science , the Andrey KolmogorovKolmogorovcomplexity of an object, such as a piece of text, is a measure of the computation al resources needed to specify the object. Kolmogorovcomplexity is also known as descriptive complexity , Kolmogorov Gregory Chaitin Chaitin complexity , stochastic complexity ... set. Thus, the Kolmogorovcomplexity of the raw file encoding this bitmap is much less than 1.62 million ... to the choice of description language is discussed below. It can be shown that the Kolmogorovcomplexity ... whose Kolmogorovcomplexity is small relative to the string s size are not considered to be complex. The notion of Kolmogorovcomplexity can be used to state and prove impossibility results akin ... Kolmogorovcomplexity, we must first specify a description language for strings. Such a description ... in the description is the Kolmogorovcomplexity of s , written K s . Symbolically, math K ... Algorithmic information theory is the area of computer science that studies Kolmogorovcomplexity ... of KolmogorovComplexity is based on a crucial theorem first discovered by Ray Solomonoff who published ... digits can be based. Kolmogorov used this theorem to define several functions of strings complexity ... community, however, was to associate this type of complexity with Kolmogorov, who was concerned with randomness ... other variants of Kolmogorovcomplexity or algorithmic information. The most widely used one ... to Kolmogorovcomplexity based on Blum axioms Blum 1967 was introduced by Mark Burgin in the paper ... to KolmogorovComplexity and Its Applications date 1997 02 27 ref Basic results In the following ... forall s K s leq s c. quad math Incomputability of Kolmogorovcomplexity The first result is that there is no way .... Therefore, given any positive integer n , it produces a string with Kolmogorovcomplexity at least ... optimizing compiler. Chain rule for Kolmogorovcomplexity Main Chain rule for Kolmogorovcomplexity The chain rule for Kolmogorovcomplexity states that math K X,Y K X K Y X O log K X,Y . quad math ... more details
The chain rule for Kolmogorovcomplexity is an analogue of the chain rule for information entropy , which states math H X,Y H X H Y X math That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X . This follows immediately from the definitions of conditional entropy conditional and joint entropy fact from probability theory that the joint probability is the product of the marginal probability marginal and conditional probability math P X,Y P X P Y X , math The equivalent statement for Kolmogorovcomplexity does not hold exactly it is only true up to a logarithm ic factor math K X,Y K X K Y X O log K X,Y math An exact version, KP X , Y KP X KP Y X O 1 , holds for the prefix complexity KP , where X is a shortest program for X . It states that the shortest program to reproduce X and Y is using a program to reproduce X and a program to reproduce Y given X , plus Big O notation at most a logarithmic factor. Using this statement one can define Mutual information Absolute mutual information an analogue of mutual information for Kolmogorovcomplexity . Proof The direction is obvious we can write a program to produce x and y by concatenating a program to produce x , a program to produce y given access to x , and whence the log term the length of one of the programs, so that we know where to separate the two programs for x and y x log K x , y upper bounds this length . The direction is rather more difficult. The key to the proof is the construction of the set math A u,z K u,z le K x,y math that is, the construction of the set of all pairs math u,z math such that the shortest input for a universal Turing machine that produces math u,z math and some way to distinguish math u math from math z math is shorter than the shortest producing math x,y math ... last Li first Ming coauthors Vitá nyi, Paul title An introduction to Kolmogorovcomplexity and its ... more details
defined measures. In algorithmic information theory , the Kolmogorovcomplexity also called descriptive ... kinds of Kolmogorovcomplexity are studied the uniform complexity, prefix complexity, monotone complexity, time bounded Kolmogorovcomplexity, and space bounded Kolmogorovcomplexity. An axiomatic approach to Kolmogorovcomplexity based on Blum axioms Blum 1967 was introduced by Mark Burgin in the paper ... other approaches to Kolmogorovcomplexity . It is possible to treat different kinds of Kolmogorovcomplexity as particular cases of axiomatically defined generalized Kolmogorovcomplexity . Instead ... to Kolmogorovcomplexity was further developed in the book Burgin 2005 and applied to software metrics ... Kolmogorovcomplexity and duality in theory of computations, Notices of the Russian Academy of Sciences ...other uses Complexity disambiguation In general usage, complexity tends to be used to characterize something ... to characterizing complexity, many of which are reflected in this article. In a business context, complexity management is the methodology to minimize value destroying complexity and efficiently control value adding complexity in a cross functional approach. File complexity map castellani.jpg thumb 800px right A map of many of the leading scholars and areas of research in complexity science Overview .... Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements ... are specified. Warren Weaver has posited that the complexity of a particular system is the degree of difficulty .... In Weaver s view, complexity comes in two forms disorganized complexity, and organized complexity. ref Cite journal last Weaver first Warren title Science and Complexity journal American Scientist ... contemporary thinking about complexity. ref cite book last Johnson first Steven title Emergence ..., multiple relational regimes, and state spaces might be summarized as implying that complexity ... or model or mathematical expression, as is later set out herein. Disorganized complexity vs ... more details
Kolm complexity lect.jpg thumb Kolmogorov left works on his talk Tallinn , Estonian SSR , 1973 . Image ... was a founder of algorithmic complexity theory , often referred to as KolmogorovcomplexityKolmogorovcomplexity theory , which he began to develop around this time. Kolmogorov was married to Anna ... Kolmogorov interpretation Kolmogorov microscales Kolmogorov space KolmogorovcomplexityKolmogorov ...Infobox scientist name Andrey Kolmogorov image Kolmogorov m.jpg birth date birth date 1903 04 25 df y ... Prize 1987 signature kolmog sig.jpg footnotes Andrey Nikolaevich Kolmogorov lang ru ... , topology , intuitionistic logic , turbulence , classical mechanics and computational complexity . Biography Early life Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth ... Civil War . Kolmogorov was educated in his aunt s village school, and his earliest literary efforts ... to a Gymnasium school gymnasium , graduating from it in 1920. In 1920, Kolmogorov began to study at the Moscow State University and the Chemistry Technological Institute. Kolmogorov gained a reputation ..., W. H. Freeman, 2001 pp. 137&ndash 50. ref At the same time 1921&ndash 1922 , Kolmogorov derived and proved ... In 1922 Kolmogorov constructed a Convergence of Fourier series Fourier series that diverges ... to devote his life to mathematics . In 1925 Kolmogorov graduated from Moscow State University , and began ... who involved Kolmogorov in 1936 in an ugly political persecution of their common teacher, the so called Luzin case or Luzin affair . Kolmogorov together with Khinchin A. Khinchin became interested ... of classical formal logic can be formulated as those of intuitionistic logic. In 1929 Kolmogorov earned his Doctor of Philosophy degree, Ph.D. , at the Moscow State University . In 1930, Kolmogorov ... in German in 1931. Also in 1931, he became a professor at Moscow University. In 1933, Kolmogorov published ... expert in this field. In 1935, Kolmogorov became the first chairman of probability theory at the Moscow ... more details
Kolmogorov s theorem is any of several different results by Andrey Kolmogorov In statistics Kolmogorov Smirnov test In probability theory Hahn Kolmogorov theorem Kolmogorov existence theorem Kolmogorov continuity theorem Kolmogorov s three series theorem Kolmogorov s zero one law Chapman Kolmogorov equation s Kolmogorov inequalities Kolmogorov s inequality Kolmogorov s inequality for positive submartingales In functional analysis Landau Kolmogorov inequality disambig pl Twierdzenie Ko mogorowa ... more details
Andrey KolmogorovKolmogorov microscales are the smallest scale ratio scale s in Turbulence turbulent flow . They are defined ref Landahl, M.T. & E. Mollo Christensen. Turbulence and Random Processes in Fluid Mechanics. Cambridge, 2ed, 1992. ref by class wikitable Kolmogorov length scale math eta left frac nu 3 epsilon right 1 4 math Kolmogorov time scale math tau eta left frac nu epsilon right 1 2 math Kolmogorov velocity scale math u eta left nu epsilon right 1 4 math where math epsilon math is the average rate of energy dissipation per unit mass, and math nu math is the kinematic viscosity of the fluid. In his 1941 theory, A. N. Kolmogorov introduced the idea that the smallest scales of turbulence are universal similar for every turbulent flow and that they depend only on math epsilon math and math nu math . The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis . Since the dimension of kinematic viscosity is length sup 2 sup time, and the dimension of the energy dissipation rate per unit mass is length sup 2 sup time sup 3 sup , the only combination that has the dimension of time is math tau eta nu epsilon 1 2 math which is the Kolmorogov time scale. Similarly, the Kolmogorov length scale is the only combination of math epsilon math and math nu math that has dimension of length. The Kolmogorov 1941 theory is a mean field theory since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In fluid turbulence , the energy dissipation rate fluctuates in space and time, so it is possible to think of the microscales as quantities that also vary in space and time. However, standard practice is to use mean field values since they represent the typical values of the smallest scales in a given flow ... Kolmogorov Microscales Category Turbulence de Mikroskala von Kolmogorow es Escala de Kolmog rov it Scala di Kolmogorov pt Escala de Kolmogorov ... more details
Kolmogorov equations , including Kolmogorov forward equations and Kolmogorov backward equations , characterize random dynamic processes. In the theory of continuous time Markov process es these names refer to pairs of equations that were highlighted in Andrei Kolmogorov s 1931 work. Each pair is composed by a forward and a backward system of equations. The first pair in Kolmogorov s work corresponds to equations for the probabilities in jump process es such that in a small time interval there is an overwhelming probability that the state will remain unchanged however, if it changes, the change may be radical ref name f49 . The second pair of forward and backward equations describe the evolution of probability densities such as those represented by diffusion and by Brownian motion there it is certain ... time Markov process they refer to the Kolmogorov forward equations Markov jump processes a special case is known in Natural sciences as master equation and the Kolmogorov backward equations Markov ... forward equation and to the Kolmogorov backward equations diffusion . History The equations are named after Andrei Kolmogorov s since they were highlighted in his 1931 foundational work. ref name k31 Andrei Kolmogorov, ber die analytisehen Methoden in der Wahrseheinliehkeitsreehnung On Analytical ... ref William Feller makes reference to the equations for the jump process as Kolmogorov s equations . ref name f40 Willy Feller, On Boundaries and Lateral Conditions for the Kolmogorov Differential ... for each member of Kolmogorov s pair, while he refers to the diffusion equations as forward and backward ... Much later, by 1957, Feller refers to the equations for the jump process as Kolmogorov forward equations and Kolmogorov backward equations . ref name f57 William Feller, 1957. On Boundaries and Lateral Conditions for the Kolmogorov Differential Equations http www.jstor.org stable 1970064 ref Other ... it Equazione retrospettiva di Kolmogorov ... more details
In probability theory , Kolmogorov s criterion , named after Andrey Kolmogorov , is a theorem in Markov process es concerning stationary Markov chain s i.e. ones with stationary transition probabilities, also called Markov chain Variations time homogeneous Markov chains . The theorem states that such a chain is time reversibility reversible if and only if its transition probabilities satisfy math p j 1 j 2 p j 2 j 3 cdots p j n 1 j n p j n j 1 p j 1 j n p j n j n 1 cdots p j 3 j 2 p j 2 j 1 math for all finite sequences of states math j 1, j 2, ldots, j n in S . math Here p sub ij sub are elements of the transition matrix P and S is the state space of the chain. Proofs of this theorem are available in the literature. ref F.P. Kelly 1979 http www.statslab.cam.ac.uk frank BOOKS kelly book.html Reversibility and Stochastic Networks , Wiley. ISBN 0471276014 p. 22 ref Notes references See also Kolmogorov s generalized criterion Category Markov processes ... more details
that can be placed on a topological space. The Kolmogorov quotient Topological indistinguishability ... the Kolmogorov quotient of X , which we will denote KQ X . Of course, if X was T sub 0 sub to begin with, then KQ X and X are natural category theory natural ly homeomorphic . Categorically, Kolmogorov spaces are a reflective subcategory of topological spaces, and the Kolmogorov quotient is the reflector. Topological spaces X and Y are Kolmogorov equivalent when their Kolmogorov quotients are homeomorphic ... and Y are Kolmogorov equivalent, then X has such a property if and only if Y does. On the other hand ... 0 sub space with the same structures and properties by taking the Kolmogorov quotient. The example of L ... with this topology. When we form the Kolmogorov quotient, the actual L sup 2 sup R , these structures ... mechanics generally want to study. Note that the notation L sup 2 sup R usually denotes the Kolmogorov ... if and only if the Kolmogorov quotient KQ X is Hausdorff. This is a sensible, albeit less ... be added or removed arbitrarily using the concept of Kolmogorov quotient. External links http www.mathematik.tu ... Properties of topological spaces ca Espai de Kolmogorov de Kolmogoroff Raum es Espacio de Kolmog rov ko T0 it Spazio T0 nl Kolmogorov ruimte pl Przestrze T0 pt Espa o de Kolmogorov sv Kolmogorovrum ... more details
In probability theory , Kolmogorov s inequality is a so called maximal inequality mathematics inequality that gives a bound on the probability that the partial sum s of a Finite set finite collection of independent random variables exceed some specified bound. The inequality is named after the Russia n mathematician Andrey Kolmogorov . Citation needed date May 2007 Statement of the inequality Let X sub 1 sub , ..., X sub n sub R be Statistical independence independent random variable s defined on a common probability space , F , Pr , with expected value E X sub k sub 0 and variance Var X sub k sub < for k 1, ..., n . Then, for each > 0, math Pr left max 1 leq k leq n S k geq lambda right leq frac 1 lambda 2 operatorname Var S n equiv frac 1 lambda 2 sum k 1 n operatorname Var X k , math where S sub k sub X sub 1 sub ... X sub k sub . Proof The following argument is due to Kareem Amin and employs discrete martingale s. As argued in the discussion of Doob s martingale inequality , the sequence math S 1, S 2, dots, S n math is a martingale. Without loss of generality , we can assume that math S 0 0 math and math S i geq 0 math for all math i math . Define math Z i i 0 n math as follows. Let math Z 0 0 math , and math Z i 1 left begin array ll S i 1 & text if displaystyle max 1 leq j leq i S j lambda Z i & text otherwise end array right. math for all math i math . Then math Z i i 0 n math is a also a martingale. Since math S i S i 1 math is independent and mean zero, math begin align sum i 1 n text E S i S i 1 2 & sum i 1 n text E S i 2 2 S i S i 1 S i 1 ... s inequality Doob s martingale inequality Etemadi s inequality Landau Kolmogorov inequality Markov ... xviii 509 planetmath id 3687 title Kolmogorov s inequality Category Probability theory Category Stochastic ... Ungleichung fr In C3 A9galit C3 A9 de Kolmogorov km pl Nier wno Ko mogorowa ... more details
Wiktionary complexityComplexity may refer to Complex systems Complexity theory disambiguation Kolmogorovcomplexity Los Angeles Complexity , a professional gaming team Computational complexity theory , in computer science Game complexity See also Complex disambiguation Disambig es Complejidad desambiguaci n ... more details
Effective complexity is a measure of complexity defined in a 2003 paper by Murray Gell Mann and Seth Lloyd that attempts to measure the amount of non random information in a system. ref http www.santafe.edu research publications workingpapers 03 12 068.pdf ref It has been criticised as being dependent on the subjective decisions made as to which parts of the information in the system are to be discounted as random. ref http cat.inist.fr ?aModele afficheN&cpsidt 14976916 ref See also Kolmogorovcomplexity Crude complexity Logical depth Total information Self dissimilarity Forecasting complexity Effective measure complexity References reflist External links http www.cs.brandeis.edu pablo complex.maker.html Category Information theory Category Computational complexity theory math stub ... more details
In an attempt to explain how humans perceive relevance, Cognitive complexity is defined as an extension of the notion of Kolmogorovcomplexity . It amounts to the length of the shortest description ...Cognitive Cognitive complexity describes cognition along a simplicity complexity axis. It is the subject ... last Bell first R.C. title Cognitive complexity work The Internet Encyclopaedia of Personal Construct ... Analyzing Organizations Through Cognitive Complexity author Villanova University accessdate 29 April ... Cognitive Complexity in Human Computer Interaction last Rauterberg first Matthias authorlink Matthias ... footnotes date April 2010 Cognitive complexity is a psychological characteristic or psychological ... skill of a person. A person who is measured high on cognitive complexity tends to perceive ... another complexity and at the other end by the use of few constructs with limited relationships to one ... complexity can have various meanings the number of mental structures we use, how abstract they are, and how ..., S.E. 1998 , Cognitive complexity . In J.C. McCroskey, J.A. Daly, M.M. Martin, & M.J. Beatty Eds ... science see Complexity In human computer interaction , cognitive or psychological complexity ... complexity theory computational complexity . ref name thomas 2008 cite book first1 John C. last1 ... Complexity year 2008 pages 498 507 title The human computer interaction handbook Fundamentals, Evolving ... one hundred people is simpler in a village in Congo rather than in an Inuit village. Cognitive complexity ... to describe than to generate. Human individuals attach two complexity values to events description complexity see above definition generation complexity the size of the minimum set of parameter ... such as an encounter with an Inuit woman in Congo, one must add up the complexity of each event ... A tutorial on Simplicity Theory cite web last Bell first R.C. title Cognitive complexity work The Internet ..., S. 2002 . http etd.lsu.edu docs available etd 0410102 134451 unrestricted Bryan dis.pdf Cognitive complexity ... more details
In computational complexity theory , QP may refer to Quasi polynomial time , whose corresponding complexity class is named QP Exact Quantum Polynomial time, whose complexity class is named EQP complexity Bounded error Quantum Polynomial time, whose associated class is BQP disambig Category Complexity classes ... more details
test is based on the Kolmogorovcomplexity of a pattern T that is exhibited by an event E that has ... on an even face. blockquote Kolmogorovcomplexity provides a measure of the computational resources ... T , the number of other patterns may have Kolmogorovcomplexity no larger than that of T is denoted ... of Kolmogorovcomplexity theory, this calculation is problematic. Quoting Ellsberry and Shallit ...Intelligent Design Specified complexity is an argument proposed by William Dembski and used by him and others ... complexity is a reliable marker of design by an intelligent agent, a central tenet to intelligent ... of specified complexity is widely regarded as mathematically unsound and has not been the basis for further independent work in information theory , complexity theory , or biology . ref cite web url .... 3 8. ref Specified complexity is one of the two main arguments used by intelligent design proponents, the other being irreducible complexity . In Dembski s terminology, a specified pattern is one that admits ... argues that it is impossible for specified complexity to exist in patterns displayed by configurations ... or generate configurations of high specified complexity. In intelligent design literature, an intelligent ... . Touchstone Journal, Volume 12, Issue 4, July August 1999. ref Specified complexity is what Dembski ... Time Magazine, 15 August 2005, page 32 ref Critics also reject applying specified complexity to infer design as an argument from ignorance . Definition Orgel s original use The term specified complexity ... complexity. Crystals are usually taken as the prototypes of simple well specified structures .... The crystals fail to qualify as living because they lack complexity the mixtures of polymers ... Living organisms are mysterious not for their complexity per se, but for their tightly specified complexity ref Paul Davies 1999 . The Fifth Miracle p. 112 ref blockquote Dembski s definition For Dembski, specified complexity is a property which can be observed in living things. However, whereas ... more details
Complexity theory may refer to Computational complexity theory , a field in theoretical computer science and mathematics The study of complex systems Complexity theory and organizations , the application of complexity theory to strategy Complexity economics , the application of complexity theory to economics See also Systems theory Complexity disambig ar fr Th orie de la complexit hr Teorija slo enosti ru ... more details
Strategic complexity may refer to an alternative name for the field of Complexity theory and organizations the degree of complexity of elements of a strategy the number of elements of a strategic activity system, see Competitive Strategy disambig ... more details
In computational complexity theory complexity theory , ZPL Zero error Probabilistic Logarithmic space is the set of problems solvable by a probabilistic Turing machine which always yields the correct answer and uses logarithmic space on average. Probabilistic algorithms that always give the correct answer are called Las Vegas algorithm s. Unlike its deterministic counterpart L complexity L , a ZPL machine can potentially use exponential time by exploiting randomness. If ZPL is restricted to polynomial time, we get the more interesting class ZPLP complexity ZPLP . A surprising result is that ZPL is equal to both RL complexity RL and NL complexity NL thus, if a problem can be solved in logarithmic space with nondeterminism or with one sided error, it can be solved with no error and logarithmic space on average. See the articles on RL complexity RL and NL complexity NL for more information about ZPL. category Probabilistic complexity classes comp sci theory stub ... more details
In computational complexity theory , the complexity class NE is the set of decision problem s that can be solved by a non deterministic Turing machine in time Big O notation O k sup n sup for some k . NE , unlike the similar class NEXPTIME , is not closed under Polynomial time reduction polynomial time many one reduction s. See also E complexity . References ComplexityZoo NE N ne . comp sci theory stub DEFAULTSORT Ne Complexity Category Complexity classes ... more details
In Computability theory computer science computability and Computational complexity theory complexity theory , ALL is the class of all decision problem s. Relations to other classes ALL contains all complexity classes of decision problems, including RE complexity RE and co RE . External links CZoo Class ALL A all ComplexityClasses Category Complexity classes es ALL clase de complejidad zh ALL ... more details
Computational Complexity may refer to Computational complexity theory Computational Complexity journal disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
Accidental complexity is complexity that arises in computer program s or their development process computer programming which is non essential to the problem to be solved. While essential complexity is inherent and unavoidable, accidental complexity is caused by the approach chosen to solve the problem. ref cite book last Holt first John title UML for systems engineering watching the wheels ISBN 978 0 86341 354 4 pages 8 publisher Institution of Engineering and Technology IET date 2004 ref While sometimes accidental complexity can be due to mistakes such as ineffective planning, or low priority placed on a project, some accidental complexity always occurs as the side effect of solving any problem. For example, the complexity caused by out of memory errors is an accidental complexity to most programs that occurs because one decided to use a computer to solve the problem. While accidental complexity is to be minimized in any good architecture, design, and implementation, excessive accidental complexity is an example of an anti pattern . References reflist Category Anti patterns Category Software project management Category Articles lacking sources from June 2009 Category All articles lacking sources comp sci stub compu prog stub es Accidental complexity it Complessit involontaria ... more details
Synchronization Complexity is a quantified attribute see also measurement of a characteristic of a concurrent software product. It measures the additional complexity incurred by the synchronization constructs used in the software, and does that by analyzing the software source code. It is essentially an extension of the Cyclomatic complexity for multitasking multithreaded programs. Further reading http www.synchronizationcomplexity.com Synchronization Complexity Category Software metrics soft eng stub he ... more details
In computational complexity theory , a certificate also called a witness is a string that certifies the answer to a computation, or certifies the membership of some string in a language. A certificate is often thought of as a solution path within a verification process, which is used to check whether a problem gives the answer Yes or No . In the decision tree model of computation, certificate complexity is the minimum number of the math n math input variables of a decision tree that need to be assigned a value in order to definitely establish the value of the Boolean function math f math . References Citation last1 Buhrman first1 Harry last2 Wolf first2 Ronald title Complexity Measures and Decision Tree Complexity A Survey year 2002 . http www.cs.princeton.edu theory complexity dectreechap.pdf Computational Complexity a Modern Approach by Sanjeev Arora and Boaz Barak Category Computational complexity theory comp sci theory stub ... more details
Complexity management is a business methodology that deals with the analysis and optimization of complexity in enterprises. Effects of complexity pertain to all business process es along the value chain and hence complexity management requires a holism holistic approach. Effective complexity management ... over all costs and values of complexity, an approach which identifies the optimization benefits, related ... ensurement of the sustainable infrastructure such as IT tools, incentives and processes. Complexity ... analytics and simulation of complexity optimization measures and their related domino effects within the entire value chain. Fields of complexity in enterprises Complexity appears in the following ... involved Complexity in enterprises is driven by Market volatility changing market conditions like raw material supply and sales volumes drive business process complexity Fragmented customer demands drive product portfolio and feature complexity Globalization drives complexity of served markets and company locations Mergers & acquisitions drive complexity in all fields Silo oriented cultures drive complexity in organization, IT systems and business processes Increasing customer pressure drives complexity in product portfolio and features Approach Constant complexity management can result in a significant ... more than 1billion each due to unnecessary complexity. ref cite news last Chynoweth first Carly ... . Strategy The relevance of complexity for the success of a given business model is being evaluated. If complexity has an important role for the success of an enterprise it needs to be embedded in the corporate strategy . Transparency Fact based transparency over the costs of complexity as well as its value is created along the entire value chain. The structure of complexity is analyzed and visualized by using tools such as variant trees or complexity funnels. Quantitative transparency regarding true contribution is established by a pragmatic activity based costing effort. Good complexity value ... more details
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