We model randomized complexity classes in the style of Implicit Computational Complexity. We introduce PSTA, a probabilistic version of STA, the type-theoretical counterpart of Soft Linear Logic. PSTA is a type assignment for an extension of Simpson's Linear Lambda Calculus and its surface reduction, where Linear additives express random choice. Linear additives are weaker than the usual ones; they allow for duplications harmlessly affecting the computational cost of normalization. PSTA is sound and complete w.r.t. probabilistic polynomial time functions and characterizes the probabilistic complexity classes PP and BPP, the latter slightly less implicitly than PP.

中文翻译：

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概率软类型分配

我们以隐式计算复杂性的风格对随机复杂性类进行建模。我们介绍了 PSTA，它是 STA 的概率版本，是软线性逻辑的类型理论对应物。PSTA 是 Simpson 线性 Lambda 演算的扩展及其表面归约的类型分配，其中线性添加剂表示随机选择。线性添加剂比普通添加剂弱；它们允许无害地影响归一化的计算成本的重复。PSTA 是可靠且完整的概率多项式时间函数，并表征概率复杂度类 PP 和 BPP，后者比 PP 隐含性稍低。