Many-Valued Logics and Holographic Proofs

We reformulate the subject of holographic proof checking in terms of three-valued logic. In this reformulation the recursive proof checking idea of Arora and Safra gets an especially elegant form. Our approach gives a more concise and accurate treatment of the holographic proof theory, and yields easy to check proofs about holographic proofs. A consequence of our results is that for any Ɛ > 0 MAX3SAT instances cannot be approximated in TIME(2n1-Ɛ) within a factor which tends to 1 when n tends to infinity, unless 3SAT can be solved in TIME(2n1-Ɛ) for some Ɛ > 0.