complexity class NL
E679191
Complexity class NL is the set of decision problems solvable by a nondeterministic Turing machine using logarithmic space, central to studying space-bounded computation and problems like graph reachability.
All labels observed (1)
| Label | Occurrences |
|---|---|
| complexity class NL canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7666907 — 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 NL Context triple: [Complexity Theory, defines, complexity class NL]
-
A.
Undirected connectivity in log-space
"Undirected connectivity in log-space" is a landmark theoretical computer science paper by Omer Reingold that proved the complexity classes L and SL are equal by giving a deterministic log-space algorithm for undirected graph connectivity.
-
B.
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.
-
C.
Cook–Levin theorem
The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
-
D.
P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
-
E.
Furst–Saxe–Sipser lower bounds
Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
- 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 NL Target entity description: Complexity class NL is the set of decision problems solvable by a nondeterministic Turing machine using logarithmic space, central to studying space-bounded computation and problems like graph reachability.
-
A.
Undirected connectivity in log-space
"Undirected connectivity in log-space" is a landmark theoretical computer science paper by Omer Reingold that proved the complexity classes L and SL are equal by giving a deterministic log-space algorithm for undirected graph connectivity.
-
B.
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.
-
C.
Cook–Levin theorem
The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
-
D.
P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
-
E.
Furst–Saxe–Sipser lower bounds
Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf | complexity class ⓘ |
| acceptanceCondition | existence of an accepting computation path ⓘ |
| alternativeName | NLOGSPACE NERFINISHED ⓘ |
| centralTo | space-bounded computation ⓘ |
| characterizedBy | existence of a path in a configuration graph using O(log n) space ⓘ |
| closedUnder |
Kleene star
NERFINISHED
ⓘ
concatenation ⓘ homomorphism ⓘ inverse homomorphism ⓘ logspace many-one reductions ⓘ union ⓘ |
| complementClass | coNL ⓘ |
| completeProblem |
2-SAT (under logspace reductions)
ⓘ
ST-CONNECTIVITY ⓘ context-free grammar membership (under logspace reductions) ⓘ directed s-t reachability ⓘ graph reachability ⓘ path existence in directed graphs ⓘ |
| configurationGraphSize | polynomial in input size ⓘ |
| contains | L ⓘ |
| definedOver | decision problems ⓘ |
| equalityProofYear | 1987 ⓘ |
| equalityProvedBy |
Neil Immerman
NERFINISHED
ⓘ
Róbert Szelepcsényi NERFINISHED ⓘ |
| fullName | Nondeterministic Logarithmic Space NERFINISHED ⓘ |
| inputAccess | read-only input tape ⓘ |
| inputSizeNotation | n ⓘ |
| logspaceReductionsUsedFor | NL-completeness ⓘ |
| machineModel | nondeterministic Turing machine ⓘ |
| notKnownToBeClosedUnder | complement ⓘ |
| openQuestion |
whether L = NL
ⓘ
whether NL = P ⓘ |
| outputType | decision (yes/no) ⓘ |
| rejectionCondition | no accepting computation path ⓘ |
| relatedResult | NL = coNL ⓘ |
| relatedTo |
L
ⓘ
P ⓘ PSPACE NERFINISHED ⓘ coNL ⓘ |
| resourceBound | logarithmic space ⓘ |
| spaceMeasure | O(log n) work tape cells ⓘ |
| subsetOf |
P
ⓘ
PSPACE NERFINISHED ⓘ |
| supersetOf | L ⓘ |
| typicalMachineRestriction | single work tape with O(log n) cells ⓘ |
| typicalProblemDomain |
graph problems
ⓘ
reachability problems ⓘ verification of simple properties ⓘ |
| usedIn |
complexity theory
ⓘ
theory of computation ⓘ |
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 NL Description of subject: Complexity class NL is the set of decision problems solvable by a nondeterministic Turing machine using logarithmic space, central to studying space-bounded computation and problems like graph reachability.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.