A Higher-Order Characterization of Probabilistic Polynomial Time
Ugo Dal Lago, Paolo Parisen Toldin · Lecture notes in computer science · 2012
We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than \(\frac{1}{2}\). Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann’s SLR with a probabilistic primitive, which enjoys basic properties such as subject reduction and confluence. Polynomial time soundness of RSLR is obtained by syntactical means, as opposed to the standard literature on SLR-derived systems, which use semantics in an essential way.