Probabilistic verifiers for asymmetric debates

TL;DR

This paper demonstrates that probabilistic verifiers can effectively check asymmetric debates, outperforming deterministic ones, and can decide complex languages within exponential time bounds, expanding the capabilities of debate systems.

Contribution

It introduces probabilistic verifiers for asymmetric debates, showing they outperform deterministic verifiers and can decide broader classes of languages within exponential time.

Findings

Probabilistic verifiers outperform deterministic ones in asymmetric debates.

Languages in NSPACE(s(n)) have debates decidable in 2^{s(n)} time with a blind prover.

Finite automata can solve P problems with small error using such debates.

Abstract

We examine the power of silent constant-space probabilistic verifiers that watch asymmetric debates (where one side is unable to see some of the messages of the other) between two deterministic provers, and try to determine who is right. We prove that probabilistic verifiers outperform their deterministic counterparts as asymmetric debate checkers. It is shown that the membership problem for every language in NSPACE(s(n)) has a 2^{s(n)}-time debate where one prover is completely blind to the other one, for polynomially bounded space constructible s(n). When partial information is allowed to be seen by the handicapped prover, the class of languages debatable in 2^{s(n)} time contains TIME(2^{s(n)}), so a probabilistic finite automaton can solve any decision problem in P with small error in polynomial time with the aid of such a debate. We also compare our systems with those with a single prover, and with competing-prover interactive proof systems.