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 ... s largest companies are on average losing more than 1billion each due to unnecessary complexity ... date 13 March 2011 ref Reducing complexity requires subsequent activities around the four pillars strategy ... of complexity for the success of a given business model is being evaluated. If complexity has ... . 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 adding is distinguished ... more details
In computational complexity theory , the complexity class FL is the set of function problem s which can be solved by a deterministic Turing machine in a logarithm ic amount of memory space . Citation needed date September 2009 As in the definition of L complexity L , the machine reads its input from a read only tape and writes its output to a write only tape the logarithmic space restriction applies only to the read write working tape. Loosely speaking, a function problem takes a complicated input and produces a perhaps equally complicated output. Function problems are distinguished from decision problem s, which produce only Yes or No answers and corresponds to the set L complexity L of decision problem s which can be solved in deterministic logspace. FL is a subset of FP complexity FP , the set of function problems which can be solved in deterministic polynomial time . FL is known to contain several natural problems, including the multiplication of two numbers. Similarly one may define FNL , which has the same relation with NL complexity NL as FNP complexity FNP has with NP complexity NP . References refbegin C. Alvarez and B. Jenner. A very hard log space counting class, Theoretical Computer Science 107 3 30, 1993. defined FNL, but not FL refend External links CZoo FNL F fnl DEFAULTSORT Fl Complexity Category Complexity classes comp sci theory stub ... more details
Second order logic is an extension of FO complexity first order with second order logic second order s quantifiers, hence the reader should first read FO complexity to be able to understand this article. In descriptive complexity we can see that the languages recognised by SO formulae is exactly equal to the language decided by a Turing machine in the PH complexity polynomial hierarchy . Extensions of SO with some operators also give us the same expressivity than some well known complexity class . ref N. Immerman Descriptive complexity 1999 Springer , Every information of this page can be checked in this book. ref , so it is a way to do proofs about the complexity of some problems without having ... of FO complexity FO formulae where we add quantification over second order variables, hence we will use the terms defined in the FO complexity FO article without defining them again. Property Normal ... on variable on second order and then a FO formula in prenex normal form. Relation to complexity classes SO is equal to Complexity Zoo P PH PH , more precisely we have that formula in prenex ... to math Sigma 1 math which is NP complexity NP , and with only universal quantification is equal .... This class is equal to P complexity P . Those formulaes can be made in prenex form where the second ... OR there is at most two variables. This class is equal to NL complexity NL . Those ... without loss of generalities. Transitive closure is PSPACE SO tc is to SO what FO complexity Transitive closure is NL FO TC is to FO complexity FO . The TC operator can now also take second order variable as argument. SO TC is equal to Complexity Zoo P pspace PSPACE . Least fixed point is EXPTIME SO LFP is to SO what FO complexity Least Fixed Point is PTIME FO LFP is to FO complexity FO . The LFP ... SO t n is to SO what FO complexity Iterating FO t n is to FO complexity FO . But we now also ... another way to write SO LFP See also FO complexity First order HO complexity High order References ... more details
Context date October 2009 In theoretical computer science, Almost Wide Probabilistic Polynomial Time AWPP is a complexity class for problems in the context of quantum computing . AWPP contains the BQP Bounded error, Quantum, Polynomial time class, which contains the decision problem s solvable by a quantum computer in polynomial time , with an error probability of at most 1 3 for all instances. In fact, it is the best known classical upper bound for BQP. Furthermore, it is contained in the APP complexity class APP class. References references http people.cs.uchicago.edu fortnow papers quantum.pdf Provides information on the connection between various complexity classes. http eccc.hpi web.de eccc reports 2002 TR02 036 index.html Definition of AWPP and connection to APP and PP. http arxiv.org abs cs 9811023 Proof of BPQ in AWPP. Gap definable counting classes by S. Fenner, L. Fortnow, and S. Kurtz from the Journal of Computer and System Sciences. Pages 116 148, 1994, issue 48. Contains definitions. An oracle builder s toolkit by S. Fenner, L. Fortnow, S. Kurtz, and L. Li. in 8th IEEE Structure in Complexity Theory Conference Proceedings. Pages 120 131, 1993. Contains definitions. http qwiki.stanford.edu index.php Complexity Zoo A awpp Complexity Zoo Contains a list of complexity classes, including AWPP, and their relation to other classes. Category Probabilistic complexity classes Category Quantum complexity theory ... 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 zh NE ... more details
Logarithmic Hierarchy is the complexity class of all computational problem s solvable in a Logarithmic growth logarithmic amount of computation time on an alternating Turing machine with a bounded number of alternation. It is a special case of hierarchy of Alternating Turing machine Bounded alternation bounded alternating Turing machine . It is equal to FO complexity FO and to FO complexity FO uniform AC0 ref N. Immerman Descriptive complexity 1999 Springer , page 85. ref . The math i math th level of the Logarithmic Time Hierarchy is the set of languages recognised by alternating Turing machine in logtime with Random access Turing machine random access and math i 1 math alternation, beginning with existential state. LH is the union of all levels. References Reflist ComplexityClasses Category Complexity classes Comp sci theory stub ... more details
Programming complexity or software complexity is a term that encompasses numerous properties of a piece of software, all of which affect internal interactions. According to several commentators, there is a distinction between the terms complex and complicated. Complicated implies being difficult to understand but with time and effort, ultimately knowable. Complex, on the other hand, describes the interactions between a number of entities. As the number of entities increases, the number of interactions ... to know and understand all of them. Similarly, higher levels of complexity in software increase ... impossible. The idea of linking software complexity to the maintainability of the software has been ... one that uses deterministic complexity models. Measures Many measures of software complexity have been proposed. Many of these, although yielding a good representation of complexity, do not lend themselves to easy measurement. Some of the more commonly used metrics are cyclomatic complexity McCabes cyclomatic complexity metric Halstead complexity measures Halsteads software science metrics Henry ... ref which measures complexity as a function of fan in and fan out. They define fan in of a procedure ... to and from procedures that call or are called by, the procedure in question. Henry and Kafura s complexity .... They introduce six OO complexity metrics weighted methods per class, coupling between object classes ... There are several other metrics that can be used to measure programming complexity Branching complexity Sneed Metric Data access complexity Card Metric Data complexity Chapin Metric Data flow complexity Elshof Metric Decisional complexity McClure Metric Types Associated with, and dependent on the complexity of an existing program, is the complexity associated with changing the program. The complexity ... complexity 1 nowiki nowiki . ref Accidental complexity Relates to difficulties a programmer faces ... language may reduce it. Essential complexity Is caused by the characteristics of the problem ... more details
In computational complexity theory , EQP sometimes called QP , which stands for exact quantum polynomial time, is the class of decision problems solvable by a quantum computer which outputs the correct answer with probability 1 and runs in polynomial time with probability 1. It is the quantum analogue of the complexity class P complexity P . In other words, there is an algorithm for a quantum computer a quantum algorithm that solves the decision problem exactly and is guaranteed to run in polynomial time. References references CZoo EQP E eqp quantum computing ComplexityClasses Category Quantum complexity theory ... more details
In computational complexity theory , the complexity class PH is the union of all complexity classes in the polynomial hierarchy math mbox PH bigcup k in mathbb N Delta k mbox P math PH was first defined by Larry Stockmeyer . It is a special case of hierarchy of Alternating Turing machine Bounded alternation bounded alternating Turing machine . It is contained in P sup P sup P sup PP sup by Toda s theorem the class of problems that are decidable by a polynomial time Turing machine with access to a Sharp P P or equivalently PP complexity class PP oracle machine oracle , and also in PSPACE . PH has a simple descriptive complexity logical characterization it is the set of languages expressible by second order logic . PH contains almost all well known complexity classes inside PSPACE in particular, it contains P complexity P , NP complexity NP , and co NP . It even contains probabilistic classes such as Bounded error probabilistic polynomial BPP and RP complexity RP . However, there is some evidence that BQP , the class of problems solvable in polynomial time by a quantum computer , is not contained in PH Aaronson 2010 . P NP if and only if P PH . This may simplify a potential proof of P NP , since it s only necessary to separate P from the more general class PH . References Larry J. Stockmeyer , The polynomial hierarchy , Theoretical Computer Science , Vol. 3 1976 , pp. 1 22. Scott Aaronson , BQP and the Polynomial Hierarchy, ACM STOC 2010 , arxiv 0910.4698 , ECCC 2009 09 104 . CZoo PH P ph ComplexityClasses Category Complexity classes comp sci theory stub es PH clase de complejidad ko PH ja PH ru PH zh PH ... more details
Unreferenced date February 2007 In computational complexity theory , the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently, if we define decision problems as sets of finite strings, then the complement set theory complement of this set over some fixed domain is its complement problem. For example, one important problem is whether a number is a prime number . Its complement is to determine whether a number is a composite number a number which is not prime . Here the domain of the complement is the set of all integers exceeding one. There is a Turing reduction from every problem to its complement problem. The complement operation is an Involution mathematics involution , meaning it undoes itself , or the complement of the complement is the original problem. We can generalize this to the complement of a complexity class , called the complement class , which is the set of complements of every problem in the class. If a class ... of the complexity class itself as a set of problems, which would contain a great deal more problems ... classes, especially NP complexity NP , are believed to be distinct from their complement classes although this has not been proven . The closure mathematics closure of any complexity class under Turing ..., such as the integer factorization , which is in the intersection of NP complexity NP and co NP . Every deterministic complexity class DSPACE f n , DTIME f n for all f n is closed under complement ... for nondeterministic complexity classes, because if there exist both computation paths which accept ... surprising complexity results shown to date showed that the complexity classes NL complexity NL and SL complexity SL are in fact closed under complement, whereas before it was widely believed they were ... equals L complexity L , which is a deterministic class. Every class which is low complexity low for itself is closed under complement. Category Computational complexity theory pl Dope nienie teoria ... more details
orphan date August 2009 Integrative complexity is a research Psychometrics psychometric that refers to the degree to which thinking and reasoning involve the recognition and integration of multiple Perspective cognitive perspectives and possibilities and their interrelated Contingency contingencies . ref http www.stanford.edu group diversity coding.htm Integrative Complexity Bot generated title ref Integrative complexity is a measure of the intellectual style used by individuals or groups in processing information, problem solving , and decision making . Complexity looks at the structure of one s thoughts, while ignoring the contents. It is scorable from almost any Language verbal materials Writing written materials, such as book s, Article publishing articles , Letter message letters , and transcript as well as audio visual material. The measure of integrative complexity has two components differentiation and integration. Differentiation refers to the perception of different dimension s when considering an issue. Integration refers to the Recall memory recognition of cognitive connections among differentiated dimensions or perspectives. ref http www.psych.ubc.ca psuedfeld CXY.html Suedfeld s Integrative Complexity Research Bot generated title ref In a 1988 study it was demonstrated that changes in Integrative Complexity could be potentially used in international violence prediction . ref http jcr.sagepub.com cgi content abstract 32 4 626 Changes in Integrative Complexity Prior to Surprise Attacks, J. of Conflict Resolution 32 4 by Suedfeld and Bluck 1988 . ref These findings were seen again a 1995 article by Guttieri, Wallace, and Suedfeld looking at the Cuban Missile Crisis . ref http jcr.sagepub.com cgi content abstract 39 4 595 The Integrative Complexity of American Decision Makers in The Cuban Missile Crisis, J. of Conflict Resolution 39 4 . ref References reflist Category Experimental psychology psych stub ... more details
In circuit complexity , AC is a complexity class hierarchy. Each class, AC sup i sup , consists of the formal language languages recognized by Boolean circuit s with depth math O log i n math and a polynomial polynomial number of fanin unlimited fanin AND gate AND and OR gate s. The name AC was chosen by analogy to NC complexity NC , with the A in the name standing for alternating and referring both to the alternation between the AND and OR gates in the circuits and to alternating Turing machine s. ref harvtxt Regan 1999 , page 27 18. ref The smallest AC class is AC0 AC sup 0 sup , consisting of constant depth unlimited fanin circuits. The total hierarchy of AC classes is defined as blockquote math mbox AC bigcup i geq 0 mbox AC i math blockquote Relation to NC The AC classes are related to the NC complexity NC classes, which are defined similarly, but with gates having only constant fanin. For each i , we have math mbox NC i subseteq mbox AC i subseteq mbox NC i 1 . math As an immediate consequence of this, we have that NC AC. Variations The power of the AC classes can be affected by adding additional gates. If we add gates which calculate the modulo operation for some modulus m , we have the classes ACC complexity ACC sup i sup m . Notes reflist References citation last Regan first Kenneth W. contribution Complexity classes title Algorithms and Theory of Computation Handbook publisher CRC Press year 1999 . citation last Vollmer first Heribert title Introduction to Circuit Complexity year 1999 publisher Springer Verlag location Berlin isbn 3 540 64310 9 . ComplexityClasses Category Circuit complexity Category Complexity classes ... more details
Citations missing date October 2008 In computational complexity theory , a computational problem is complete for a complexity class if it is, in a formal sense, one of the hardest or most expressive problems in the complexity class. If a problem has the property that if you know how to solve it it allows to quickly solve any problem in a complexity class, it is called hard for that class. More formally, a problem p is called hard for a complexity class C under a given type of reduction complexity reduction , if there is a reduction of this type from any problem in C to p . If a problem is both hard for a class, and a member of the class, it is complete for that class under the given type of reduction . A problem that is complete for a class C is said to be C complete , and the class of all problems complete for C is denoted C complete . The first complete class to be defined and the most well known is NP complete , a class that contains many difficult to solve problems that arise in practice. Similarly, a problem hard for a class C is called C hard , e.g. NP hard . Normally it is assumed that the reduction in question does not have higher computational complexity than the class itself. Therefore it may be said that if a C complete problem has a computationally easy solution, then all problems in C have an easy solution. Generally, complexity classes that have a recursive enumeration have known complete problems, whereas those that do not, don t have any known complete problems. For example, NP complexity NP , co NP , PLS complexity PLS , PPA complexity PPA all have known natural complete problems, while RP complexity RP , ZPP complexity ZPP , Bounded error probabilistic polynomial BPP and TFNP do not have any known complete problems although such a problem may be discovered in the future . Fact date July 2008 There are classes without complete problems. For example, Sipser ... References reflist Category Computational complexity theory de Vollst ndigkeit Komplexit tstheorie ... more details
Essential complexity refers to a situation where all reasonable solutions to a problem must be complicated and possibly confusing because the simple solutions would not adequately solve the problem. It stands in contrast to accidental complexity , which arises purely from mismatches in the particular choice of tools and methods applied in the solution. This term has been used since, at least, the mid 1980s. Turing Award winner Fred Brooks has used this term and its antonym of accidental complexity since the mid 1980s. He has also updated his views in 1995 for an anniversary edition of Mythical Man Month, chapter 17 No Silver Bullet Refired . ref name Brooks, Proc. IFIP Brooks, Proc. IFIP Brooks, Proc. IFIP ref ref Brooks, IEEE Computer ref ref Brooks, Mythical Man Month, Silver Bullet Refired ref Cyclomatic complexity main Cyclomatic complexity Essential complexity is also used with a different meaning in connection with cyclomatic complexity . In this context, essential complexity refers to the cyclomatic complexity after iteratively replacing all well structured control structures with a single statement. Structures such as if then else and while loops are considered well structured. Unconstrained use of goto statements can produce programs which can not be reduced in this way. For example, the following C program fragment has an essential complexity of 1, because the inner if statement and the for can be reduced for i 0 i 3 i if a i 0 b i 2 The following C program fragment has an essential complexity of more than one. It finds the first row of z which is all zero and puts that index in i if there is none, it puts 1 in i. for i 0 i m i for j 0 j n j if z i j 0 goto non zero ... of the main strategies against essential complexity in No Silver Bullet Decision to decision path Occam s Razor No silver bullet Cyclomatic complexity Further reading cite journal title No Silver Bullet ... Essential Complexity Category Software project management Category Software metrics ... more details
Unreferenced date December 2009 PR is the complexity class of all primitive recursive function s or, equivalently, the set of all formal language s that can be decided by such a function. This includes addition, multiplication, exponentiation, tetration , etc. The Ackermann function is an example of a function that is not primitive recursive, showing that PR is strictly contained in R complexity R . PR functions can be explicitly enumerated, whereas not all functions R can be. This shows that PR has a syntactic definition, whereas R lacks one. On the other hand, we can enumerate any recursively enumerable set see also its complexity class RE complexity RE by a primitive recursive function in the following sense given an input M , k , where M is a Turing machine and k is an integer, if M halts within k steps then output M otherwise output nothing. Then the union of the outputs, over all possible inputs M , k , is exactly the set of M that halt. PR strictly contains ELEMENTARY . References ComplexityZoo PR P pr . ComplexityClasses DEFAULTSORT Pr Complexity Category Complexity classes ko PR ja PR zh PR ... more details
In computational complexity theory , BPL Bounded error Probabilistic Logarithmic space , ref http qwiki.stanford.edu index.php Complexity Zoo B bpl Complexity Zoo BPL ref sometimes called BPLP Bounded error Probabilistic Logarithmic space Polynomial time , ref citation last1 Borodin first1 A. author1 link Allan Borodin last2 Cook first2 S. A. author2 link Stephen Cook last3 Dymond first3 P. W. last4 Ruzzo first4 W. L. last5 Tompa first5 M. doi 10.1137 0218038 issue 3 journal SIAM Journal on Computing pages 559 578 title Two applications of inductive counting for complementation problems volume 18 year 1989 ref is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machine s with two sided error . It is named in analogy with Bounded error probabilistic polynomial BPP , which is similar but has no logarithmic space restriction. The probabilistic Turing machines in the definition of BPL may only accept or reject incorrectly less than 1 3 of the time this is called two sided error . The constant 1 3 is arbitrary any x with 0 x 1 2 would suffice. This error can be made 2 sup p x sup times smaller for any polynomial p x without using ... error is more general than one sided error, RL complexity RL and its complement complexity complement co RL are contained in BPL . BPL is also contained in PL complexity PL , which is similar except that the error bound is 1 2, instead of a constant less than 1 2 like the class PP complexity PP , the class ... in SC complexity SC . ref citation last Nisan first N. authorlink Noam Nisan doi 10.1007 ... issue 1 journal Computational Complexity pages 1 11 title RL SC volume 4 year 1994 ref SC is the class ... simulate logarithmic space probabilistic algorithms. BPL is contained in NC complexity NC and in DSPACE ... Complexity theory lecture notes ref and in L poly . References reflist ComplexityClasses Category Probabilistic complexity classes zh BPL ... more details
Self complexity SC is a term that refers to a person s perceived knowledge of himself or herself, based ... traits, and goals of the individual, ref name Linville85 Linville, P.W. 1985 . Self complexity ... Linville, P.W. 1987 . Self complexity as a cognitive buffer against stress related illness ... complexity theory, an individual who has a number of self aspects that are unique in their attributes will have greater self complexity than one who has only a few self aspects, or whose self aspects are closely associated to one another. ref name Linville87 In other words, self complexity may invoke ..., NY Taylor & Francis. ref The Self Complexity Model The term self complexity was first coined by psychologist ... for self complexity suggests that self aspects are activated in the context of a relevant experience .... ref name Linville87 Consequently, the self complexity model suggests that highly self complex individuals ... and or indistinct self aspects i.e., low self complexity . ref name Linville85 ref name Linville87 ..., J.G., & Rawsthorne, L.J. 2005 . Self complexity and the authenticity of self aspects Effects on well ... relevant feedback individuals high in self complexity will have less of their self concept represented ... ref name Ryan Approaches to Self Complexity Developmental Perspective A variety of different views are held concerning the nature of self complexity. From a developmental perspective, self complexity .... ref name Evans Evans, D.W. 1994 . Self complexity and its relation to development, symptomatology ... self complexity , resulting in a simplified self concept. As children grow in terms of their physical ... a greater number of distinct self aspects i.e., increasing self complexity and thus reflect a more developed ... understanding of self complexity development. Clinical and Personality Perspectives Contrary to the developmental ... protective factors of self complexity that carry into adulthood. ref name Evans Specifically ... personality disorder features The role of self discrepancies and self complexity. Psychology ... more details
In computational complexity theory complexity theory , UP Unambiguous Non deterministic Polynomial time is the complexity class of decision problem s solvable in polynomial time on a non deterministic Turing machine with at most one accepting path for each input. UP contains P complexity P and is contained in NP complexity NP . A common reformulation of NP states that a language is in NP if and only if a given answer can be verified by a deterministic machine in polynomial time. Similarly, a language is in UP if a given answer can be verified in polynomial time, and the verifier machine only accepts at most one answer for each problem instance. More formally, a language L belongs to UP if there exists a two input polynomial time algorithm A and a constant c such that if x in L , then there exists a unique certificate y with y O x sup c sup such that A x,y 1 if x isn t in L, there is no certificate y with y O x sup c sup such that A x,y 1 Algorithm A verifies L in polynomial time. UP and its complement complexity complement co UP contain both the integer factorization problem and parity game problem because determined effort has yet to find a polynomial time solution to any of these problems, it is suspected to be difficult to show P UP , or even P UP co UP . The Valiant Vazirani theorem states that NP is contained in RP sup Promise UP sup , which means that there is a randomized reduction from any problem in NP to a problem in promise problem Promise UP . UP is not known to have any Complete complexity complete problems. ref CZoo UP U up ref References Reflist ComplexityClasses Category Complexity classes es UP clase de complejidad ko UP ja UP zh UP ... more details
In computational complexity theory , the complexity class FNP is the function problem extension of the decision problem class NP complexity NP . The name is somewhat of a misnomer, since technically it is a class of binary relation s, not functions, as the following formal definition explains A binary relation P x , y , where y is at most polynomially longer than x , is in FNP if and only if there is a deterministic not nondeterministic polynomial time algorithm that can determine whether P x , y holds given both x and y . This definition does not involve nondeterminism and is analogous to the verifier definition of NP . See FP complexity FP for an explanation of the distinction between FP and FNP . There is an NP language directly corresponding to every FNP relation, sometimes called the decision problem induced by or corresponding to said FNP relation. It is the language formed by taking all the x for which P x , y holds given some y however, there may be more than one FNP relation for a particular decision problem. Many problems in NP , including many NP complete problems, ask whether a particular object exists, such as a satisfying assignment, a graph coloring, or a clique of a certain size. The FNP versions of these problems ask not only if it exists but what its value is if it does. This means that the FNP version of every NP complete problem is NP hard . Bellare and Goldwasser showed in 1994 using some standard assumptions that there exist problems in NP such that their FNP versions are not self reducibility self reducible , implying that they are harder than their corresponding decision problem. FP FNP if and only if P NP problem P NP . See also TFNP References refbegin Elaine Rich, Automata, computability and complexity theory and applications , Prentice Hall, 2008 .... http citeseerx.ist.psu.edu viewdoc summary?doi 10.1.1.117.4445 The complexity of decision ... FNP F fnp DEFAULTSORT Fnp Complexity Category Complexity classes es FNP clase de complejidad he FNP ... more details
In computational complexity theory , the complexity class FP is the set of function problem s which can be solved by a deterministic Turing machine in polynomial time it is the function problem version of the decision problem class P complexity P . Roughly speaking, it is the class of functions that can be efficiently computed on classical computers without randomization. FP is formally defined as follows A binary relation P x , y is in FP if and only if there is a deterministic polynomial time algorithm that, given x , can find some y such that P x , y holds. The difference between FP and P is that problems in P have one bit, yes no answers, while problems in FP can have any output that can be computed in polynomial time. For example, adding two numbers is an FP problem, while determining if their sum is odd is in P . More complex is the relationship between FP and FNP complexity FNP . FNP is defined as follows A binary relation P x , y , where y is at most polynomially longer than x , is in FNP if and only if there is a deterministic polynomial time algorithm that can determine whether P x , y holds given both x and y . That is, instead of merely verifying y , the algorithm for solving an FP problem must find its value. This is similar to the computation verification relationship between P NP problem P and NP it also shows that FP is contained in FNP . In fact, FP FNP if and only if P NP problem P NP . Polynomial time function problems are fundamental in defining polynomial ... that uses logarithmic space has at most polynomially many configurations, FL complexity FL , the set ... whether FL FP this is analogous to the problem of determining whether the decision classes P complexity P and L complexity L are equal. References Elaine Rich, Automata, computability and complexity theory ... and FNP , pp. 689 694 External links http qwiki.stanford.edu wiki Complexity Zoo F fp Complexity Zoo FP DEFAULTSORT Fp Complexity Category Complexity classes de FP Komplexit tsklasse es FP clase de complejidad ... more details
Multiple issues unreferenced December 2009 wikify December 2009 orphan December 2009 Network complexity is the number of nodes and alternative paths that exist within a computer network , as well as the variety of communication media, communications equipment, protocols, and hardware and software platforms found in the network. Simple network A small LAN with no alternative paths, a single communication protocol, and identical hardware and software platforms across nodes would be classified as a simple network. Complex network an enterprise wide network that uses multiple communication media and communication protocols to interconnect geographically distributed networks with dissimilar hardware and software platforms would be classified as a complex network. DEFAULTSORT Network Complexity Category Computer network analysis Complexity ... more details
In computational complexity theory , L also known as LSPACE is the complexity class containing decision problem s which can be solved by a deterministic Turing machine using a logarithm ic amount of memory space . Logarithmic space is sufficient to hold a constant number of pointer computer programming pointer s into the input and a logarithmic number of boolean flags and many basic logspace algorithms use the memory in this way. L is a subclass of NL complexity NL , which is the class of languages decidable in logarithm ic space on a nondeterministic Turing machine . Using the construction of Savitch s theorem , one can see that NL is contained in the complexity class P complexity P of problems solvable in deterministic polynomial time. Thus L NL P . The inclusion of L into P can also be proved more directly a decider using O log n space cannot use more than 2 sup O log n sup n sup O 1 sup time, because this is the total number of possible configurations. Every non trivial problem in L is Complete complexity complete under log space reduction s so weaker reductions are required to identify meaningful notions of L completeness, the most common being FO complexity first order reductions. Important List of unsolved problems in computer science ... of function problem s is FL complexity FL . FL is often used to define logspace reduction s. A breakthrough ... ST connectivity in Log Space . Omer Reingold. Electronic Colloquium on Computational Complexity ... two vertices in a given undirected graph , is in L , establishing that L SL complexity SL , since ... connected component into a clique graph theory clique . L is low complexity low for itself, because ... space in log space, reusing the same space for each query. Use outside of complexity world The main ... 1993 title Computational Complexity publisher Addison Wesley edition 1st edition isbn 0 201 53082 1 ... the complexity of polynomial size branching program s ComplexityClasses Category Complexity classes ... more details
In computational complexity theory , PLS , which stands for Polynomial Local Search, is a complexity class that models the difficulty of finding a local optimum locally optimal solution to an optimization problem . An instance of PLS has the structure of an implicit graph , defined by a polynomial time algorithm for computing the neighborhood graph theory neighbors of each vertex graph theory vertex in the graph, together with another polynomial time algorithm for computing a cost for each vertex. A valid solution to the instance is a vertex v in the graph for which no neighbor of v has smaller cost. If there is more than one such vertex, they are all valid. Examples of PLS complete problems include local optimum relatives of the travelling salesman problem , maximum cut and satisfiability , as well as finding a pure Nash equilibrium in a congestion game . PLS is a subclass of TFNP , a complexity class closely related to NP that describes computational problems in which a solution is guaranteed to exist and can be recognized in polynomial time. For a problem in PLS, a solution is guaranteed to exist because the minimum cost vertex of the entire graph is a valid solution, and the validity of a solution can be checked by computing its neighbors and comparing the costs of each one. References Citation last1 Yannakakis first1 Mihalis author1 link Mihalis Yannakakis title Equilibria, fixed points, and complexity classes publisher Elsevier year 2009 journal Computer Science Review volume 3 issue 2 pages 71 85 . comp sci theory stub Category Complexity classes he PLS ... more details
In descriptive complexity , a query is a mapping from structures of one signature logic signature to structures of another vocabulary. Neil Immerman , in his book Descriptive Complexity , use s the concept of query as the fundamental paradigm of computation p. 17 . Given signatures math sigma math and math tau math , we define the set of structure mathematical logic structure s on each language, math mbox STRUC sigma math and math mbox STRUC tau math . A query is then any mapping blockquote math I mbox STRUC sigma to mbox STRUC tau math blockquote Computational complexity theory can then be phrased in terms of the power of the mathematical logic necessary to express a given query. Order independent queries A query is order independent if the ordering of objects in the structure does not affect the results of the query. In databases, these queries correspond to generic query generic queries Immerman 1999, p. 18 . This isn t a great reference for this information, since it s in the background section. A reference that goes into more detail would be great. A query is order independent iff math I mathfrak A equiv I mathfrak B math for any isomorphic structures math mathfrak A math and math mathfrak B math . References cite book last Immerman first Neil authorlink Neil Immerman title Descriptive Complexity year 1999 publisher Springer Verlag location New York isbn 0 387 98600 6 comp sci theory stub Category Descriptive complexity ... more details
In computational complexity theory , RL Randomized Logarithmic space , ref CZoo RL R rl ref sometimes called RLP Randomized Logarithmic space Polynomial time , ref A. Borodin, S.A. Cook, P.W. Dymond, W.L. Ruzzo, and M. Tompa. Two applications of inductive counting for complementation problems. SIAM Journal on Computing, 18 3 559&ndash 578. 1989. ref is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machine s with one sided error . It is named in analogy with RP complexity RP , which is similar but has no logarithmic space restriction. The probabilistic Turing machines in the definition of RL never accept incorrectly but are allowed to reject incorrectly less than 1 3 of the time this is called one sided error . The constant 1 3 is arbitrary any x with 0 x 1 would suffice. This error can be made 2 sup p x sup times smaller for any polynomial p x without using more than polynomial time or logarithmic space by running the algorithm repeatedly. Sometimes the name RL is reserved for the class of problems solvable by logarithmic space probabilistic machines in unbounded time. However, this class can be shown to be equal to NL complexity NL using a probabilistic counter, and so is usually referred to as NL instead this also shows that RL is contained in NL . RL is contained in BPL complexity BPL , which is similar but allows two sided error incorrect accepts . RL contains L complexity L , the problems solvable by deterministic Turing machine s in log space, since its definition is just more general. Noam Nisan showed in 1992 the weak derandomization result that RL is contained in SC complexity SC , ref citation last Nisan .... ref This is the holy grail of the efforts in the field of unconditional derandomization of complexity classes. A major step forward was Omer Reingold s proof that SL complexity SL is equal to L . References reflist ComplexityClasses DEFAULTSORT Rl Complexity Category Probabilistic complexity classes ... more details
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