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在公开硬币（证明者可观察其结果）之外，使用有界数量的私密硬币所产生的影响。尽管在验证器具有足够大的时间和空间界限时，私密币与公共币机器的互换不会改变可验证语言的类别，但这种区别对常空间验证器的能力具有众所周知的影响。我们证明，常数数量的私密币"预算"（与输入长度无关）显著增强了具有有限状态验证器的公共币交互式证明的能力，并给出了复杂度类 $\rm P$ 的一个新刻画：该类别语言可由这类机器在期望多项式时间内以任意小误差进行验证。