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Decidability Explorer

Explore the fundamental limits of computation through decidable, undecidable, and semi-decidable problems

Decidability Explorer

Explore decidable, undecidable, and semi-decidable problems

Decidability Explorer 🔍

Explore the fundamental limits of computation through decidable, undecidable, and semi-decidable problems

Decidable

Problems with algorithms that always terminate and give correct answers

Always halts
Always correct

Semi-decidable

Problems that can be recognized but not decided

Halts on "yes" instances
May loop on "no" instances

Undecidable

Problems with no algorithmic solution

No algorithm exists
Fundamental limitation

Problems

Click to explore each problem

Regular Language Membership

Given a regular language L and string w, determine if w ∈ L

decidable

Context-Free Language Emptiness

Given a CFG G, determine if L(G) = ∅

decidable

Halting Problem

Given a TM M and input w, determine if M halts on w

undecidable

Turing Machine Acceptance

Given a TM M and input w, determine if M accepts w

semi-decidable

Turing Machine Equivalence

Given two TMs M₁ and M₂, determine if L(M₁) = L(M₂)

undecidable

Turing Machine Finiteness

Given a TM M, determine if L(M) is finite

undecidable

Select a Problem

Choose a problem from the list to explore its decidability properties