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Randomized polynomial time class of computational complexity theory
In computational complexity theory, randomized polynomial time (RP) is the complexity class of decision problems for which a probabilistic Turing machine
RP_(complexity)
Concept in computer science
Turing machines, but, for clarity, note that other complexity classes based on them include BPP and RP. The class BQP is based on another machine with randomness:
ZPP_(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
Topics referred to by the same term
RP, R-P, Rp, R-p, or rp may refer to: Look up rp in Wiktionary, the free dictionary. Rainforest Partnership, an environmental organization based in Austin
RP
Concept in computer science
} has circuit complexity 2Ω(n) then P = BPP. RP ZPP BQP List of complexity classes Valentine Kabanets, CMPT 710 - Complexity Theory: Lecture 16,
BPP_(complexity)
Inherent difficulty of computational problems
known complexity classes between P {\displaystyle {\textsf {P}}} and PSPACE {\displaystyle {\textsf {PSPACE}}} , such as RP {\displaystyle {\textsf {RP}}}
Computational complexity theory
Computational_complexity_theory
Highly refined form of kerosene used as rocket fuel
RP-1 (Rocket Propellant-1 or Refined Petroleum-1) and similar fuels like RG-1 and T-1 are highly refined kerosene formulations used as rocket fuel. Liquid-fueled
RP-1
Estimate of time taken for running an algorithm
the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
Complexity class used to classify decision problems
problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems
NP_(complexity)
Class of problems solvable in polynomial time
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can
P_(complexity)
(Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial
RL_(complexity)
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)
Topics referred to by the same term
Paraguayan trade union federation co-RP, a complexity class of computational complexity theory closely related to RP (complexity) Corps (disambiguation) This
Corp
Algorithm that employs a degree of randomness as part of its logic or procedure
algorithms are considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision problems
Randomized_algorithm
In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently
Complement_(complexity)
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
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
Proof checkable by a randomized algorithm
In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a
Probabilistically checkable proof
Probabilistically_checkable_proof
Complexity class (logarithmic space)
BPP, ZPP, PP, and RP, there are several random versions of L. Bounded-error Probability L (BPL) is defined like BPP, as the complexity class of problems
L_(complexity)
If there is a polynomial time algorithm for unambiguous-SAT, then NP equals RP
theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT, then NP = RP. It was proven by Leslie
Valiant–Vazirani_theorem
Application of complexity science to economics
Complexity economics, or economic complexity, is the application of complexity science to the problems of economics. It relaxes several common assumptions
Complexity_economics
Algorithm analysis method
smoothed complexity polynomial in n and 1/s, where s is the input perturbation size, unless PPAD ≤ RP. In particular, the smoothed complexity of the Lemke-Howson
Smoothed_analysis
Mathematical model of computation
be solvable in logarithmic space. Complexity classes arising from other definitions of acceptance include RP, co-RP, and ZPP. If the machine is restricted
Probabilistic_Turing_machine
Type of randomized algorithm
algorithms with a bounded probability of two-sided errors, and the complexity class RP describes problems that can be solved by a Monte Carlo algorithm
Monte_Carlo_algorithm
Technique in analytical chemistry
HPLC (RP-HPLC) is the most widespread mode of chromatography. It has a non-polar stationary phase and an aqueous, moderately polar mobile phase. RP-HPLC
High-performance liquid chromatography
High-performance_liquid_chromatography
Class of Diesel-Electric locomotives
The RP-210 was a streamlined 1,000 hp (750 kW) locomotive built in 1956 by Baldwin-Lima-Hamilton, specifically to operate with the experimental, all-aluminum
Baldwin_RP-210
Type of randomized algorithm
The complexity class of decision problems that have Las Vegas algorithms with expected polynomial runtime is ZPP. It turns out that ZPP = RP ∩ co-RP {\displaystyle
Las_Vegas_algorithm
Mid-engined fighter aircraft
interceptor, later in its development it was decided to reduce the cost and complexity of the engine by removing the turbocharger. High-altitude performance
Bell_P-63_Kingcobra
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Problem in math and computer science
Igor Potapov (Eds.): Reachability Problems - 5th International Workshop, RP 2011, Genoa, Italy, September 28–30, 2011. Proceedings. Lecture Notes in Computer
Reachability_problem
Problem of determining if a Boolean formula could be made true
property is used in several theorems in complexity theory: NP ⊆ P/poly ⇒ PH = Σ2 (Karp–Lipton theorem) NP ⊆ BPP ⇒ NP = RP P = NP ⇒ FP = FNP Since the SAT problem
Boolean satisfiability problem
Boolean_satisfiability_problem
Fruit of the rose plant
particularly rich in vitamin C, containing 426 mg per 100 g or 0.4% by weight (w/w). RP-HPLC assays of fresh rose hips and several commercially available products
Rose_hip
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
natural numbers are a mathematical model used in studying computational complexity theory. They are a special case of circuits. The object is a labeled directed
Circuits over sets of natural numbers
Circuits_over_sets_of_natural_numbers
Logarithm to the base of the mathematical constant e
Formulas". Logarithm. Encyclopedia Britannica. Retrieved 2020-08-29. Burn, R.P. (2001). "Alphonse Antonio de Sarasa and logarithms". Historia Mathematica
Natural_logarithm
Chilean-Spanish-American physicist, author and entrepreneur
César A. (2021). "Economic complexity theory and applications". Nature Reviews Physics. 3 (2): 92–113. Bibcode:2021NatRP...3...92H. doi:10.1038/s42254-020-00275-1
César_Hidalgo
Rocket engine operation method
RS-27A—American RP-1/LOX engine first flown in 1990. Vulcain—A family of European first stage engines using LH2/LOX flown on Ariane 5 and Ariane 6. Merlin—RP-1/LOX
Gas-generator_cycle
structures, computability, computational complexity, automata theory and formal languages: CCC - Computational Complexity Conference FCT – International Symposium
List of computer science conferences
List_of_computer_science_conferences
Form of albinism
31 March 2007. Boissy RE, Nordlund JJ (22 August 2005). Ortonne JP, Vinson RP, Perry V, Gelfand JM, James WD (eds.). "Albinism". eMedicine. WebMD. Archived
Oculocutaneous_albinism
Russian-American physicist (born 1963)
to quantum algorithms, quantum complexity classes, and fault-tolerant quantum computation. He introduced the complexity class QMA (Quantum Merlin–Arthur)
Alexei_Kitaev
Genre of electronic music
evolved from the earlier, rapid rhythms of ghetto house, a change pioneered by RP Boo, DJ Rashad and DJ Clent. It may draw from the rapid rhythms and sub-bass
Footwork_(genre)
events throughout 2024 and paticipated in a 2020 Egg Hunt event. Brookhaven RP (also known as Brookhaven) is a massively multiplayer online role-playing
List_of_Roblox_games
Set of problems solved by small circuits
computational complexity theory, P/poly is a complexity class that can be defined in both circuit complexity and non-uniform complexity. Since the two
P/poly
Formal language in mathematics and computer science
languages is often called R, although this name is also used for the class RP. This type of language was not defined in the Chomsky hierarchy. All recursive
Recursive_language
Indicator for the complexity of texts
aids. Automated readability index Readability Kincaid, J.P.; Fishburne, R.P.; Rogers, R.L.; Chissom, B.S. (1975). Derivation of new readability formulas
Flesch–Kincaid readability tests
Flesch–Kincaid_readability_tests
1962 concept for a reusable, sea-launched rocket
000 lbf) thrust engine burning RP-1 and LOX (liquid oxygen). The tank pressure was 32 atm (3,200 kPa; 470 psi) for the RP-1 and 17 atm (1,700 kPa; 250 psi)
Sea_Dragon_(rocket)
Detection of leaks in pipelines
thanks to reduced downtime and inspection time. According to the API document "RP 1130", LDS are divided into internally based LDS and externally based LDS
Leak_detection
przeciwdziałaniu narkomanii". Internetowy System Aktów Prawnych. Kancelaria Sejmu RP. Archived from the original on 14 October 2017. Retrieved 15 October 2017
Legal status of psilocybin mushrooms
Legal_status_of_psilocybin_mushrooms
Indonesian infrastructure projects
National Strategic Projects have been completed with an investment value of Rp 467.4 trillion. The number of completed projects is equivalent to 41% of the
National_Strategic_Projects
Probabilistic primality test
Solovay–Strassen algorithm shows that the decision problem COMPOSITE is in the complexity class RP. Artjuhov, M. M. (1966–1967), "Certain criteria for primality of
Solovay–Strassen primality test
Solovay–Strassen_primality_test
Function in algebraic graph theory
multiplicative factor by a bounded-error probabilistic algorithm unless NP = RP, because any multiplicative approximation would distinguish the values 0 and
Chromatic_polynomial
Indian American professor of computer science (born 1957)
around the design of algorithms, together with work on computational complexity theory, cryptography, and algorithmic game theory. During the 1980s, he
Vijay_Vazirani
Methodic assignment of colors to elements of a graph
chromatic polynomial at any rational point k ≥ 1.5 except for k = 2 unless NP = RP. For edge coloring, the proof of Vizing's result gives an algorithm that uses
Graph_coloring
Country in Central Europe
region: the view from Prague and Bratislava. p.293. ISBN 80-224-0852-2 "RP's History Online – Habsburgs". Archiv.radio.cz. Archived from the original
Czech_Republic
Integer factorization algorithm
Algorithm". BIT. 20 (2): 176–184. doi:10.1007/BF01933190. S2CID 17181286. Brent, R.P.; Pollard, J. M. (1981). "Factorization of the Eighth Fermat Number". Mathematics
Pollard's_rho_algorithm
Group of techniques to quickly construct physical objects
This economy has encouraged online service bureaus. Historical surveys of RP technology start with discussions of simulacra production techniques used
Rapid_prototyping
British limited television series
which slips between Urdu, Arabic, MLE (Multicultural London English) and RP". Jones also praised the casting and performance, concluding that the series
Bait_(TV_series)
1986 breakup of American orbiter
from the original on August 24, 2021. Retrieved August 24, 2021. Feynman, R.P. (June 6, 1986). "Personal Observations on Reliability of Shuttle". Report
Space Shuttle Challenger disaster
Space_Shuttle_Challenger_disaster
Rocket engine operation method
through specific impulse, while its main disadvantage is engineering complexity. Typically, propellant flows through two kinds of combustion chambers;
Staged_combustion_cycle
through three steps; Creation of riparian reserves Restoration of channel complexity Silviculture practices These steps will help restore riparian forest ecosystems
Management of Pacific Northwest riparian forests
Management_of_Pacific_Northwest_riparian_forests
Sequence of DNA that determines traits in an organism
Perennial. ISBN 0-06-019497-9 Banerjee S, Bhandary P, Woodhouse M, Sen TZ, Wise RP, Andorf CM (April 2021). "FINDER: an automated software package to annotate
Gene
Vowel sound represented by ⟨ɐ⟩ in IPA
British English is moving away from the [ɐ] quality towards [ʌ] found in RP spoken in the first half of the 20th century (e.g. in Daniel Jones's speech)
Near-open_central_vowel
Problem in computer science
complexity subfield of computer science. It generalises the Boolean satisfiability problem (SAT) which is a decision problem considered in complexity
MAX-3SAT
Efficient algorithm to count points on elliptic curves
{\displaystyle r} we have r ϕ ( P ) = ϕ ( r P ) {\displaystyle r\phi (P)=\phi (rP)} . Thus ϕ ( P ) {\displaystyle \phi (P)} will have the same order as P {\displaystyle
Schoof's_algorithm
standard RP by the mid-20th century. In General American, the lot vowel has become unrounded and merged into /ɑ/ (the father–bother merger). This leaves RP with
Phonological history of English open back vowels
Phonological_history_of_English_open_back_vowels
Problem of counting solutions to logic formulas
negations (#MONOTONE-2-CNF). It is known that, assuming that NP is different from RP, #MONOTONE-2-CNF also cannot be approximated by a fully polynomial-time approximation
♯SAT
321–331.{{cite journal}}: CS1 maint: multiple names: authors list (link) Mears R.P. (1950). "The climbing rope defined" (PDF). The Alpine Journal. 57 (280):
History_of_cannabis_in_Italy
Model of computation
, where I {\displaystyle I} is the identity matrix. In computational complexity theory, DQC1; also known as the deterministic quantum computation with
One_clean_qubit
Chinese medium to heavy-lift launch vehicle
Geostationary transfer orbit (GTO). The Long March 7 can use 0, 2 or 4 boosters using RP-1 / LOX propellant. They are powered by a single oxidizer-rich staged combustion
Long_March_7
Archipelagic country in Southeast Asia
September 28, 2020. Retrieved April 21, 2023. Lee-Brago, Pia (May 30, 2003). "RP seeks observer status in OIC". The Philippine Star. Archived from the original
Philippines
Portfolio optimization model in finance
standard deviation of the portfolio. The CML equation is : RP = IRF + (RM – IRF)σP/σM where, RP = expected return of portfolio IRF = risk-free rate of interest
Markowitz_model
led from an earlier project, Spaniel, a surface-to-air missile based on the RP-3 rocket motor. During development, a variation known as Air Spaniel was considered
Artemis_(missile)
Every polynomial has a real or complex root
coefficients Rp(x)(a, b) and Sp(x)(a, b) are independent of x and completely defined by the coefficients of p(x). In terms of representation, Rp(x)(a, b)
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Data visualisation technique
projection of the data set onto a 2-dimensional subspace (of the Euclidean space Rp where the data resides). The subspaces are selected by taking small steps
Grand Tour (data visualisation)
Grand_Tour_(data_visualisation)
Economics theory
payment; U(W0) – Utility of the minimal payment; U(W1) – Utility of the maximal payment; W0 – Minimal payment; W1 – Maximal payment; RP – Risk premium
Risk_aversion
29 June 2021 – via ResearchGate. Deocaris CC, Alinsug MV, Cabelin GR, Jose RP (2024). "Neurigona susanrocesae, the first Neurigona species from the Philippines"
List of organisms named after famous people (born 1925–1949)
List_of_organisms_named_after_famous_people_(born_1925–1949)
Species of fish
Latin for "javelin" or "spear", referring to its elongate body form. Vari, R.P. and A.S. Harold, 2001. Phylogenetic study of the Neotropical fish genera
Creagrutus_runa
Brain stimulation through physical and social surroundings
enrichment affects the complexity and length of the dendrite arbors (upon which synapses form). Higher-order dendrite branch complexity is increased in enriched
Environmental_enrichment
Province in Sumatra, Indonesia
one of the country's most prosperous provinces, having a GDP per capita of Rp 72,571,750 (US$8,300.82) as of 2011, the fourth highest among all provinces
Riau_Islands
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
Domain of microorganisms
a021113. doi:10.1101/cshperspect.a021113. PMC 4526729. PMID 25818664. Fagan RP, Fairweather NF (March 2014). "Biogenesis and functions of bacterial S-layers"
Bacteria
Type of adverse event
Briand, Ed.) ISSN 1726-5886 [1] Douville, H., K. Raghavan, J. Renwick, R.P. Allan, P.A. Arias, M. Barlow, R. Cerezo-Mota, A. Cherchi, T.Y. Gan, J. Gergis
Natural_disaster
Quantum mechanics idea
quantum teleportation". Nature Reviews Physics. 5 (6): 339–353. Bibcode:2023NatRP...5..339H. doi:10.1038/s42254-023-00588-x. ISSN 2522-5820. Ji, Zhaoxu; Fan
Entanglement_swapping
System to identify resources on a network
such as DNSSEC records, or for human queries such as responsible person (RP) records. As a general-purpose database, the DNS has also been used in combating
Domain_Name_System
Engineering discipline
International System Safety Society API RP 14C p.1 API RP 14C p.vi API RP 14C p.15-16 API RP 14C p.28 API RP 14C p.57 API RP 14C p.29 "ISO 14617-1:2005 Graphical
Safety_engineering
Solid part of maxilla
Ruczinski, I; Scott, AF; Beaty, TH; Kramer, FJ; Wienker, TF; Steegers-Theunissen, RP; Rubini, M; Mossey, PA; Hoffman, P; Lange, C; Chichon, S; Propping, P; Knapp
Hard_palate
Algorithm for determining whether a number is prime
coRP. In 1992, the Adleman–Huang algorithm reduced the complexity to Z P P = R P ∩ c o R P {\displaystyle {\mathsf {{\color {Blue}ZPP}=RP\cap coRP}}}
Primality_test
12, 2012. Osorio, Ma. Elisa (February 20, 2009). "Toshiba unit to expand RP operations". The Philippine Star. Archived from the original on November 26
Economy_of_the_Philippines
Information systems theory
analysed the adoption, finding that compatibility, relative advantage, and complexity had the most significant relationships with adoption across a broad range
Technology_acceptance_model
Disorder of depression and mood episodes
1017/S003329172200201X. PMC 9647517. PMID 36016504. Shao W, Shao K, Bentall RP (2026). "Comorbid Schizophrenia and Psychotic Symptoms in Patients With Bipolar
Bipolar_disorder
Hypertension occurring during pregnancy
1016/j.fertnstert.2017.05.001. PMID 28577615. Beckmann CR, Ling FW, Smith RP, Barzansky BM, Herbert WN, Laube DW, eds. (2010). Obstetrics and gynecology
Pre-eclampsia
President of Indonesia from 1967 to 1998
rupiah to drop in value from a pre-crisis level of Rp. 2,600 to a low point in early 1998 of around Rp. 17,000. Consequently, many companies were bankrupted
Suharto
Bone in the penis
Retrieved 27 October 2015. Baryshnikov, Gennady F.; Bininda-Emonds, Olaf R.P.; Abramov, Alexei V. (2003). "Morphological variability and evolution of
Baculum
Network addressing and routing methodology
Source Discovery Protocol (MSDP) and its advantageous application as Anycast RP is an intra-domain feature that provides redundancy and load-sharing capabilities
Anycast
Problematic excessive alcohol consumption
1111/j.1530-0277.2009.01044.x. PMC 2883563. PMID 19764935. Crews FT, Vetreno RP, Broadwater MA, Robinson DL (2016). "Adolescent Alcohol Exposure Persistently
Alcoholism
ISBN 978-0-7546-6668-4. Leonard AE (2006). "Female Religious Orders". In Hsia RP (ed.). A companion to the Reformation world. Oxford: Blackwell. pp. 237–254
History_of_medicine
Sound frequency changes responsible for perceptions of loudness, pitch and timbre
339V. doi:10.1121/1.424503. PMID 9921660. Grimault N, Micheyl C, Carlyon RP, Arthaud P, Collet L (July 2000). "Influence of peripheral resolvability on
Temporal envelope and fine structure
Temporal_envelope_and_fine_structure
Psychosis beginning suddenly in the first two weeks after childbirth
psychose par une méthode neurolytique dérivée de l'hibernothérapie; le 4560 RP utilisée seul en cure prolongée et continue. Comptes Rendus de la Congrès
Postpartum_psychosis
Number divisible only by 1 and itself
(2000). "A centennial history of the prime number theorem". In Bambah, R.P.; Dumir, V.C.; Hans-Gill, R.J. (eds.). Number Theory. Trends in Mathematics
Prime_number
differentiate them from traditional roguelikes. Roguelite See above. Role-playing (RP) A broad set of behaviours within video games where players change their behaviour
Glossary_of_video_game_terms
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