A Logic-style Version of Interactive Proofs

Interactive proofs are de ned in terms of a conversation between two Turing machines, the prover and the veri er. We de ne an equivalent kind of proof in terms more usual for logic: our proofs are derivations from axioms by rules of inference. Namely, we consider proofs in formal arithmetic extended by some additional rule that uses random numbers. Such a proof can be considerably shorter than any proof of the same formula in arithmetic (however, a proof in the randomized system is allowed to have a small probability of error). This kind of proof is a special case of Arthur-Merlin proofs: Merlin generates a proof, Arthur supplies random numbers and checks the proof. On the other hand, we show that if a language L belongs to PSPACE then membership in L has polynomially long proofs in our system. This result, together with the well-known equality IP =PSPACE, shows equivalence in power between interactive proofs and polynomially long proofs in our extension of arithmetic.y yCopyright c 1996 Evgeny Dantsin. This technical report and other technical reports in this series can be obtained at ftp.csd.uu.se in the directory pub/papers/reports or at http://www.csd.uu.se/~thomas/reports.html. Some reports can be updated from time to time, check one of these addresses for the latest version. Section