Oracle

An oracle is a theoretical "black box" that can give an answer to any instance of a certain problem in a single operation. The problem ⁠can be of any complexity class. It can even be an undecidable problem such as the halting problem. This is linked with the concept of Turing degrees.

Turing machines

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Types of oracles

• 0': decide the halting problem for computable programs.
• 1': decide the halting problem for programs containing 0', such as Beeping Busy Beaver
• Ω': decide the halting problem of any program, including programs containing Ω'^{[citation needed]}
• Ω2': decide if a program is well-founded (do not create any kind of paradox)^{[citation needed]}

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