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In graph Frontier
Theory of ComputationComputer ScienceComputational ComplexityEstablished

Decidability

A problem is decidable if some algorithm always halts with a correct yes/no answer; some problems, like the halting problem, are not.

DecidabilityComputability theoryComputabilityHalting problemComputational complexity theoryTuring machineChurch-Turing ThesisComputational ComplexityGödel's incompleteness theorems

At a glance

Type
computation
Disciplines 3
Theory of ComputationComputer ScienceComputational Complexity
Mental models 0
—
Role in the graph
Connector

Key signals

Cross-disciplinary reach
Disciplines
3
  • Theory of Computation
  • Computer Science
  • Computational Complexity
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

System context

Decidabilityis part ofComputabilityEstablished

Open Computability →

Decidability is a part of Computability.

Decidabilityis part ofComputability theoryEstablished

Open Computability theory →

Decidability is a computability question.

Mechanism: It asks whether an algorithm can always answer a problem correctly and halt; some problems provably cannot.

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Currently dark in the atlas: no key date stored · 3 of 3 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Structural neighbourhood: 3 → 8 → 19 concepts reachable within 3 hops.

    structural · Structural reach — being reachable is not the same as being understood.

  • All 3 of its relationships stay within its own discipline — a field-specific concept in the current atlas.

    structural · Structural graph analysis — not a claim of importance, causation or history.

0%

cross-field
3 within-field, 0 cross-field

0 of 3 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Theory of Computation

Through this lens it connects to Computability and Halting problem.

Decidability through the Theory of Computation lens →

Computer Science

Through this lens it connects to Computability, Halting problem and Computability theory.

Decidability through the Computer Science lens →

Computational Complexity

Through this lens it connects to Halting problem.

Decidability through the Computational Complexity lens →

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

The scientific picture
  • Connects 3 other ideas across 3 disciplines.
  • Most of its connections are of the “Kind & structure” kind.

Derived from the graph’s real structure — observations, not a score.

Sources