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PR is the complexity class of all primitive recursive functions—or, equivalently, the set of all formal languages that can be decided in time bounded by
PR_(complexity)
Topics referred to by the same term
Look up PR or .pr in Wiktionary, the free dictionary. PR, P.R., Pr, pr, or Pr. may refer to: P.R. (TV series), a Canadian television sitcom Partisan Review
PR
Class of problems in computer science
In complexity theory, PP, or PPT is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability
PP_(complexity)
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
Complexity of sending information in a distributed algorithm
communication complexity, such as the PR-box, or some noisy PR-boxes satisfying some conditions. One approach to studying randomized communication complexity is
Communication_complexity
Attribute of machine learning models
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function
Sample_complexity
Interactive proof system in computational complexity theory
In computational complexity theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin
Arthur–Merlin_protocol
Measure of complexity of real-valued functions
learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with
Rademacher_complexity
Management of public communication of organizations
Public relations (PR) is the practice of managing and disseminating information from an individual or an organization (such as a business, government agency
Public_relations
Algorithm that employs a degree of randomness as part of its logic or procedure
Carlo algorithms are considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision
Randomized_algorithm
Concept in probability theory
Pr [ E ] {\textstyle \operatorname {Pr} [E]} be strictly positive in order for the postselection to be well-defined. See also PostBQP, a complexity
Postselection
Algorithm characteristic in computations
In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the
Average-case_complexity
Discrete Fourier transform algorithm
of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O ( n 2 ) {\textstyle O(n^{2})} , which arises
Fast_Fourier_transform
Computational complexity class of problems
In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial
BQP
On collapse of the polynomial hierarchy if NP is in non-uniform polynomial time class
In complexity theory, the Karp–Lipton theorem states that if the Boolean satisfiability problem (SAT) can be solved by Boolean circuits with a polynomial
Karp–Lipton_theorem
Mathematical model of computation
that includes several important complexity classes is allowing for an error probability of 1/3. For instance, the complexity class BPP is defined as the class
Probabilistic_Turing_machine
In computational complexity theory, Håstad's switching lemma is a key tool for proving lower bounds on the size of constant-depth Boolean circuits. It
Switching_lemma
Tree-based computer data structure
Bayer, Edward M. McCreight Complexities in big O notation Space complexity Space O ( n ) {\displaystyle O(n)} Time complexity Function Amortized Worst case
B-tree
Complexity class from interactive proofs
In computational complexity theory, the class IP (which stands for interactive proof) is the class of problems solvable by an interactive proof system
IP_(complexity)
Probabilistic graphical representation of causal relationships
rule of probability, Pr ( G , S , R ) = Pr ( G ∣ S , R ) Pr ( S ∣ R ) Pr ( R ) {\displaystyle \Pr(G,S,R)=\Pr(G\mid S,R)\Pr(S\mid R)\Pr(R)} where G = "Grass
Bayesian_network
Permutation of the elements of a set in which no element appears in its original position
Article 03.1.2. Bibcode:2003JIntS...6...12H – via cs.uwaterloo.ca. de Montmort, P.R. (1713) [1708]. Essay d'analyse sur les jeux de hazard (in French) (Revue
Derangement
Independent publisher associated with Princeton University
Series in Astrophysics (David N. Spergel, editor) Princeton Series in Complexity (Simon A. Levin and Steven H. Strogatz, editors) Princeton Series in Evolutionary
Princeton_University_Press
Inequality in information theory
"A short note on an inequality between KL and TV". arXiv:2202.07198 [math.PR]. Lattimore, Tor; Szepesvari, Csaba (2020). Bandit Algorithms (PDF). Cambridge
Bretagnolle–Huber_inequality
Category of nationality rights
6 months, but varies based on the complexity of the case. The processing fee is S$100, which is not refundable. PR status is central to Singapore nationality
Permanent residency in Singapore
Permanent_residency_in_Singapore
Multi-winner electoral system
transferable vote (STV) or proportional-ranked choice voting (P-RCV), also known as PR-STV and "proportional representation by means of the single transferable vote"
Single_transferable_vote
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Dopamine reuptake inhibitor
PR-608 is a potent dopamine reuptake inhibitor belonging to the diphenylbutylpiperazine class of agents (related to the diphenylbutylpiperidine class)
PR-000608
Property whereby no efficient algorithm can distinguish two distributions
In computational complexity and cryptography, two families of distributions are computationally indistinguishable if no efficient algorithm can tell the
Computational indistinguishability
Computational_indistinguishability
Function computable with bounded loops
below. The set of primitive recursive functions is known as PR in computational complexity theory. A primitive recursive function takes a fixed number
Primitive_recursive_function
Hungarian-American mathematician and computer scientist
his work in reliable computation, randomness in computing, algorithmic complexity, algorithmic probability, and information theory. Peter Gacs attended
Peter_Gacs
Computational problem with high complexity
In computational complexity theory, a nonelementary problem is a problem that is not a member of the class ELEMENTARY. As a class it is sometimes denoted
Nonelementary_problem
Function used in computer cryptography
"easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. This has
One-way_function
Standard for assessing computer system vulnerabilities
access vector (AV) shows how a vulnerability may be exploited. The access complexity (AC) metric describes how easy or difficult it is to exploit the discovered
Common Vulnerability Scoring System
Common_Vulnerability_Scoring_System
up. The notion of list-decoding has many interesting applications in complexity theory. The way the channel noise is modeled plays a crucial role in that
List_decoding
American lobbyists, Ukraine has launched a "PR machine," creating a structure of international advertising and PR agencies that actively introduce prepared
Ukrainian information war during Russian invasion of Ukraine
Ukrainian_information_war_during_Russian_invasion_of_Ukraine
Algorithm for solving the minimum-cost flow problem
(December 1967). The out-of-kilter algorithm: a primer — Memorandum RM-5472-PR (PDF). Santa Monica, California, USA: The Rand Corporation. Retrieved 2018-01-16
Out-of-kilter_algorithm
Field of machine learning
{A}}} , of the agent; P a ( s , s ′ ) = Pr ( S t + 1 = s ′ ∣ S t = s , A t = a ) {\displaystyle P_{a}(s,s')=\Pr(S_{t+1}{=}s'\mid S_{t}{=}s,A_{t}{=}a)}
Reinforcement_learning
Establishes the limits to possible data compression
dependencies (whose source is not an i.i.d. random variable), the Kolmogorov complexity, which quantifies the minimal description length of an object, is more
Shannon's source coding theorem
Shannon's_source_coding_theorem
operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
Tree data structure that partitions a 2D area
usually expressed as x, y coordinates value; for example a name Point-region (PR) quadtrees are very similar to region quadtrees. The difference is the type
Quadtree
Dimensional–categorical hybrid model of personality disorders
diagnoses". Contrary to the aforementioned concern regarding possible complexities introduced by the AMPD, ease of use has also been described as being
Alternative DSM-5 model for personality disorders
Alternative_DSM-5_model_for_personality_disorders
In computational complexity theory and cryptography, averaging argument is a standard argument for proving theorems. It usually allows us to convert probabilistic
Averaging_argument
8-speed automatic from 2008
to 0.2 seconds. In order to avoid a further increase in manufacturing complexity while expanding the number of gear ratios, ZF switched from the conventional
ZF_8HP_transmission
Abstract machine that models computation
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two
Interactive_proof_system
Notion in supervised machine learning
Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion
Vapnik–Chervonenkis_dimension
Study of computation
models of computation. The second question is addressed by computational complexity theory, which studies the time and space costs associated with different
Computer_science
distributions, the complexity can be reduced to O ( m 2 k ) {\displaystyle O(m^{2k})} . Thus, in the case of two populations, the complexity is polynomial
Bapat–Beg_theorem
Russian pseudo-scientist and sect leader
received the "Diploma of Professor" for "Safety of objects of extreme complexity" from the Russian federation, a Doctor of Engineering Sciences diploma
Grigori_Grabovoi
endeavours (i.e., projects) characterized by large investment commitment, vast complexity (especially in organisational terms), and long-lasting impact on the economy
List_of_megaprojects_in_India
Mathematical inequality explaining concentration of random variables
non-negative function, then Pr ( X ≥ a ) = Pr ( Φ ( X ) ≥ Φ ( a ) ) ≤ E ( Φ ( X ) ) Φ ( a ) . {\displaystyle \Pr(X\geq a)=\Pr(\Phi (X)\geq \Phi (a))\leq
Concentration_inequality
Class of interactive proof
\}} and Pr ( E P ~ ( x ) ( x ) ∈ W ( x ) ) ≥ Pr ( P ~ ( x ) ↔ V ( x ) → 1 ) − κ ( x ) . {\displaystyle \Pr(E^{{\tilde {P}}(x)}(x)\in W(x))\geq \Pr({\tilde
Proof_of_knowledge
Structuring text as input to generative artificial intelligence
r [ Y i | X ~ ∗ X i ] {\displaystyle \arg \max _{\tilde {X}}\sum _{i}\log Pr[Y^{i}|{\tilde {X}}\ast X^{i}]} where X ~ {\displaystyle {\tilde {X}}} ranges
Prompt_engineering
Most of those companies have subsequently disappeared, as the increasing complexity of GPUs substantially increased research and development costs. Many of
List of graphics chips and card companies
List_of_graphics_chips_and_card_companies
reputation as the "world's factory" through its manufacturing exports. The complexity of its exports increased over time, and as of 2019 it accounts for approximately
Economy_of_China
1967–1990 state in Western Asia
influence in the region. Additionally, the oil find added a layer of complexity to the already intricate relationship between South and North Yemen, both
South_Yemen
the historical significance of Berlusconi's victory, together with the complexity of his alliance, the British historian Martin Clark observed: "It was
1994_Italian_general_election
Complexity class
In computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum
PostBQP
Measure of similarity and diversity between sets
the complexity to O ( k ) {\displaystyle O(k)} , where k {\displaystyle k} is the number of non-zero attributes. # Psuedocode for O(k) complexity function
Jaccard_index
Edge-matching puzzle
"Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity" (PDF). Retrieved 12 August 2007. "LGR – TetraVex and the Unsolvable Puzzle"
Eternity_II_puzzle
2024 video game
gameplay mechanics and visuals, but sentiment towards its story and design complexity was more mixed. Unicorn Overlord is a tactical role-playing game in which
Unicorn_Overlord
Probabilistic primality test
Bayes' law: Pr ( ¬ P ∣ M R k ) = Pr ( ¬ P ∧ M R k ) Pr ( ¬ P ∧ M R k ) + Pr ( P ∧ M R k ) = 1 1 + Pr ( M R k ∣ P ) Pr ( M R k ∣ ¬ P ) Pr ( P ) Pr ( ¬ P )
Miller–Rabin_primality_test
Free online crowdsourced encyclopedia
with certainty. New editors often struggle to understand Wikipedia's complexity. Experienced editors are encouraged not to "bite" the newcomers in order
Wikipedia
Algorithm to multiply two numbers
by every digit in the second and adding the results. This has a time complexity of O ( n 2 ) {\displaystyle O(n^{2})} , where n is the number of digits
Multiplication_algorithm
Distribution estimation technique
designing good biased distributions becomes more complicated as the system complexity increases. Complex systems are the systems with long memory since complex
Importance_sampling
American semiconductor company
as well as GPT-J 6B, GPT-3 13B, and GPT-NeoX 20B with reduced software complexity and infrastructure. In August 2022, the Computer History Museum in Mountain
Cerebras_Systems
Bounded-error probabilistic polynomial time is contained in the polynomial time hierarchy
In computational complexity theory, the Sipser–Lautemann theorem or Sipser–Gács–Lautemann theorem states that bounded-error probabilistic polynomial (BPP)
Sipser–Lautemann_theorem
2023 studio album by Olivia Rodrigo
tribulations. The album received universal critical acclaim for its lyrical wit, complexity, topicality, aesthetic and energy. Reviews noted both humorous and emotionally
Guts_(album)
fishes from the Friuli Carbonate Platform (Italy). Evidence of increase of complexity of benthic invertebrate community from the López de Bertodano Formation
2025_in_paleontology
Lagerstätte (Cambrian Stage 4), South China: Implications for community complexity and geographic variation". Global and Planetary Change. 245 104641. Bibcode:2025GPC
List_of_lagerstätten
Observatory of Economic Complexity, through visualizations such as the Product Exports Treemaps and new indexes such as the Economic Complexity Index (ECI), which
The_Product_Space
American mathematician and philosopher (born 1960)
specified complexity and irreducible complexity. The scientific community sees intelligent design—and Dembski's concept of specified complexity—as a form
William_A._Dembski
Former offshore oil drilling rig
analysts reporting that the aftermath was of unprecedented scale and complexity compared to previous disasters which themselves took many years to resolve
Deepwater_Horizon
Panoramic film format
technology has been rarely produced for Hollywood studio films due to the complexity of the additional CGI work as side footage. Lee Jae-seon, who collaborated
ScreenX
Field of mathematics and science based on non-linear systems and initial conditions
ISBN 978-0-7868-6844-5. Yoshisuke Ueda, The Road To Chaos, Aerial Pr, 1993. M. Mitchell Waldrop, Complexity : The Emerging Science at the Edge of Order and Chaos
Chaos_theory
Random process independent of past history
chains are processes where Pr ( X n + 1 = x ∣ X n = y ) = Pr ( X n = x ∣ X n − 1 = y ) {\displaystyle \Pr(X_{n+1}=x\mid X_{n}=y)=\Pr(X_{n}=x\mid X_{n-1}=y)}
Markov_chain
Head movement in rodents upon 5-HT2A receptor activation
confounds and caveats to this potential use of HTR data, related to the complexities of HTR as a pharmacodynamic readout; for example, as a function of off-target
Head-twitch_response
Corinnidae): two more examples of spider templates with a large range of complexity in the genitalia". Zool. J. Linn. Soc. 162 (2): 271–350. doi:10.1111/j
List of organisms named after famous people (born 1925–1949)
List_of_organisms_named_after_famous_people_(born_1925–1949)
American author (born 1971)
York Times. Finn, John (August 27, 2013). "Wooster Forum to Examine the Complexity of Race". The College of Wooster. Retrieved October 10, 2014. Hampton
Touré_(journalist)
Mathematical model for sequential decision making under uncertainty
probability is sometimes written Pr ( s , a , s ′ ) {\displaystyle \Pr(s,a,s')} , Pr ( s ′ ∣ s , a ) {\displaystyle \Pr(s'\mid s,a)} or, rarely, p s ′ s
Markov_decision_process
both length and width), which offers high storage capacity and lower complexity of device construction and operation if precise time control of droplets
Droplet-based_microfluidics
Chemical element with atomic number 59 (Pr)
[green] 2 Pr (s) + 3 Cl2 (g) → 2 PrCl3 (s) [green] 2 Pr (s) + 3 Br2 (g) → 2 PrBr3 (s) [green] 2 Pr (s) + 3 I2 (g) → 2 PrI3 (s) tetrafluoride, PrF4, is also
Praseodymium
Class of religious beliefs
"erroneous" by archaeologist Timothy Insoll, who stated that "it removes complexity, a precondition of religion now, in all its variants." Tylor's definition
Animism
Roman politician and Stoic (95–46 BC)
(pr. 152 BC) Marcus Porcius Cato (cos. 118 BC) Marcus Porcius Cato (pr. c. 92 BC) Gaius Porcius Cato (cos. 114 BC) Marcus Porcius Cato Salonianus (pr.
Cato_the_Younger
Season of television series
the series most violent moments, though they also used CGI due to the complexity of shooting, using the practical effects as a reference. Having already
The_Boys_season_1
Counter-Strike 2 tournament
Esports Team Liquid paiN Gaming FURIA Esports MIBR M80 Imperial Esports Complexity Gaming Fluxo Wildcard NRG Esports Legacy The MongolZ Lynn Vision Gaming
Blast_Austin_Major_2025
Data structure in computer science
subdivides the space it represents into eight octants. In a point region (PR) octree (analogous to a point quadtree), the node stores an explicit three-dimensional
Octree
Ratio of competing statistical models
) Pr ( M 1 ) Pr ( M 2 | D ) Pr ( D ) Pr ( M 2 ) = Pr ( M 1 | D ) Pr ( M 2 | D ) Pr ( M 2 ) Pr ( M 1 ) . {\displaystyle K={\frac {\Pr(D|M_{1})}{\Pr(D|M_{2})}}={\frac
Bayes_factor
Lego theme based on Star Wars
some of the most notable sets in the Lego Star Wars line. With similar complexity to the Ultimate Collector Series sets, sets in the Master Builder Series
Lego_Star_Wars
Multiplayer video game developed by Riot Games
Legends players are up in arms after an update to get rid of 'unnecessary complexity' makes it a struggle for new players to earn anything". PC Gamer. Retrieved
League_of_Legends
Rule of logical inference
granted. If Pr ( P → Q ) = x {\displaystyle \Pr(P\rightarrow Q)=x} and Pr ( P ) = y {\displaystyle \Pr(P)=y} , then Pr ( Q ) {\displaystyle \Pr(Q)} must
Modus_ponens
First era of the Phanerozoic Eon
correlation between different sites around the world. Trace fossils reflect the complexity of the body plan of the organism that made them. Ediacaran trace fossils
Paleozoic
2017 American crime drama television series
11, 2017. Grobar, Matt (April 16, 2018). "Mr. Mercedes Cast & EP Talk Complexity Of Characters, Reveal Season 2 Premiere Date – The Contenders Emmys".
Mr._Mercedes_(TV_series)
novelist known for exploring the intellectual history of Baghdad and the complexities of Iraqi identity. Hassan Blasim: Often called "the best living Arab
List_of_Iraqis
Performance-based building design is an approach to the design of any complexity of building, from single-detached homes up to and including high-rise
Performance-based building design
Performance-based_building_design
South Korean actress (born 1996)
Ha Sang-soo (portrayed by Yoo Yeon-seok) who introduces new emotional complexity to her life. In February 2024, Moon debuted as an author with the publication
Moon_Ga-young
Organic chemical that functions both as a hormone and a neurotransmitter
Baler RD (January 2014). "Addiction science: Uncovering neurobiological complexity". Neuropharmacology. 76 (Pt B): 235–49. doi:10.1016/j.neuropharm.2013
Dopamine
Slovenian-American actor (born 1957)
17, 2008. Levin, Gary (January 5, 2009). "'Damages' returns in all its complexity." USA Today. p. 01D. Retrieved via Biography In Context database, November
Željko_Ivanek
Animal behavior scientist
Hanser SF. (2002). Using information theory to assess the diversity, complexity and development of communicative repertoires. Journal of Comparative Psychology
Brenda_McCowan
Inactive oil or gas sites in Alberta with no solvent owner
public interest". Cases, such as Lexin and Sequoia, shed light on the complexity and opacity of ownership groups. It also drew attention to the way in
Orphan wells in Alberta, Canada
Orphan_wells_in_Alberta,_Canada
Country in Southeast Asia and Oceania
Goldstein 2024, pp. 11, 14, 56–57. "Indonesia". The Observatory of Economic Complexity. 2023. Retrieved 8 May 2025. Suryanta, B. (2021). Indonesia's Integration
Indonesia
PR COMPLEXITY
PR COMPLEXITY
Surname or Lastname
English (mainly West Midlands)
English (mainly West Midlands) : from Middle English pr(i)est ‘minister of the Church’ (Old English prēost, from Latin presbyter, Greek presbyteros ‘elder’, ‘counselor’, comparative of presbys ‘old man’), used as a nickname, either for someone with a pious manner or possibly for someone who had played the part of a priest in a pageant. It may also have been an occupational name for someone in the service of a priest, and occasionally it may have been used to denote someone suspected of being the son of a priest.A John Priest is recorded as being in Woburn, MA, as early as 1675. The Mayflower Pilgrim Digory Priest of Holland died the first winter at Plymouth in 1620, leaving behind a widow who remarried and two daughters, who did not pass on the family name.
Surname or Lastname
English
English : occupational name for a priest’s servant, from Middle English pr(i)est ‘priest’, ‘minister’ + man ‘man’.Jewish (Ashkenazic) : occupational name for someone who did ironing and pressing of clothes, from Yiddish pres ‘flat iron’ + man ‘man’.
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Italian, Jamaican, Kannada, Latin, Portuguese, Tamil
Warlike; From the God Mars; Dedicated to Mars; Protector of Man; Martial One; War Like; Defence; Of the Sea; Pr
PR COMPLEXITY
PR COMPLEXITY
Boy/Male
Hindu, Indian, Traditional
Ever Victorious
Boy/Male
Australian, Christian, French, Hebrew, Jewish
Young Deer; Deer; Gold; Reducing to Ashes; Young Mountain
Boy/Male
Celtic English
From the hill meadow.
Boy/Male
Norse
Fighter.
Boy/Male
Hindu
Remembrance
Boy/Male
Bengali, Hindu, Indian, Marathi
Famous
Boy/Male
Biblical
Sorrowful, hated.
Boy/Male
Bengali, Hindu, Indian
Offer to God; Bug
Girl/Female
Indian, Tamil, Telugu
One Having a Very Clean Character
Boy/Male
Arabic, Muslim
Great Sahabi of the Prophet
PR COMPLEXITY
PR COMPLEXITY
PR COMPLEXITY
PR COMPLEXITY
PR COMPLEXITY
superl.
Being in the first part, pr period, of growth; as, a young plant; a young tree.
n.
One who asserts; one who avers pr maintains; an assertor.
n.
An instrument for determining the dip of beds or strata, pr the slope of an embankment or cutting; a kind of plumb level.
n.
The quality pr state of being vehement; impetuous force; impetuosity; violence; fury; as, the vehemence.
p. pr.
of Shet
n.
Difficult delivery pr parturition.
imp. & p. p. Fenced
/); p. pr. & vb. n.) of Fence
n.
A position or condition which affords entrance, control, pr possession, etc.; as, the key of a line of defense; the key of a country; the key of a political situation. Hence, that which serves to unlock, open, discover, or solve something unknown or difficult; as, the key to a riddle; the key to a problem.
v. t.
To set pr place wrongly.
v. t.
To make a plot, map, pr plan, of; to mark the position of on a plan; to delineate.
t
ing (p. pr. & vb. n.) of Wit
imp. & p. p. Adored
/); p. pr. & vb. n.) of Adore