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Oracle Induction Proofs — AI Alignment Forum

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{ 0 , 1 } L and { 0 , 1 } ∗ are the sets of all bitstrings of length L , and the set of all finite bitstrings, respectively. Elements of these sets are denoted by x . The length i prefix of x is denoted by x : i . B L is the set of all satisfiable booleans with all variables having an index ≤ L , and B is the set of all satisfiable booleans. Similarly, B ∗ L and B ∗ are the set of all booleans with all variables having an index ≤ L , and the set of all booleans. Elements of these sets are denoted by B . B ∧ B ′ is also a boolean. Bitstrings x may be interpreted as boolean constraints saying that the prefix of the bitstring must equal x . f is a function N + → N + that is time-constructible, monotonically increasing, and f ( t ) > t , which gives the runtime bound for traders. l is some function N + → N + upper-bounded by 2 f ( t ) that is time-constructible, monotonically increasing, and l ( t ) > t . It gives the most distant bit the oracle inductor

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