complexity class RP
E679190
Complexity class RP is a probabilistic class of decision problems solvable in polynomial time by a randomized algorithm that never falsely accepts a no-instance but may with bounded probability reject a yes-instance.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Randomized Polynomial time | 1 |
| complexity class RP canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7666904 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: complexity class RP Context triple: [Complexity Theory, defines, complexity class RP]
-
A.
NP-completeness
NP-completeness is a central concept in computational complexity theory that classifies decision problems believed to be among the hardest in NP, such that a polynomial-time solution to any one of them would yield polynomial-time solutions to all problems in NP.
-
B.
Valiant–Vazirani theorem
The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
-
C.
PCP theorem
The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
-
D.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
-
E.
Adleman–Pomerance–Rumely primality test
The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: complexity class RP Target entity description: Complexity class RP is a probabilistic class of decision problems solvable in polynomial time by a randomized algorithm that never falsely accepts a no-instance but may with bounded probability reject a yes-instance.
-
A.
NP-completeness
NP-completeness is a central concept in computational complexity theory that classifies decision problems believed to be among the hardest in NP, such that a polynomial-time solution to any one of them would yield polynomial-time solutions to all problems in NP.
-
B.
Valiant–Vazirani theorem
The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
-
C.
PCP theorem
The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
-
D.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
-
E.
Adleman–Pomerance–Rumely primality test
The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
complexity class
ⓘ
probabilistic complexity class ⓘ |
| abbreviationOf |
Randomized Polynomial time
ⓘ
linked to:
complexity class RP
|
| acceptanceCondition | if x is in the language then the machine accepts x with probability at least 1/2 ⓘ |
| acceptanceErrorType | false negatives allowed ⓘ |
| algorithmType | Monte Carlo algorithm with one-sided error ⓘ |
| amplificationProperty | error probability can be reduced exponentially by independent repetition ⓘ |
| canonicalExampleProblem | primality testing before deterministic polynomial-time algorithms were discovered ⓘ |
| closureProperty |
closed under intersection with deterministic polynomial-time languages
ⓘ
closed under polynomial-time many-one reductions ⓘ closed under union with deterministic polynomial-time languages ⓘ |
| complementClass | coRP ⓘ |
| complexityMeasure | time complexity measured in worst-case polynomial time ⓘ |
| computationModel | Turing machine with access to random bits ⓘ |
| decisionProblemType | languages over finite alphabets ⓘ |
| definedOver | decision problems ⓘ |
| derandomizationQuestion | whether RP equals P is a central open problem in derandomization ⓘ |
| equivalentDefinition | languages L for which there exists a probabilistic polynomial-time Turing machine M such that x in L implies Pr[M(x) accepts] ≥ 1/2 and x not in L implies Pr[M(x) accepts] = 0 ⓘ |
| errorDirection | may reject some yes-instances with bounded probability ⓘ |
| errorOn | yes-instances only ⓘ |
| errorProbabilityBound | acceptance probability for yes-instances is at least 1/2 ⓘ |
| errorType | one-sided error ⓘ |
| fullName | Randomized Polynomial time ⓘ |
| historicalContext | introduced in the study of randomized algorithms and probabilistic complexity in the late 1970s and early 1980s ⓘ |
| inputType | finite binary strings ⓘ |
| machineModel | probabilistic Turing machine ⓘ |
| noErrorGuarantee | never accepts a no-instance ⓘ |
| noErrorOn | no-instances ⓘ |
| probabilityThresholdEquivalence | changing the success probability constant does not change the class ⓘ |
| probabilityThresholdFlexibility | any constant c with 0 < c < 1 can replace 1/2 in the definition ⓘ |
| randomnessType | uses unbiased random bits ⓘ |
| rejectionCondition | if x is not in the language then the machine accepts x with probability 0 ⓘ |
| rejectionErrorType | false positives not allowed ⓘ |
| relationshipToLasVegas | Las Vegas algorithms correspond to ZPP, not RP ⓘ |
| relationToBPP |
RP is a subset of BPP
ⓘ
it is unknown whether RP equals BPP ⓘ |
| relationTocoRP | coRP is the class of complements of languages in RP ⓘ |
| relationToNP |
RP is a subset of NP ∩ coNP is not known
ⓘ
it is unknown whether RP equals NP ⓘ |
| relationToP |
P is a subset of RP
ⓘ
it is unknown whether RP equals P ⓘ |
| relationToZPP | ZPP equals RP ∩ coRP ⓘ |
| researchArea | computational complexity theory ⓘ |
| subsetOf |
BPP
ⓘ
PSPACE ⓘ |
| supersetOf | P ⓘ |
| timeBound | polynomial time ⓘ |
| typicalBoundOnError | error probability can be made at most 2^{-k} for any k by repetition ⓘ |
| typicalUse | modeling efficient randomized algorithms with one-sided error ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: complexity class RP Description of subject: Complexity class RP is a probabilistic class of decision problems solvable in polynomial time by a randomized algorithm that never falsely accepts a no-instance but may with bounded probability reject a yes-instance.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
complexity class RP
linked to: complexity class RP