In computational complexity theory , NL Nondeterministic Logarithmic space is the complexity class containing ... ic amount of memory space . NL is a generalization of L complexity L , the class for logspace problems ... It is known that NL is contained in P complexity P , since there is a polynomial time algorithm for 2 satisfiability , but it is not known whether NL P or whether L NL . It is known that NL co NL , where co NL is the class of languages whose complement complexity complement s are in NL . This result ... Theorem , who received the 1995 G del Prize for this work. In circuit complexity , NL can be placed within the NC complexity NC hierarchy. In Papadimitriou 1994, Theorem 16.1, we have math mathbf NC 1 subseteq mathbf L subseteq mathbf NL subseteq mathbf NC 2. math More precisely, NL is contained in AC complexity AC sup 1 sup . It is known that NL is equal to ZPL complexity ZPL , the class ... powerful. Descriptive complexity There is a simple logical characterization of NL it contains .... References CZoo NL N nl cite book last Papadimitriou first C. title Computational Complexity publisher ... . ComplexityClasses DEFAULTSORT NlComplexity Category Complexity classes de NL Komplexit tsklasse es ... Turing machine , we have that L is contained in NL . NL can be formally defined in terms of the computational resource nondeterministic space or NSPACE as NL NSPACE log n . Important results in complexity theory allow us to relate this complexity class with other classes, telling us about the relative ... us which problems can be solved with this resource. Unfortunately, like much of complexity theory, many important questions about NL are still open problem open see Unsolved problems in computer science . Occasionally NL is referred to as RL due to its Probabilistic definition probabilistic definition below however, this name is more frequently used to refer to RL complexity randomized logarithmic space , which is not known to equal NL . NL complete problems Several problems are known to be NL ... more details
wiktionary NL .nlNL can stand for Places Netherlands , ISO 3166 1 alpha 2 country code .nl , the Internet country code top level domain ccTLD for the Netherlands Newfoundland and Labrador , a Canadian Province North Lanarkshire , a council area of Scotland Nuevo Le n , a northeastern Mexican state abbreviation a Finnish abbreviation NL for Neuvostoliitto Soviet Union Computers Newline , a special character in computing signifying the end of a line of text nl Unix , a Unix utility for numbering lines nl format , a file format for presenting mathematical programming problems NLcomplexity , a computational complexity class Abbreviations an abbreviation of Nomen loci Latin for place name Shaheen Air International IATA airline designator National League , one of two leagues in Major League Baseball Other Dutch language , its ISO 639 2 alpha 2 language code Nationale Liste National List , an Israeli political party Turkish new lira , a type of currency No liability , an Australian form of limited liability company New Line , a film production studio Northern line , a London Underground line Northern Lights online game Northern Lights online game , a MUD, or text based online role playing game Normal limits , an acronym used in medicine for a value within reference range disambiguation cs NL de NL es NL eo Nl fa NL fr NL ko NL it NL sw NL lv NL lt NLnlNL ja NL no NL pt NL ro NL ru Nl sk NL sl NL fi Nl sv NL zh NL ... more details
About the top level domain .nl the file format nl format Infobox Top level domain name .nl background CCF image Image Sidn.png .nl Stichting Internet Domeinregistratie Nederland introduced April 25, 1986 ... registration pdf Regulations for registration of .nl domain names disputepolicy http www.sidn.nl ... .nl is the Internet country code top level domain ccTLD for the Netherlands . Registrations are processed ... ccTLD ever to be registered. ref nl http www.sidn.nl nieuws nieuwsbericht article sidn registreert 3000000ste nl domeinnaam SIDN registreert 3.000.000ste .nl domeinnaam SIDN registers 3 millionth .nl domain name , http www.sidn.nl Official website of SIDN ref The authority for the .nl domain was handed over to Piet Beertema of the Centrum Wiskunde & Informatica in 1986. Since January 31, 1996 .nl ... 1900 registrars. ref https www.sidn.nl fileadmin docs PDF files NL Website stats 2011 04 NL.pdf SIDN ... companies, such as Philips Research . Individuals are allowed to register a second level .nl ... a small fee if they cooperate. The cost of a .nl domain varies, but depending on the Domain name registrar registrar the price is around 7 to 15 euro s. 38 of the .nl domains are registered by individuals. ref https www.sidn.nl nieuws nieuwsbericht article in 25 jaar naar ruim 44 miljoen actieve nl domeinnamen SIDN ref References Reflist External links http www.iana.org root whois nl.htm IANA .nl whois information http www.sidn.nl .nl Registry website https www.sidn.nl nc over nl registrar zoeken registrars alfabetisch List of .nl participants http www.nu.nl internet 2498932 ruim 44 miljoen actieve nl domeinnamen.html 4.4 Million active .nl domains Dutch ccTLD DEFAULTSORT Nl Category Country ... of European National Top Level Domain Registries members af .nl ar .nl ast .nl az .nl be .nl be x old .nl bs .nl bg .nl ca .nl cv .nl cs .nl cy .nl da .nl et .nl el .nl es .nl eo .nl eu .nl fa .nl fr .nl xal .nl ko .nl hy .nl hr .nl bpy . id .nl is .nl it .nl krc .nl ka .nl lv .nl lb .nl li .nl ... more details
other uses Complexity disambiguation In general usage, complexity tends to be used to characterize something ... Complexity supramolecular self assembly of synthetic and biological building blocks in water ... b922348g ref there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article. Neil Johnson describes complexity science as the study of the phenomena ... first Neil F. title Two s Company, Three is Complexity A simple guide to the science of all sciences ..., 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 ... regime. Many definitions tend to postulate or assume that complexity expresses a condition of numerous ... are specified. Warren Weaver has posited that the complexity of a particular system is the degree ... unsubstatiated citation please read the discussions page . 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 volume 36 pages 536 44 year 1948 url http www.ceptualinstitute.com ... 2007 11 21 ref Warren Weaver Weaver s paper has influenced contemporary thinking about complexity ... spaces might be summarized as implying that complexity arises from the number of distinguishable relational ... set out herein. Disorganized complexity vs. organized complexity One of the problems in addressing complexity issues has been formalizing the intuitive conceptual distinction between the large ... between disorganized complexity and organized complexity . In Weaver s view, disorganized complexity ... more. Though the interactions of the parts in a disorganized complexity situation can be seen as largely ... methods. A prime example of disorganized complexity is a gas in a container, with the gas ... more details
Multiple issues expert subject March 2010 confusing March 2010 In computational complexity theory , NL complete is a complexity class which is complete complexity complete for NLcomplexityNL , the complexity class containing decision problem s which can be solved by a nondeterministic Turing machine using L complexity a logarithmic amount of memory space . It contains the most difficult or expressive problems in NL . If a method exists for solving any one of the NL complete problems in logarithmic memory space, then NL L . One important NL complete problem is ST connectivity or Reachability Papadimitriou 1994 Thrm. 16.2 , the problem of determining whether, given a directed graph G and two nodes s and t on that graph, there is a path from s to t . ST connectivity can be seen to be in NL , because we start at the node s and nondeterministically walk to every other reachable node. ST connectivity can be seen to be NL hard by considering the computation state graph of any other NL algorithm, and considering that the other algorithm will accept if and only if there is a nondetermistic path from the starting state to an accepting state. Another important NL complete problem is 2 satisfiability Papadimitriou 1994 Thrm. 16.3 , the problem of determining whether a boolean formula in conjunctive normal form with two variables per clause is satisfiable. References cite class book style font style normal Christos Papadimitriou Papadimitriou, Christos H. & 32 1994 . Computational Complexity , Reading, Massachusetts & 32 Addison Wesley. ISBN 0 201 53082 1. cite DEFAULTSORT Nl Complete Category complexity classes ... more details
lowercase nlnl is a Unix utility for numbering lines, either from a file or from standard input, reproducing output on standard output. It has a number of switches a number all lines t number lines with printable text only n no line numbering string number only those lines containing the regular expression defined in the string supplied. The default applied switch is t . nl also supports a number of command line options. Example nl tf 1 echo press cr 2 read cr 3 done The following example numbers only the lines that begin with a capital letter A matching on the regular expression A . filename is optional. nl b p A filename apple 1 Apple BANANA 2 Allspice strawberry It can be useful as an alternative to tt grep grep n tt cat somefile aaa bbb ccc ddd nl somefile grep ccc 3 ccc See also wc Unix wc the word count command cat Unix cat concatenate command n flag is equivalent to nl a List of Unix programs External links http www.linuxmanpages.com man1 nl.1.php The program s manpage Category Unix SUS2008 utilities el Nl Unix fr Nl Unix ru Nl ... more details
TMF NL is a digital music television channel broadcasting on all major digital platform in the Netherlands since 2005. The channel only plays videos by Dutch artists and is a spin off of successful Dutch music channel The Music Factory TMF . MTV Networks MTV Networks Europe Viacom Category Dutch television programs Netherlands tv stub Tv prog stub nl TMF NL ... more details
Infobox file format icon logo screenshot extension .nl mime type code uniform type magic owner Robert Fourer br David Gay br Brian Kernighan br Bell Labs genre mathematical programming container for contained by extended from extended to standard free lowercase nlnl is a file format for presenting and archiving mathematical programming problems. ref cite techreport author David Gay title Writing .nl Files institution Sandia National Laboratories year 2005 address Albuquerque, NM url http citeseerx.ist.psu.edu viewdoc download?doi 10.1.1.60.9659&rep rep1&type pdf format Portable Document Format PDF ref It supports Linear programming linear and Nonlinear programming nonlinear optimization problems as well as Complementarity theory complementarity problems MPECs , in discrete or continuous variables. Initially this format has been invented for connecting solvers to AMPL ref cite techreport author David Gay title Hooking Your Solver to AMPL institution Bell Laboratories year 1993 number 97 4 06 address Murray Hill, NJ url http www.ampl.com REFS hooking2.pdf format Portable Document Format PDF ref but then it has been adopted by other systems such as COIN OR as one of the input formats and FortSP for interacting with external solvers. The nl format is low level and is designed for compactness, not for readability. It has both binary and textual representation. Many solvers such as CPLEX , Gurobi and MOSEK accept this format either directly or through special driver programs. The AMPL Solver Library ASL which allows to read the nl files and provides the automatic differentiation functionality is open source. It is used in many solvers to implement AMPL connection. References Reflist See also sol format a file format for presenting solutions of mathematical programming problems Category Mathematical optimization Category Operations research Category Mathematical optimization software Category Computer file formats uk nl ... more details
NL Industries NYSE NL , the former National Lead Company is lead smelting company now based in Houston, Texas . File NL Industries Dutch Boy Paint Specimen Stock Certificate, c.1975.jpg thumb NL Industries Dutch Boy Paint Specimen Stock Certificate, c.1975 History It began business in Philadelphia in 1772. The name National Lead Company was used since 1891 after a series of mergers. During WWII, National Lead later NL entered the consumer market for titanium paints, creating a product line under the name Dutch Boy. Dutch Boy paints competed with other brands that contained mineral products supplied by National Lead.National Lead Company changed its name to NL Industries in 1971. The company headquarters is in Houston, Texas . ref cite web url http www.library.hbs.edu hc lehman chrono.html?company national lead company title National Lead Company accessdate 2011 10 24 quote The National Lead Company, now known as NL Industries, began business in Philadelphia in 1772. Several lead manufacturers banded together and incorporated as the National Lead Company in 1891. The company has been well known for its white lead paints, sold since 1907 under the Dutch Boy label. Over the twentieth century, the company has produced many other products, including titanium dioxide paint, atomic bomb elements, and ball bearing slides. ... publisher Harvard University ref National Lead was one of the 12 original stocks included in the Dow Jones Industrial Average at the time of its creation on May 26, 1896. ref http www.fool.com Features 1996 sp0529a.htm History of the Dow , The Motley Fool , May 29, 1996. Accessed October 24, 2011. ref References reflist External links official http www.nl ind.com Category 1772 establishments Category Lead Category History of Philadelphia, Pennsylvania Category Companies based in Houston, Texas Category Former components of the Dow Jones Industrial Average ... more details
primarysources date May 2010 Infobox Sport governing body assocname Baseball NL abbrev logo Logo baseball nl.jpg sport Baseball category image caption jurisdiction Newfoundland and Labrador founded Start date yyyy aff affdate region regionyear headquarters location president John Janes chairman chiefexec secretary coach womenscoach key staff operating income sponsor Sport Canada , Baseball Canada year closed replaced prevfounded url sport.ca nlbaseball countryflag Canada countryflag2 Newfoundland and Labrador Baseball NL is the provincial governing body for baseball in Newfoundland and Labrador . ref http www.sport.ca nlbaseball ref References references Category Sport in Newfoundland and Labrador Category Baseball governing bodies in Canada Baseball in Canada ... more details
of the late Pim Fortuyn . The E n in the name E n NL , meaning one , emphasizes national unity where NL is the standard abbreviation of the Netherlands. The party broadly stands for opposition to mass ... , joined the party ref nl icon cite news title LPF zet Eerdmans uit fractie url http www.nos.nl nos ... Groep Eerdmans Van Schijndel . ref nl icon cite news title Eerdmans met Van Schijndel in n fractie ... date 2006 09 24 ref The definitive list of candidates was presented on September 30, 2006. ref nl ... this. ref nl icon cite news title Islam lijkt op oprukkend nazisme url http www.nos.nl nosjournaal ... itself but on islamization as a civic phenomenon. ref nl icon cite news title Pastors hoeft ... niet terug te nemen vk.html publisher Nu.nl date 2006 11 22 ref Elections E n NL took part in the Dutch ... Labour Party minister Wim Kok in 1991. ref nl icon cite news title E nNL wil afschaffing ontwikkelingsgeld ... Elsevier magazine Elsevier date 2006 10 06 ref The key issues are ref nl icon Election program ... Political parties in the Netherlands Category Political parties established in 2006 de E nNL nl E nNL ... more details
Infobox Company company name Ben company logo File Ben NL logo.png company type Subsidiary of T Mobile foundation 1999 Relaunched as a brand in March 2008 industry Wireless Services products Global System for Mobile Communications GSM , General Packet Radio Service GPRS , Enhanced Data Rates for GSM Evolution EDGE , Universal Mobile Telecommunications System UMTS HSDPA , Wireless LAN WLAN Hotspots WiFi , Mobile VoIP T Mobile HotSpot Home homepage http www.ben.nl www.ben.nl Ben NL or Ben is a Netherlands Dutch virtual mobile network operated by T Mobile NL. It offers voice, text and data service at highly discounted rates. Ben only offers 3 subscription types ranging in price from 4,95 for 100 minutes text messages per month to 14,95 for 500 minutes text messages per month. In order to keep its prices down, Ben has a very limited customer service offering a Ben subscription can only be purchased online and most customer administration is in the form of online self service. Also, Ben does not offer subsidies for new handsets. Instead it assumes that its customers will already have a handset. Ben offers its voice, text and data services on the Global System for Mobile Communications GSM , General Packet Radio Service GPRS , Enhanced Data Rates for GSM Evolution EDGE and Universal Mobile Telecommunications System UMTS HSDPA networks of its parent company T Mobile NL. History On August 28, 2000, Belgacom, T Mobile International, and Tele Danmark applied for permission to share control of Ben Nederland Holding Ben . At that time, Belgacom was the principal telecommunications provider in Belgium, Tele Danmark the principal telecommunications provider in Denmark, and T Mobile International a mobile telephony service provider and subsidiary of Deutsche Telekom. Ben was to become ... mobile telecommunications assets, and the name Ben was changed to T Mobile NL. The name and trademark ... nl Ben mobiele communicatie ... more details
primarysources date July 2008 Infobox University name Kaospilots Netherlands native name image name latin name established endowment staff faculty president principal rector chancellor vice chancellor dean head label head students undergrad postgrad doctoral city Rotterdam state country Netherlands campus free label free colors colours mascot affiliations website http www.knowmads.nl Kaospilots was a school located in Rotterdam , the Netherlands from 2007 2009. It was a partner school to the original KaosPilot school in Denmark. The Kaospilots program is based in the real world and includes multiple projects with partners and clients of the school. Educational subjects are Entrepreneurship & New Business Design Social Innovation & Sustainability Marketing & Creativity Personal Leadership International Project Design Process Design In 2009 the school Kaospilot NL closed. After the close down of Koaspilots NL some of its former students and staff, in particular, Pieter Spinder started their own school called Knowmads. References references External links http knowmads.nl Knowmads http www.kaospilot.dk KaosPilots Denmark coord missing Netherlands Category Business schools in the Netherlands fr KaosPilots ... 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 NLcomplexityNL 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 NLcomplexityNL for more information about ZPL. Category Probabilistic complexity classes comp sci theory stub ... 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 NLcomplexityNL 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
OR there is at most two variables. This class is equal to NLcomplexityNL . Those ...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 ... are equal to NL SO Krom is the set of boolean queries definable with second order formulae in conjunctive ... 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 ... more details
surprising complexity results shown to date showed that the complexity classes NLcomplexityNL and SL complexity SL are in fact closed under complement, whereas before it was widely believed they were ...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 ... 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
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 NLcomplexityNL , 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 ... configurations. Every non trivial problem in L is Complete complexity complete under log space reduction ... common being FO complexity first order reductions. Important List of unsolved problems in computer science open problems include whether L P , and whether L NL . The related class 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 ... L and NL, pp.294 296. cite book author Michael R. Garey and David S. Johnson year 1979 title Computers ... the complexity of polynomial size branching program s ComplexityClasses Category Complexity classes ... more details
Wiktionary complexity In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. Complexity may also refer to Complex systems Complexity theory disambiguation Kolmogorov complexity Los Angeles Complexity , a professional gaming team Computational complexity theory , in computer science Game complexity Computational complexity of mathematical operations Time complexity See also Complex disambiguation Disambig es Complejidad desambiguaci n ... 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 NLcomplexityNL 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
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
Complexity theory may refer to The study of a complex system or complex systems Complexity theory and organizations , the application of complexity theory to strategy Complexity economics , the application of complexity theory to economics Chaos theory , the study of the behavior of dynamical systems that are highly sensitive to initial conditions Computational complexity theory , a field in theoretical computer science and mathematics Algorithmic information theory See also Systems theory Complexity Disambiguation ar fr Th orie de la complexit hr Teorija slo enosti ru ... more details
In computational complexity theory , SC Steve s Class, named after Stephen Cook ref ComplexityZoo SC S sc ref is the complexity class of problems solvable by a deterministic Turing machine in polynomial time class P complexity P and polylogarithmic space class PolyL that is, Big O notation O log n sup k sup space for some constant k . It may also be called DTISP poly, polylog , where DTISP stands for deterministic time and space . Note that the definition of SC differs from P math cap math PolyL , since for the former, it is required that the algorithm runs both in polynomial time and polylogarithmic space while for the latter, two separate algorithms will suffice One that runs in polynomial time, and another which runs in polylogarithmic space it is unknown whether these are equivalent . Deterministic context free language DCFL , the strict subset of context free language s recognized by deterministic pushdown automaton deterministic pushdown automata , is contained in SC , as shown by Cook in 1979. ref S. A. Cook. Deterministic CFL s are accepted simultaneously in polynomial time and log squared space. Proceedings of ACM STOC 79, pp. 338&ndash 345. 1979. ref It is open if directed st connectivity is in SC , although it is known to be in P math cap math PolyL because of a DFS algorithm and Savitch s theorem . This question is equivalent to NLcomplexityNL SC . RL complexity RL and BPL complexity BPL are classes of problems acceptable by probabilistic Turing machines in logarithmic space and polynomial time. Noam Nisan showed in 1992 the weak derandomization result that both are contained in SC . ref citation last Nisan first Noam author link Noam Nisan contribution RL SC doi 10.1145 129712.129772 location Victoria, British Columbia, Canada pages 619 623 title Proceedings of the 24th ACM Symposium on Theory of computing STOC 92 year 1992 . ref In other words, given polylogarithmic .... References reflist comp sci theory stub ComplexityClasses DEFAULTSORT Sc Complexity Category Complexity ... more details
Refimprove date December 2009 In computational complexity theory , an advice string is an extra input to a Turing machine which is allowed to depend on the length n of the input, but not on input itself. A decision problem is in the complexity class P f n if there is a polynomial time Turing machine M with the following property for any n , there is an advice string A of length f n such that, for any input x of length n , the machine M correctly decides the problem on the input x , given x and A . The most common complexity class involving advice is P poly where advice length f n can be any polynomial in n . P poly is equal to the class of decision problems such that, for every n , there exists a polynomial size Boolean circuit correctly deciding the problem on all inputs of length n . One direction of the equivalence is easy to see. If, for every n , there is a polynomial size Boolean circuit A n deciding the problem, we can use a Turing machine that interprets the advice string as a description of the circuit. Then, given the description of A n as the advice, the machine will correctly decide the problem on all inputs of length n . The other direction uses a simulation of a polynomial time Turing machine by a polynomial size circuit as in one proof of Cook s Theorem . Simulating a Turing machine with advice is no more complicated than simulating an ordinary machine, since the advice string can be incorporated into the circuit. Because of this equivalence, P poly is sometimes defined as the class of decision problems solvable by polynomial size Boolean circuits, or by polynomial ... of length f n gives the complexity class NP complexity NP f n . If we are allowed an advice of length ... than exponential length is not meaningful. Similarly, the class L poly can be defined as L complexity deterministic logspace with a polynomial amount of advice. Known results include The classes NL ... Lipton theorem . References reflist DEFAULTSORT Advice Complexity Category Computational complexity ... more details
machine Space f n NLcomplexityNL Non deterministic Turing machine Space O log n NPSPACE Non deterministic ...In computational complexity theory , a complexity class is a set of Computational problem problems of related resource based complexity. A typical complexity class has a definition of the form the set ... resource resource R, where n is the size of the input. For example, the class NP complexity NP is the set ... Turing machine in polynomial space . The simpler complexity classes are defined by the following ... s. However, complexity classes can be defined based on function problem s an example is FP complexity FP , counting problem complexity counting problem s e.g. Sharp P P , optimization problem s, promise ... Turing machine, but many complexity classes are based on nondeterministic Turing machine s, boolean ... time , logarithmic space , constant depth , etc. Many complexity classes can be characterized in terms of the mathematical logic needed to express them see descriptive complexity . Bounding the computation time above by some concrete function f n often yields complexity classes that depend on the chosen ... are polynomially related Harv Goldreich 2008 loc Chapter 1.2 . This forms the basis for the complexity class P complexity P , which is the set of decision problems solvable by a deterministic Turing machine within polynomial time. The corresponding set of function problems is FP complexity FP . The Blum axioms can be used to define complexity classes without referring to a concrete computational model . Important complexity classes Many important complexity classes can be defined by bounding the time or space used by the algorithm. Some important complexity classes of decision problems defined in this manner are the following class wikitable Complexity class Model of computation Resource constraint DTIME f n Deterministic Turing machine Time f n P complexity P Deterministic Turing machine ... Turing machine Time f n NP complexity NP Non deterministic Turing machine Time poly n NEXPTIME Non deterministic ... more details
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