Ask HN: Trusted-Untrusted Secure Computing Puzzle

Alice has a secret, complex function F(A,B) that takes one input from her, and one from Bob. Alice is trustworthy and honest. Bob is not. Normally, Alice generates her input, Bob sends her his input, and she publicly announces the official result of F(A,B). Alice's inputs are random. Bob's inputs depend on the list of all previous official results of F(A,B).

Alice wants to go on vacation, but Bob will still want F(A,B) results when she is away. He proposes that she pre-generate a list of N inputs, and give him a function G(B) such that G(B)=F(A,B) for the first N executions, and no valid result thereafter. He would give her his list of N inputs when she returns. Alice suspects that Bob will try to create a simulator for F(A,B), and use any knowledge of her inputs to optimize his own.

Is it possible for Alice to go on vacation, while also enabling Bob to calculate results without the possibility of cheating? If not, is it possible for Alice to prove that Bob had been cheating, and simply discard Bob's list of inputs?