AI safety via debate uses two competing models to help a human judge verify complex computational tasks. Previous work has established what problems debate can solve in principle, but has not analysed the practical cost of human oversight: how many queries must the judge make to the debate transcript? We introduce Debate Query Complexity}(DQC), the minimum number of bits a verifier must inspect to correctly decide a debate. Surprisingly, we find that PSPACE/poly (the class of problems which debate can efficiently decide) is precisely the class of functions decidable with O(log n) queries. This characterisation shows that debate is remarkably query-efficient: even for highly complex problems, logarithmic oversight suffices. We also establish that functions depending on all their input bits require Omega(log n) queries, and that any function computable by a circuit of size s satisfies DQC(f) <= log(s) + 3. Interestingly, this last result implies that proving DQC lower bounds of log(n) + 6 for languages in P would yield new circuit lower bounds, connecting debate query complexity to central questions in circuit complexity.

翻译：通过辩论实现人工智能安全的方法利用两个相互竞争的模型来协助人类裁判验证复杂的计算任务。先前的研究已经确立了辩论在原则上能够解决的问题，但尚未分析人类监督的实际成本：裁判需要对辩论记录进行多少次查询？我们引入了辩论查询复杂度（DQC），即验证者为了正确判定一场辩论所需检查的最小比特数。令人惊讶的是，我们发现PSPACE/poly（辩论能够高效判定的问题类别）恰好是那些可通过O(log n)次查询判定的函数类别。这一特征表明辩论具有显著的查询效率：即使对于高度复杂的问题，对数级别的监督便已足够。我们还证明，依赖于所有输入比特的函数需要Ω(log n)次查询，并且任何可由规模为s的电路计算的函数满足DQC(f) ≤ log(s) + 3。有趣的是，最后这一结果意味着，若能为P类语言证明log(n) + 6的DQC下界，将产生新的电路下界，从而将辩论查询复杂度与电路复杂性中的核心问题联系起来。