IP = PSPACE Using Error-Correcting Codes

The $\mathbf{IP}$ Theorem, which asserts that $\mathbf{IP}=\mathbf{PSPACE}$ [Lund et al., J. ACM, 39 (1992), pp. 859--868; Shamir, J. ACM, 39 (1992), pp. 878--880], is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial. The intuition that underlies the use of polynomials is commonly explained by the fact that polynomials constitute good error-correcting codes. However, the known proofs seem tailored to the use of polynomials and do not generalize to arbitrary error-correcting codes. In this work, we show that the $\mathbf{IP}$ theorem can be proved by using general error-correcting codes and their tensor products. We believe that this establishes a rigorous basis for the aforementioned intuition and sheds further light on the $\mathbf{IP}$ theorem.