The Revitalized Relationship Between Probabilistically Checkable Debate Systems, IP, and PSpace

Abstract

In 1990, PSPACE was shown to be identical to IP, the class of languages with interactive proofs [11, 2]. Recently, PSPACE was again recharacterized, this time in terms of (Random) Probabilistically Checkable Debate Systems [4, 5]. In particular, it was shown that SPACE = PCDS[log n, 1] = RPCDS [log n, 1]. We study the relativized behaviour of the classes defined by these debates systems in comparison with the classes IP and PSPACE.