Probabilistic Soft Type Assignment

Abstract: 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.