常数硬币完全信息辩论系统：$\mathsf{P}$ 类语言具有任意小强错误的判定
Constant-Coin Complete-Information Debates for $\mathsf{P}$ with Arbitrarily Small Strong Error
- Department of Computer Engineering, Boğaziçi University（博阿齐希大学计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文针对P类语言，构造了使用常数随机比特的完全信息辩论验证器，实现任意小的强错误，通过模拟交替多头自动机并允许反驳者弃权来确保终止。
中文摘要 AI 辅助
我们研究完全信息辩论系统，其中概率有限状态验证器读取证明者和反驳者的交替消息。Demirci、Say 和 Yakaryılmaz 证明了 $\mathsf{P}$ 中的每个语言都有这样的辩论，可用常数个随机比特和任意小的弱错误进行验证。他们的强错误构造（也将非终止视为失败）不允许任意错误缩减。我们弥补了这一空白：对于每个 $L\in\mathsf{P}$ 和每个 $\varepsilon>0$，存在一个使用常数个私有硬币抛掷的常数空间验证器，具有完全完备性和至多 $\varepsilon$ 的强错误。该验证器模拟一个多项式时间交替多头有限自动机，并私下抽查其一个输入头。关键观察是，对于非成员输入，当证明者首次错误报告头读取时，反驳者可以放弃该轮。这确保了当反驳者遵循指定策略时，针对任何证明者都能终止，并允许通过重复进行强错误缩减。
英文摘要
We study complete-information debate systems in which a probabilistic finite-state verifier reads the alternating messages of a prover and a refuter. Demirci, Say, and Yakaryılmaz showed that every language in $\mathsf{P}$ has such debates checkable with a constant number of random bits and arbitrarily small weak error. Their strong-error construction, which also counts nontermination as failure, did not permit arbitrary error reduction. We close this gap: for every $L\in\mathsf{P}$ and every $\varepsilon>0$, there is a constant-space verifier using a constant number of private coin tosses that has perfect completeness and strong error at most $\varepsilon$. The verifier simulates a polynomial-time alternating multihead finite automaton, privately spot-checking one of its input heads. The key observation is that, on a nonmember, the refuter may concede any round in which the prover first misreports a head reading. This ensures termination against every prover when the refuter follows the specified strategy, and permits strong-error reduction by repetition.
