Complexity: Wikipedia summary by WikiSummarizer

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# **Wikipedia article: Complexity**

## Complexity

# Complexity (100)

### · On**e of the problems in addressing complexity issues has been distinguishing conceptually between the large number of variances in relationships **

### · The approaches that embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in a defined system.

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**Wikipedia article: Complexity**

# Complexity

# Complexity (100)

## · In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article.

## · The approaches that embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in a defined system.

## · One of the problems in addressing complexity issues has been distinguishing conceptually between the large number of variances in relationships extant in random collections, and the sometimes large, but smaller, number of relationships between elements in systems where constraints (related to correlation of otherwise independent elements) simultaneously reduce the variations from element independence and create distinguishable regimes of more-uniform, or correlated, relationships, or interactions.

## · Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between "disorganized complexity" and "organized complexity".

## · Though the interactions of the parts in a "disorganized complexity" situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods.

## · The source of disorganized complexity is the large number of parts in the system of interest, and the lack of correlation between elements in the system.

## · For instance, for many functions (problems), such a computational complexity as time of computation is smaller when multitape Turing machines are used than when Turing machines with one tape are used.

## · Random Access Machines allow one to even more decrease time complexity (Greenlaw and Hoover 1998: 226), while inductive Turing machines can decrease even the complexity class of a function, language or set (Burgin 2005).

## · In several scientific fields, "complexity" has a specific meaning : In computational complexity theory, the amounts of resources required for the execution of algorithms is studied.

## · In algorithmic information theory, the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string.

## · An axiomatic approach to Kolmogorov complexity based on Blum axioms (Blum 1967) was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov (Burgin 1982).

## · The axiomatic approach to Kolmogorov complexity was further developed in the book (Burgin 2005) and applied to software metrics (Burgin and Debnath, 2003; Debnath and Burgin, 2003).

## · In mathematics, Krohn-Rhodes complexity is an important topic in the study of finite semigroups and automata.

## · This differs from the computational complexity described above in that it is a measure of the design of the software.

## · The topic is commonly recognized as social complexity that is often related to the use of computer simulation in social science, i.e.: computational sociology.

## · It is orthogonal to the forms of complexity discussed so far, which are called horizontal complexity Bejan and Lorente showed that complexity is modest (not maximum, not increasing), and is a feature of the natural phenomenon of design generation in nature, which is predicted by the Constructal law.

# algorithms (100)

## · In several scientific fields, "complexity" has a specific meaning : In computational complexity theory, the amounts of resources required for the execution of algorithms is studied.

# science (85)

## · The study of these complex linkages is the main goal of network theory and network science.

## · In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article.

## · In social science, the study on the emergence of macro-properties from the micro-properties, also known as macro-micro view in sociology.

## · The topic is commonly recognized as social complexity that is often related to the use of computer simulation in social science, i.e.: computational sociology.

# Kolmogorov Complexity (67)

## · In algorithmic information theory, the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string.

## · An axiomatic approach to Kolmogorov complexity based on Blum axioms (Blum 1967) was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov (Burgin 1982).

## · The axiomatic approach to Kolmogorov complexity was further developed in the book (Burgin 2005) and applied to software metrics (Burgin and Debnath, 2003; Debnath and Burgin, 2003).

# organized complexity (64)

## · Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between "disorganized complexity" and "organized complexity".

# Burgin (61)

## · Random Access Machines allow one to even more decrease time complexity (Greenlaw and Hoover 1998: 226), while inductive Turing machines can decrease even the complexity class of a function, language or set (Burgin 2005).

## · An axiomatic approach to Kolmogorov complexity based on Blum axioms (Blum 1967) was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov (Burgin 1982).

## · The axiomatic approach to Kolmogorov complexity was further developed in the book (Burgin 2005) and applied to software metrics (Burgin and Debnath, 2003; Debnath and Burgin, 2003).

# correlation (50)

## · One of the problems in addressing complexity issues has been distinguishing conceptually between the large number of variances in relationships extant in random collections, and the sometimes large, but smaller, number of relationships between elements in systems where constraints (related to correlation of otherwise independent elements) simultaneously reduce the variations from element independence and create distinguishable regimes of more-uniform, or correlated, relationships, or interactions.

## · The source of disorganized complexity is the large number of parts in the system of interest, and the lack of correlation between elements in the system.

# disorganized complexity (50)

## · Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between "disorganized complexity" and "organized complexity".

## · Though the interactions of the parts in a "disorganized complexity" situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods.

## · The source of disorganized complexity is the large number of parts in the system of interest, and the lack of correlation between elements in the system.

# network (50)

## · The study of these complex linkages is the main goal of network theory and network science.

# string (42)

## · In algorithmic information theory, the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string.

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