Meta tags:
Headings (most frequently used words):
complexity, problems, classes, machine, and, problem, np, computational, theory, models, measures, important, on, instances, the, of, other, in, contents, open, intractability, continuous, history, see, also, works, references, external, links, representing, decision, as, formal, languages, function, measuring, size, an, instance, turing, best, worst, average, case, upper, lower, bounds, defining, hierarchy, theorems, reduction, versus, not, known, to, be, or, complete, separations, between, citations, textbooks, surveys,
Text of the page (most frequently used words):
the (356), #complexity (162), displaystyle (155), #problem (121), and (107), time (88), problems (87), that (84), computational (75), for (64), are (62), theory (61), textsf (61), turing (49), this (48), can (47), algorithm (43), classes (43), machine (41), not (37), edit (35), with (29), complete (25), decision (24), polynomial (24), known (24), deterministic (24), computer (23), algorithms (23), input (23), log (23), mathematical (22), hierarchy (22), set (21), computing (21), machines (21), space (21), such (21), instance (21), analysis (20), most (20), one (19), used (19), other (18), mathematics (18), computation (18), size (18), all (18), case (18), from (17), model (17), class (17), which (17), software (16), solve (16), solved (16), many (16), poly (16), non (15), science (15), graph (15), any (15), defined (15), information (14), important (14), these (14), resources (14), more (14), language (13), pspace (13), instances (13), but (13), since (13), models (13), function (12), than (12), some (12), hard (11), has (11), doi (11), 978 (11), isbn (11), however (11), example (11), would (11), solution (11), there (11), integer (11), best (11), big (11), text (10), using (10), number (10), worst (10), average (10), have (10), two (10), given (10), reduction (10), about (9), may (9), different (9), operations (9), list (9), continuous (9), see (9), measures (9), thus (9), equal (9), yes (9), possible (9), particular (9), inputs (9), large (8), systems (8), general (8), network (8), system (8), formal (8), theoretical (8), dtime (8), bpp (8), pdf (8), 2006 (8), isomorphism (8), also (8), each (8), its (8), theorem (8), theorems (8), same (8), then (8), whether (8), answer (8), main (8), reductions (8), lower (8), toggle (7), wikipedia (7), discrete (7), measure (7), field (7), quantum (7), security (7), very (7), another (7), practical (7), much (7), amount (7), between (7), believed (7), factorization (7), bounds (7), taken (7), page (6), was (6), control (6), related (6), numerical (6), differential (6), real (6), history (6), open (6), intractability (6), s2cid (6), versus (6), called (6), when (6), include (6), running (6), based (6), say (6), efficient (6), over (6), they (6), article (6), said (6), difficult (6), how (6), required (6), resource (6), following (6), binary (6), string (6), solving (6), what (6), output (6), languages (5), search (5), use (5), commons (5), retrieved (5), automata (5), programming (5), circuit (5), boolean (5), exptime (5), press (5), new (5), richard (5), combinatorial (5), commonly (5), solvable (5), bounded (5), definition (5), out (5), consider (5), even (5), often (5), does (5), only (5), takes (5), been (5), thesis (5), requires (5), contained (5), graphs (5), because (5), being (5), integers (5), upper (5), their (5), subsection (5), contents (4), view (4), statistics (4), terms (4), category (4), short (4), study (4), states (4), research (4), biology (4), engineering (4), algebraic (4), arithmetic (4), geometry (4), equations (4), abstract (4), type (4), order (4), future (4), electronic (4), design (4), computability (4), requirements (4), specific (4), tools (4), acm (4), proof (4), dspace (4), exponential (4), infeasible (4), bqp (4), feasible (4), links (4), bibcode (4), fortnow (4), 2003 (4), cook (4), york (4), 2009 (4), karp (4), archived (4), original (4), among (4), functions (4), institute (4), babai (4), proved (4), paper (4), edmonds (4), similarly (4), indeed (4), sense (4), intractable (4), cobham (4), etc (4), deciding (4), prime (4), where (4), sqrt (4), means (4), equally (4), reduced (4), notion (4), multiplication (4), into (4), bound (4), mathsf (4), probabilistic (4), tape (4), within (4), usually (4), notation (4), random (4), hide (4), move (4), sidebar (4), statement (3), under (3), organization (3), wikimedia (3), wikidata (3), september (3), lists (3), optimization (3), game (3), probability (3), finite (3), complex (3), linear (3), logic (3), management (3), technology (3), processing (3), digital (3), social (3), modeling (3), multi (3), hardware (3), world (3), wide (3), process (3), development (3), form (3), consumption (3), expspace (3), considered (3), suspected (3), why (3), tractable (3), 1109 (3), arxiv (3), 0001 (3), 1145 (3), stephen (3), studies (3), michael (3), 2008 (3), cambridge (3), computers (3), 2000 (3), springer (3), barak (3), computations (3), reducibility (3), trakhtenbrot (3), 1962 (3), july (3), lászló (3), journal (3), millennium (3), clay (3), ladner (3), chapter (3), references (3), blum (3), axioms (3), earlier (3), definitions (3), before (3), done (3), refer (3), small (3), practice (3), program (3), makes (3), run (3), independent (3), times (3), cases (3), shown (3), less (3), solutions (3), those (3), cannot (3), logarithmic (3), strictly (3), collapse (3), subseteq (3), basis (3), will (3), level (3), respect (3), intermediate (3), vertices (3), although (3), examples (3), question (3), types (3), prize (3), like (3), efficiently (3), member (3), both (3), likely (3), every (3), squaring (3), multiplying (3), way (3), interesting (3), make (3), needed (3), circuits (3), account (3), determinism (3), concrete (3), stated (3), together (3), otherwise (3), analyzing (3), show (3), just (3), sorting (3), costly (3), amortized (3), distribution (3), measuring (3), expressed (3), viewed (3), communication (3), precise (3), total (3), solves (3), difficulty (3), analyze (3), actions (3), bits (3), powerful (3), connected (3), salesman (3), encoded (3), whose (3), encoding (3), alphabet (3), through (3), table (2), mobile (2), contact (2), privacy (2), policy (2), available (2), additional (2), categories (2), link (2), long (2), value (2), description (2), articles (2), fields (2), org (2), portal (2), art (2), mathematicians (2), informal (2), topics (2), algebra (2), physics (2), chemistry (2), applied (2), analytic (2), euclidean (2), combinatorics (2), calculus (2), elementary (2), philosophy (2), foundations (2), major (2), enterprise (2), graphics (2), task (2), distributed (2), method (2), representation (2), intelligence (2), parallel (2), visualization (2), interaction (2), human (2), virtual (2), application (2), methods (2), library (2), storage (2), randomized (2), algorithmic (2), integrated (2), framework (2), operating (2), performance (2), architecture (2), scale (2), interactive (2), nspace (2), ntime (2), nexptime (2), qma (2), zpp (2), should (2), 1994 (2), encyclopedia (2), free (2), external (2), 2002 (2), issn (2), lance (2), homer (2), current (2), 201 (2), proceedings (2), surveys (2), course (2), introduction (2), sipser (2), 1st (2), addison (2), wesley (2), university (2), conceptual (2), goldreich (2), series (2), sciences (2), john (2), parameterized (2), boaz (2), modern (2), approach (2), arora (2), textbooks (2), 1972 (2), eds (2), june (2), boris (2), signalizing (2), transactions (2), 1956 (2), yamada (2), computable (2), ieee (2), lecture (2), hybrid (2), manuel (2), francisco (2), sieve (2), 1016 (2), october (2), 1998 (2), protein (2), structure (2), doesn (2), 2018 (2), citations (2), life (2), work (2), works (2), unsolved (2), limits (2), desirable (2), properties (2), existence (2), levin (2), term (2), myhill (2), sets (2), well (2), somewhat (2), studied (2), 1965 (2), laid (2), devoted (2), various (2), uses (2), always (2), still (2), impractical (2), realistic (2), sizes (2), generally (2), second (2), faster (2), grows (2), conversely (2), take (2), them (2), yet (2), reasonable (2), quadratic (2), satisfiability (2), ptime (2), theoretically (2), infinite (2), literally (2), though (2), nexp (2), unequal (2), either (2), proving (2), separations (2), determining (2), factor (2), fact (2), forms (2), recent (2), questions (2), ability (2), proofs (2), proposed (2), 000 (2), contains (2), special (2), hardest (2), could (2), might (2), finding (2), concept (2), allows (2), larger (2), captures (2), tells (2), subsetneq (2), precisely (2), defines (2), proper (2), quantitative (2), counting (2), npspace (2), nexpspace (2), bounding (2), relation (2), step (2), depend (2), single (2), complexities (2), corresponding (2), constant (2), common (2), factors (2), defining (2), classify (2), maximum (2), today (2), addresses (2), largest (2), assume (2), quicksort (2), uniform (2), others (2), define (2), state (2), steps (2), outputs (2), operate (2), length (2), exists (2), classifying (2), little (2), physically (2), want (2), extra (2), determine (2), branches (2), principle (2), rather (2), computed (2), traveling (2), decide (2), strings (2), objects (2), members (2), choice (2), tries (2), bitstrings (2), adjacency (2), representing (2), version (2), cities (2), latter (2), asks (2), appearance (2), upload (2), file (2), changes (2), read (2), english (2), create (2), donate (2), menu (2), add, topic, cookie, developers, code, conduct, legal, safety, contacts, disclaimers, apply, site, you, agree, registered, trademark, profit, foundation, inc, creative, attribution, sharealike, license, rendered, parsoid, last, edited, august, 2026, utc, hidden, cs1, volume, mdy, dates, 2017, https, index, php, title, computational_complexity_theory, oldid, 1371073639, yale, lux, israel, czech, republic, united, national, gnd, international, authority, databases, wikiproject, education, metamathematics, pseudomathematics, recreational, films, sociology, psychology, linguistics, geology, finance, economics, ethnomathematics, homotopy, geometric, topology, diophantine, trigonometry, synthetic, projective, convex, affine, harmonic, functional, multilinear, homological, group, commutative, glossary, timeline, areas, glossaries, outline, document, educational, word, video, games, voting, cyberwarfare, publishing, healthcare, differentiable, commerce, solid, image, compression, unit, photograph, manipulation, rendering, animation, cross, validation, reinforcement, unsupervised, supervised, learning, methodology, automated, planning, scheduling, vision, knowledge, reasoning, natural, artificial, multiprocessing, multithreading, concurrent, concurrency, ubiquitous, augmented, extended, reality, accessibility, centered, intrusion, detection, services, hacker, cryptography, retrieval, web, marketing, platform, data, mining, multimedia, support, geographic, database, efficiency, semantics, stochastic, source, team, maintenance, deployment, construction, flow, repository, configuration, environment, domain, compiler, paradigm, notations, quality, middleware, interpreter, service, evaluation, scheduler, components, protocol, networks, wireless, sensor, fault, tolerance, cyber, physical, embedded, dependability, processor, acceleration, automation, green, energy, soc, chip, integration, peripheral, printed, board, template, follows, roughly, 2012, classification, probabilistically, checkable, families, arithmetical, grzegorczyk, hierarchies, polyl, nonelementary, fnp, tfnp, apx, reg, acc, dlogtime, scott, aaronson, philosophers, care, ems, 2001, zoo, media, look, wiktionary, dictionary, mertens, stephan, physicists, 633346, 1521, 9615, 5992, 998639, 2002cse, 31m, cond, mat, 0012185, steven, 133, bulletin, eatcs, 1983, overview, 408, 14323396, 0782, 358141, 358144, 400, communications, khalil, hatem, 1976, review, partial, 15497394, 4503, 7489, 800191, 805573, 197, annual, conference, ulery, dana, 2nd, usa, thomson, 534, 95097, 53082, papadimitriou, christos, 1990, mit, 444, 88071, handbook, vol, van, leeuwen, jan, perspective, oded, 1979, books, 247570676, oclc, 0519066, 7167, 1045, freeman, company, guide, completeness, johnson, david, garey, ding, zhu, ker, wiley, sons, 471, 34506, downey, rod, 1999, monographs, berlin, verlag, 387, 94883, fellows, 1193, 68112, zbl, 521, 42426, sanjeev, miller, thatcher, plenum, 103, 2011, lncs, 4800, pillars, update, tabular, operators, uchionnye, zapiski, penzenskogo, pedinstituta, penza, pedagogoical, russian, recursive, 760, tec, 5219459, 1962irtec, 753y, 753, 1985, award, randomness, tomlin, claire, mitchell, ian, bayen, alexandre, techniques, verification, 1001, jproc, 814621, 2003ieeep, 986t, 986, oishi, meeko, campagnolo, survey, 0907, 3117, smale, steve, 1997, univ, 551, 5949193, 1017, s0962492900002774, 1997acnum, 523s, 523, acta, numerica, zobel, justin, 2015, 44716639, 132, writing, meurant, gerard, 2014, elsevier, 08093391, hopcroft, motwani, ullman, 2007, boston, san, 368, wolfram, mathworld, weblog, com, blog, factoring, 2016, quasipolynomial, 1512, 03547, 1988, low, 323, 0022, 0000, 90010, 312, schöning, uwe, arvind, vikraman, kurur, piyush, spp, 852, 002, 835, 204, notices, ams, grand, challenge, jaffe, arthur, april, december, 2010, folding, hydrophobic, hydrophilic, 9541869, pmid, 1089, cmb, leighton, berger, bonnie, 1975, 171, 14352974, 321864, 321877, 151, matter, www, claymath, wuppuluri, shyam, doria, 2020, scientific, 198790362, 981, 0006, 1142, 11270, unravelling, gregory, chaitin, transcomputational, structural, leaf, descriptive, 1967, formulated, now, specifying, result, began, flourish, 1971, practically, relevant, took, idea, leap, forward, his, landmark, showed, diverse, infamous, leonid, speed, initial, interest, increasingly, aside, favor, exciting, fusion, inherited, arsenal, ideas, had, occurred, 1955, coined, nowadays, switching, papers, studying, 1960, rudimentary, 1961, pioneer, ussr, remembers, hisao, raymond, smullyan, beginning, systematic, attributed, seminal, addition, suggested, good, stearns, juris, hartmanis, actual, explicitly, started, off, numerous, were, researchers, influential, 1936, turned, robust, flexible, simplification, alan, early, 1844, gabriel, lamé, modelling, dynamical, analog, involve, approximated, discretizations, unreasonable, useless, except, unusable, halting, 100, assuming, sake, years, magnitude, useful, technological, progress, until, gets, relatively, age, universe, identification, inexact, degree, leading, coefficient, quickly, slowly, saying, imply, written, range, routinely, handle, sat, solvers, knapsack, presburger, frequently, identified, impractically, near, handled, sometimes, interchangeably, risks, confusion, explosion, currently, again, distinct, along, lines, containing, answers, reversed, proven, clear, whence, complement, breakthrough, phrased, several, cryptographic, first, odd, unfortunately, lies, shor, left, frac, right, rsa, least, collapses, widely, due, offers, potentially, perspectives, eugene, luks, isomorphic, exist, neither, nor, few, logarithm, neq, equals, implications, find, resolving, pure, prediction, logistics, seen, abstraction, tasks, admit, hypothesis, hand, people, easily, observed, vertex, cover, hamiltonian, path, diagram, provided, outside, established, ones, able, reduce, indicate, yield, mean, motivates, harder, depends, square, giving, transformation, reduces, separation, results, cdot, prove, relaxing, bigger, know, inclusion, strict, respectively, induce, constraining, respective, pairs, properly, included, having, deduced, inclusions, proceed, statements, increase, turns, savitch, represent, constraint, manner, inside, above, yields, chosen, necessarily, allow, variations, polynomially, mid, complicated, fit, typical, depth, monotone, promise, simpler, hides, smaller, details, write, 15n, similar, helpful, demonstrate, unless, specified, falls, needs, phrase, includes, discovered, showing, pivot, smallest, never, divided, permutations, occurs, pivoting, divides, half, needing, cheap, considers, whole, assumed, appear, three, ways, mathcal, analogous, made, tree, transitions, halts, interested, criteria, denoted, easier, unusual, allowed, branch, check, possibilities, once, compute, branching, exactly, standard, literature, perhaps, surprisingly, converted, without, providing, power, memory, alternate, vary, deterministically, access, basic, fixed, rules, supply, decisions, helps, added, feature, multiple, paths, clearly, meant, realizable, gives, rise, particularly, alternating, symmetric, device, manipulates, symbols, strip, intended, anything, advanced, supercomputer, mathematician, pencil, furthermore, everything, easy, mathematically, lambda, cellular, conway, ram, church, illustration, argues, admits, wish, require, calculated, typically, measured, increases, compared, tempting, think, richer, really, recast, triples, holds, triple, corresponds, numbers, expected, notable, arbitrary, consists, associated, obtain, central, alternatively, objective, aid, consideration, returns, accept, reject, alternately, theoretic, regularly, keep, discussion, enough, achieved, ensuring, representations, transformed, considering, must, suitably, represented, directly, via, matrices, further, highlight, difference, route, kilometres, passing, germany, asking, round, trip, sites, reason, milan, travelling, collection, possibly, empty, referred, confused, itself, refers, contrast, utterance, serve, primality, testing, tour, german, closely, key, distinction, former, whereas, appropriately, restricted, turn, imposing, restrictions, distinguishes, kinds, algorithmically, roles, seven, part, processors, gates, regarded, inherently, significant, whatever, formalizes, intuition, introducing, quantifying, focuses, according, usage, explores, relationships, classifications, mechanical, inherent, item, wikiversity, projects, printable, download, print, export, switch, legacy, parser, get, shortened, url, cite, permanent, here, talk, tiếng, việt, українська, türkçe, tagalog, ไทย, српски, srpski, slovenčina, simple, srpskohrvatski, српскохрватски, русский, română, português, norsk, bokmål, nederlands, bahasa, melayu, монгол, 한국어, 日本語, italiano, hrvatski, עברית, français, suomi, فارسی, euskara, español, ελληνικά, deutsch, čeština, català, বাংলা, български, azərbaycanca, asturianu, العربية, top, personal, pages, community, learn, help, contribute, events, navigation, jump, content,
Text of the page (random words):
approach to complexity theory of numerical analysis 17 is information based complexity continuous complexity theory can also refer to complexity theory of the use of analog computation which uses continuous dynamical systems and differential equations 18 control theory can be considered a form of computation and differential equations are used in the modelling of continuous time and hybrid discrete continuous time systems 19 history edit an early example of algorithm complexity analysis is the running time analysis of the euclidean algorithm done by gabriel lamé in 1844 before the actual research explicitly devoted to the complexity of algorithmic problems started off numerous foundations were laid out by various researchers most influential among these was the definition of turing machines by alan turing in 1936 which turned out to be a very robust and flexible simplification of a computer the beginning of systematic studies in computational complexity is attributed to the seminal 1965 paper on the computational complexity of algorithms by juris hartmanis and richard e stearns which laid out the definitions of time complexity and space complexity and proved the hierarchy theorems 20 in addition in 1965 edmonds suggested to consider a good algorithm to be one with running time bounded by a polynomial of the input size 21 earlier papers studying problems solvable by turing machines with specific bounded resources include 20 john myhill s definition of linear bounded automata myhill 1960 raymond smullyan s study of rudimentary sets 1961 as well as hisao yamada s paper 22 on real time computations 1962 somewhat earlier boris trakhtenbrot 1956 a pioneer in the field from the ussr studied another specific complexity measure 23 as he remembers however my initial interest in automata theory was increasingly set aside in favor of computational complexity an exciting fusion of combinatorial methods inherited from switching theory with the conceptual arsenal of the theory of algorithms these ideas had occurred to me earlier in 1955 when i coined the term signalizing function which is nowadays commonly known as complexity measure 24 in 1967 manuel blum formulated a set of axioms now known as blum axioms specifying desirable properties of complexity measures on the set of computable functions and proved an important result the so called speed up theorem the field began to flourish in 1971 when stephen cook and leonid levin proved the existence of practically relevant problems that are np complete in 1972 richard karp took this idea a leap forward with his landmark paper reducibility among combinatorial problems in which he showed that 21 diverse combinatorial and graph theoretical problems each infamous for its computational intractability are np complete 25 see also edit computational complexity descriptive complexity theory game complexity leaf language limits of computation list of complexity classes list of computability and complexity topics list of unsolved problems in computer science parameterized complexity proof complexity quantum complexity theory structural complexity theory transcomputational problem computational complexity of mathematical operations works on complexity edit wuppuluri shyam doria francisco a eds 2020 unravelling complexity the life and work of gregory chaitin world scientific doi 10 1142 11270 isbn 978 981 12 0006 9 s2cid 198790362 references edit citations edit p vs np problem clay mathematics institute www claymath org archived from the original on july 6 2018 retrieved july 6 2018 see arora barak 2009 chapter 1 the computational model and why it doesn t matter 1 2 see sipser 2006 chapter 7 time complexity 1 2 ladner richard e 1975 on the structure of polynomial time reducibility journal of the acm 22 1 151 171 doi 10 1145 321864 321877 s2cid 14352974 berger bonnie a leighton t 1998 protein folding in the hydrophobic hydrophilic hp model is np complete journal of computational biology 5 1 27 40 doi 10 1089 cmb 1998 5 27 pmid 9541869 cook stephen april 2000 the p versus np problem pdf clay mathematics institute archived from the original pdf on december 12 2010 retrieved october 18 2006 jaffe arthur m 2006 the millennium grand challenge in mathematics pdf notices of the ams 53 6 archived pdf from the original on june 12 2006 retrieved october 18 2006 arvind vikraman kurur piyush p 2006 graph isomorphism is in spp information and computation 204 5 835 852 doi 10 1016 j ic 2006 02 002 schöning uwe 1988 graph isomorphism is in the low hierarchy journal of computer and system sciences 37 3 312 323 doi 10 1016 0022 0000 88 90010 4 babai lászló 2016 graph isomorphism in quasipolynomial time arxiv 1512 03547 cs ds fortnow lance september 13 2002 computational complexity blog factoring weblog fortnow com wolfram mathworld number field sieve boaz barak s course on computational complexity lecture 2 hopcroft j e motwani r and ullman j d 2007 introduction to automata theory languages and computation addison wesley boston san francisco new york page 368 meurant gerard 2014 algorithms and complexity elsevier p p 4 isbn 978 0 08093391 7 zobel justin 2015 writing for computer science springer p 132 isbn 978 1 44716639 9 smale steve 1997 complexity theory and numerical analysis acta numerica 6 cambridge univ press 523 551 bibcode 1997acnum 6 523s doi 10 1017 s0962492900002774 s2cid 5949193 babai lászló campagnolo manuel 2009 a survey on continuous time computations arxiv 0907 3117 cs cc tomlin claire j mitchell ian bayen alexandre m oishi meeko july 2003 computational techniques for the verification of hybrid systems proceedings of the ieee 91 7 986 1001 bibcode 2003ieeep 91 986t doi 10 1109 jproc 2003 814621 1 2 fortnow homer 2003 richard m karp combinatorics complexity and randomness 1985 turing award lecture yamada h 1962 real time computation and recursive functions not real time computable ieee transactions on electronic computers ec 11 6 753 760 bibcode 1962irtec 11 753y doi 10 1109 tec 1962 5219459 trakhtenbrot b a signalizing functions and tabular operators uchionnye zapiski penzenskogo pedinstituta transactions of the penza pedagogoical institute 4 75 87 1956 in russian boris trakhtenbrot from logic to theoretical computer science an update in pillars of computer science lncs 4800 springer 2008 karp richard m 1972 reducibility among combinatorial problems pdf in miller r e thatcher j w eds complexity of computer computations new york plenum pp 85 103 archived from the original pdf on june 29 2011 retrieved september 28 2009 textbooks edit arora sanjeev barak boaz 2009 computational complexity a modern approach cambridge university press isbn 978 0 521 42426 4 zbl 1193 68112 downey rod fellows michael 1999 parameterized complexity monographs in computer science berlin new york springer verlag isbn 978 0 387 94883 6 du ding zhu ko ker i 2000 theory of computational complexity john wiley sons isbn 978 0 471 34506 0 garey michael r johnson david s 1979 computers and intractability a guide to the theory of np completeness series of books in the mathematical sciences 1st ed new york w h freeman and company isbn 978 0 7167 1045 5 mr 0519066 oclc 247570676 goldreich oded 2008 computational complexity a conceptual perspective cambridge university press van leeuwen jan ed 1990 handbook of theoretical computer science vol a algorithms and complexity mit press isbn 978 0 444 88071 0 papadimitriou christos 1994 computational complexity 1st ed addison wesley isbn 978 0 201 53082 7 sipser michael 2006 introduction to the theory of computation 2nd ed usa thomson course technology isbn 978 0 534 95097 2 surveys edit khalil hatem ulery dana 1976 a review of current studies on complexity of algorithms for partial differential equations proceedings of the annual conference on acm 76 pp 197 201 doi 10 1145 800191 805573 isbn 978 1 4503 7489 7 s2cid 15497394 cook stephen 1983 an overview of computational complexity communications of the acm 26 6 400 408 doi 10 1145 358141 358144 issn 0001 0782 s2cid 14323396 fortnow lance homer steven 2003 a short history of computational complexity pdf bulletin of the eatcs 80 95 133 mertens stephan 2002 computational complexity for physicists computing in science engineering 4 3 31 47 arxiv cond mat 0012185 bibcode 2002cse 4c 31m doi 10 1109 5992 998639 issn 1521 9615 s2cid 633346 external links edit look up tractable feasible intractability or infeasible in wiktionary the free dictionary wikimedia commons has media related to computational complexity theory the complexity zoo computational complexity classes encyclopedia of mathematics ems press 2001 1994 scott aaronson why philosophers should care about computational complexity v t e complexity classes considered feasible dlogtime ac 0 acc 0 reg tc tc 0 l sl rl fl nl nl complete nc sc cc p p complete zpp rp bpp bqp apx fp suspected infeasible up np np complete np hard co np co np complete tfnp fnp am qma ph p pp p p complete ip pspace pspace complete considered infeasible exptime nexptime expspace 2 exptime elementary nonelementary pr r re all other complexity classes polyl qp class hierarchies polynomial hierarchy exponential hierarchy grzegorczyk hierarchy arithmetical hierarchy boolean hierarchy families of classes dtime ntime dspace nspace probabilistically checkable proof interactive proof system list of complexity classes v t e computer science this template follows roughly the 2012 acm computing classification system hardware printed circuit board peripheral integrated circuit very large scale integration system on a chip soc energy consumption green computing electronic design automation hardware acceleration processor size form systems organization computer architecture computational complexity dependability embedded system real time computing cyber physical system fault tolerance wireless sensor network networks network architecture network protocol network components network scheduler network performance evaluation network service software organization interpreter middleware virtual machine operating system software quality software notations tools programming paradigm programming language compiler domain specific language modeling language software framework integrated development environment software configuration management software library software repository software development control flow software development process requirements analysis software design software construction software deployment software engineering software maintenance programming team open source model theory of computing model of computation stochastic formal language automata theory computability theory computational complexity theory logic semantics algorithms algorithm design analysis of algorithms algorithmic efficiency randomized algorithm computational geometry mathematics of computing discrete mathematics probability statistics mathematical software information theory mathematical analysis numerical analysis theoretical computer science computational problem information systems database management information storage enterprise information social information geographic information decision support process control multimedia information data mining digital library computing platform digital marketing world wide web information retrieval security cryptography formal methods security hacker security services intrusion detection system hardware security network security information security application security human centered computing accessibility extended reality augmented virtual human computer interaction interaction design mobile computing social computing ubiquitous computing visualization concurrency concurrent computing parallel computing distributed computing multithreading multiprocessing artificial intelligence computational intelligence natural language processing knowledge representation and reasoning computer vision automated planning and scheduling search methodology control method philosophy of distributed machine learning supervised unsupervised reinforcement multi task cross validation graphics animation rendering photograph manipulation graphics processing unit image compression solid modeling applied computing quantum computing e commerce enterprise software computational mathematics computational physics computational chemistry computational biology computational social science computational engineering differentiable computing computational healthcare digital art electronic publishing cyberwarfare electronic voting video games word processing operations research educational technology document management outline glossaries category v t e major mathematics areas history timeline future lists glossary foundations category theory information theory mathematical logic order theory philosophy of mathematics set theory type theory algebra abstract commutative elementary field theory group theory homological linear multilinear analysis calculus real analysis complex analysis differential equations functional analysis harmonic analysis measure theory discrete combinatorics discrete geometry graph theory geometry algebraic numerical algebraic affine analytic arithmetic complex computational convex differential discrete euclidean finite information projective synthetic trigonometry number theory algebraic analytic arithmetic diophantine geometry topology general arithmetic algebraic differential geometric homotopy theory applied engineering mathematics ethnomathematics mathematical biology mathematical chemistry mathematical economics mathematical finance mathematical geology mathematical linguistics mathematical physics mathematical psychology mathematical sociology mathematical statistics probability statistics systems science control theory game theory operations research computational computer science theory of computation computational complexity theory numerical analysis optimization computer algebra related topics mathematicians lists informal mathematics films about mathematicians recreational mathematics pseudomathematics metamathematics mathematics and art mathematics education number large mathematics portal category commons wikiproject authority control databases international gnd national united states czech republic israel other yale lux retrieved from https en wikipedia org w index php title computational_complexity_theory oldid 1371073639 categories computational complexity theory computational fields of study hidden categories articles with short description short description is different from wikidata use mdy dates from september 2017 cs1 long volume value commons category link from wikidata this page was last edited on 24 august 2026 at 12 20 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundatio...
|
