A Higher-Order Characterization of Probabilistic Polynomial Time

Ugo Dal Lago (1, 2) , Paolo Parisen (1, 2)

1 FOCUS - Foundations of Component-based Ubiquitous Systems
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

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 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.

Mots clés: Implicit computational complexity; Probabilistic classes; Lambda calculus; Linear types

Domaines: Logique en informatique [cs.LO]

Ugo Dal Lago, Paolo Parisen. A Higher-Order Characterization of Probabilistic Polynomial Time. Information and Computation, 2015, 241, pp.114-141. ⟨10.1016/j.ic.2014.10.009⟩. ⟨hal-01231752v2⟩