NE (complexity)

In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}.

Version

v1 · 2026-09-28 · History

Domain-specific #

10929

Domain group

Applied Sciences & Engineering

Origin domain

Computer Science & Software Engineering

Subdomain

Computational Complexity Theory → Computer Science & Software Engineering

Core Idea

NE (complexity) is treated here as the recurring mathematicslogicstatistics identity summarized by this source-grounded definition: In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}. In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}. It is similar to NEXPTIME, the set of decision problems that can be solved by a non-deterministic Turing machine in time.

Scope of Application

• Documented setting. In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}.

• Documented setting. It is similar to NEXPTIME, the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{nO(1)}.

• Documented setting. By definition, it is contained in NEXPTIME.

• Documented setting. NE, unlike NEXPTIME, is not closed under polynomial-time many-one reductions.

• Documented setting. In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}.

Clarity

A clear use of NE (complexity) names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}.

Manages Complexity

NE (complexity) compresses multiple mathematicslogicstatistics details into a stable diagnostic relation. The source shows both the central mechanism—it is similar to NEXPTIME, the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{nO(1)}.—and the practical consequence—it is similar to NEXPTIME, the set of decision problems that can be solved by a non-deterministic Turing machine in time.

Abstract Reasoning

1. Type the carrier. Identify the mathematicslogicstatistics entities to which the claim applies.
2. State the relation. Use the source-grounded identity: In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}.
3. Check operation and conditions. By definition, it is contained in NEXPTIME.
4. Demand recognition evidence. NE, unlike NEXPTIME, is not closed under polynomial-time many-one reductions.
5. Test variation.

Knowledge Transfer

Within the home domain. Knowledge about NE (complexity) transfers literally when a new case preserves the same carrier type, relation, and recognition test. In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{O(n)}. It is similar to NEXPTIME, the set of decision problems that can be solved by a non-deterministic Turing machine in time 2^{nO(1)}. Beyond the home domain. No canonical parent is asserted for NE (complexity).

Relationships to Other Abstractions

Current abstraction NE (complexity) Domain-specific

Parents (1) — more general patterns this builds on

• NE (complexity) is a kind of Complexity Class Domain-specific

  NE is a complexity class bounded by nondeterministic single-exponential time.

Hierarchy paths (6) — routes to 5 parentless roots

• NE (complexity) → Complexity Class → Classification

Show alternative paths (5)

Neighborhood in Abstraction Space

NE (complexity) sits in a sparse region of the domain-specific corpus (65^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Computation Models & Complexity Classes (37 abstractions)

Nearest neighbors

• SC (complexity) — 0.85
• Unambiguous finite automaton — 0.84
• SL (complexity) — 0.84
• Parallel computation thesis — 0.84
• Boolean hierarchy — 0.84

Computed from structural-signature embeddings · 2026-10-08