A Type System for Complexity Flow Analysis

Abstract

We propose a type system for an imperative programming language, which certifies program time bounds. This type system is based on secure flow information analysis. Each program variable has a level and we prevent information from flowing from low level to higher level variables. We also introduce a downgrading mechanism in order to delineate a broader class of programs. Thus, we propose a relation between security-typed language and implicit computational complexity. We establish a characterization of the class of polynomial time functions.

Complexity Information Flow in a Multi-threaded Imperative Language

“…As in [18], we define two classes of operators called neutral and positive. For this, let be the sub-word relation over W, which is defined by v w , iff there are u and u such that w = u.v .u , where .…”

“…The objective of this paper is to study the notion of complexity flow analysis introduced in [18] in the setting of concurrency. Our model of concurrency is a simple multi-threaded imperative programming language where threads communicate through global shared variables.…”

“…From a practical standpoint, an important issue is the expressivity of the class of safe multi-threaded programs. With this work and [18], we introduce a new approach in implicit computational complexity based on a type system. This study focuses on the intrinsic mechanisms which lead to analyze computational complexity.…”

“…In this paper, we separate complexity analysis from termination analysis but the tools on termination can be combined with our results since most of them require strong normalization of the considered process as an assumption. Finally our type system in this paper may be seen as a simplification of the type system of [18] for imperative language but in return there is no declassification mechanism.…”

Characterizing Polynomial and Exponential Complexity Classes in Elementary Lambda-Calculus

“…This intuition underlies several systems: ramified and safe recursion [13,4], in which data is organized into strata; stratified comprehension [14], where strata are used for quantification; variants of linear logic [9] where programs are divided into strata thanks to a modality. More recently stratification of data has been related fruitfully to type systems for non-interference [18].…”