(2026-06) Towards a Doubly Efficient IP=PSPACE
2026-06-19
We show that every language in PSPACE decidable by a Turing machine in time admits a doubly efficient interactive proof system: the prover runs in time polynomial in T(n), and the verifier runs in time polynomial in n. This extends the best previously known regime for such proof systems from , established by Berger, Goyal, Hong, and Kalai (FOCS 2025), to .
Beyond improving the range of T, our protocol is substantially simpler than previous doubly efficient proofs for time-bounded PSPACE. Earlier constructions proceed indirectly: they first build batch interactive proofs and then invoke them as a black box to obtain doubly efficient protocols. In contrast, we give a direct construction. This not only simplifies the proof but also points to a more promising route for future improvements.