Complexity Information Flow in a Multi-threaded Imperative Language

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 demonstrate 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 regulates the information flow in a computation. This aspect is interesting in that the type system bears a resemblance to typed based information 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

Complexity Information Flow in a Multi-threaded Imperative Language

International audienceWe 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

A generic imperative language for polynomial time

The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative programming. We introduce a new approach to ramification which, among other benefits, adapts readily to fully general imperative programming. The novelty is in ramifying finite second-order objects, namely finite structures, rather than ramifying elements of free algebras. In so doing we bridge between Implicit Complexity's type theoretic characterizations of feasibility, and the data-flow approach of Static Analysis.Comment: 18 pages, submitted to a conferenc

A tier-based typed programming language characterizing Feasible Functionals

International audienceThe class of Basic Feasible Functionals BFF 2 is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a programming language with a type system guaranteeing this complexity bound. We give a characterization of BFF 2 based on an imperative language with oracle calls using a tier-based type system whose inference is decidable. Such a characterization should make it possible to link higher-order complexity with programming theory. The low complexity (cubic in the size of the program) of the type inference algorithm contrasts with the intractability of the aforementioned methods and does not restrain strongly the expressive power of the language