yingli Niu ◽  
Xiangyu Bu ◽  
Xinghua Zhang
Keyword(s):  
Field Theory ◽  
Message Passing Interface ◽  
Mean Field Theory ◽  
Mean Field ◽  
Algorithmic Complexity ◽  
Ensemble Average ◽  
Single Chain ◽  
Metropolis Monte Carlo ◽  
Rigid Rod ◽  
Chain Conformations

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

scholarly journals Algorithmic complexity of recursive and inductive algorithms

2004 ◽  
Vol 317 (1-3) ◽  
pp. 31-60 ◽  
Author(s):  
Mark Burgin
Keyword(s):  
Algorithmic Complexity

The algorithmic complexity of colour switching

1992 ◽  
Vol 43 (2) ◽  
pp. 63-68
Author(s):  
Yeow Meng Chee ◽  
Andrew Lim
Keyword(s):  
Algorithmic Complexity

scholarly journals Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 534 ◽  
Author(s):  
Hector Zenil ◽  
Narsis Kiani ◽  
Jesper Tegnér
Keyword(s):  
Algorithmic Complexity ◽  
Information Theoretic ◽  
Algorithmic Probability ◽  
Graphs And Networks ◽  
Algorithmic Information ◽  
Statistical Regularities ◽  
Review Study ◽  
Causal Nature ◽  
Definition Of

We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov–Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity—both theoretical and numerical—with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.

CLASS COUNTING AUTOMATA ON DATAWORDS

2011 ◽  
Vol 22 (04) ◽  
pp. 863-882 ◽  
Author(s):  
AMALDEV MANUEL ◽  
R. RAMANUJAM
Keyword(s):  
Petri Nets ◽  
Algorithmic Complexity ◽  
Covering Problem ◽  
Input Word ◽  
System States ◽  
Recognizable Language

In the theory of automata over infinite alphabets, a central difficulty is that of finding a suitable compromise between expressiveness and algorithmic complexity. We propose an automaton model where we count the multiplicity of data values on an input word. This is particularly useful when such languages represent behaviour of systems with unboundedly many processes, where system states carry such counts as summaries. A typical recognizable language is: "every process does at most k actions labelled a". We show that emptiness is elementarily decidable, by reduction to the covering problem on Petri nets.

About algorithmic complexity

2012 ◽  
pp. 270-285
Author(s):  
Nathalie Caspard ◽  
Bruno Leclerc ◽  
Bernard Monjardet
Keyword(s):  
Algorithmic Complexity
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