decidabilityä
Decidabilityä is a hypothetical concept in theoretical computer science that extends the standard notion of decidability. In ordinary decidability, a language L has a decision procedure that halts on every input and answers yes or no. Decidabilityä strengthens this by requiring that, in addition to a correct answer, the procedure also supplies a verifiable certificate of the answer, and does so within the same resource bounds. The certificate can be checked by a separate verifier algorithm and serves as a machine-checkable proof of correctness.
Origins and usage: The term is used in expository or speculative contexts to explore the idea of
Formal notion: A language L is decidabilityä if there exists a Turing machine M such that for
Relations: Every decidable language can be considered decidabilityä by allowing c to be trivial, so decidabilityä
Applications and limitations: The concept is primarily of theoretical interest, highlighting the role of verifiable proofs