Complexity Information Flow in a Multi-threaded Imperative Language

Abstract. We propose a type system to analyze the time consumed by multi-threaded imperative programs with a shared global memory, which delineates a class of safe multi-threaded programs. We demon-strate that a safe multi-threaded program runs in polynomial time if (i) it is strongly terminating wrt a non-deterministic scheduling policy or (ii) it terminates wrt a deterministic and quiet scheduling policy. As a consequence, we also characterize the set of polynomial time functions. The type system presented is based on the fundamental notion of data tiering, which is central in implicit computational complexity. It regu-lates the information flow in a computation. This aspect is interesting in that the type system bears a resemblance to typed based informa-tion flow analysis and notions of non-interference. As far as we know, this is the first characterization by a type system of polynomial time multi-threaded programs.