We consider the effects of allowing a finite state verifier in an interactive proof system to use a bounded number of private coins, in addition to "public" coins whose outcomes are visible to the prover. Although swapping between private and public-coin machines does not change the class of verifiable languages when the verifiers are given reasonably large time and space bounds, this distinction has well known effects for the capabilities of constant space verifiers. We show that a constant private-coin "budget" (independent of the length of the input) increases the power of public-coin interactive proofs with finite state verifiers considerably, and provide a new characterization of the complexity class $\rm P$ as the set of languages that are verifiable by such machines with arbitrarily small error in expected polynomial time.

翻译：我们研究了在交互式证明系统中允许有限状态验证器使用有限数量的私密硬币（其结果对证明方不可见）并辅以结果对证明方可见的“公开”硬币时所产生的影响。尽管在验证器拥有足够大的时间和空间界限时，交换私密硬币与公开硬币机器并不会改变可验证语言类，但对于常空间验证器的能力而言，这种区别具有众所周知的影响。我们证明，常数量私密硬币“预算”（与输入长度无关）能显著增强带有有限状态验证器的公开硬币交互式证明的能力，并给出复杂性类$\rm P$的一个新特征刻画：即由这类机器在期望多项式时间内以任意小误差可验证的语言集合。