The reachability-bound problem

Abstract

We define the reachability-bound problem to be the problem of finding a symbolic worst-case bound on the number of times a given control location inside a procedure is visited in terms of the inputs to that procedure. This has applications in bounding resources consumed by a program such as time, memory, network-traffic, power, as well as estimating quantitative properties (as opposed to boolean properties) of data in programs, such as information leakage or uncertainty propagation. Our approach to solving the reachability-bound problem brings together two different techniques for reasoning about loops in an effective manner. One of these techniques is an abstract-interpretation based iterative technique for computing precise disjunctive invariants (to summarize nested loops). The other technique is a non-iterative proof-rules based technique (for loop bound computation) that takes over the role of doing inductive reasoning, while deriving its power from the use of SMT solvers to reason about abstract loop-free fragments. Our solution to the reachability-bound problem allows us to compute precise symbolic complexity bounds for several loops in .Net base-class libraries for which earlier techniques fail. We also illustrate the precision of our algorithm for disjunctive invariant computation (which has a more general applicability beyond the reachability-bound problem) on a set of benchmark examples.

On Verifying Resource Contracts using Code Contracts

“…In this setting developers would only need to specify complex or hard-to-infer annotations, not worrying about annotations that can be easily inferred. In this matter, we plan to port our previous work on inference of memory consumption for Java [10] to .NET and extend other tools capable of inferring resource usage (e.g., [19]) in order to make them capable of dealing with dynamic memory usage.…”

“…It is well known that inferring, and even checking, quantitative bounds (e.g., resource usage) is difficult [10]. Nevertheless, there has been noticeable progress in techniques that compute symbolic resource usage [10,4] and complexity [19] upper-bounds.…”

“…Recently, there were relevant advances in resource analysis for imperative and functional programs [12,8,10,17,5,20,19,21]. Most of them are aimed at inferring of resource consumption bounds rather than verifying them.…”

“…It is well known that inferring, and even checking, quantitative bounds (e.g., resource usage) is difficult [10]. Nevertheless, there has been noticeable progress in techniques that compute symbolic resource usage [10,4] and complexity [19] upper-bounds.In this paper we focus in enforcing dynamic memory consumption contracts. This is a particularly challenging problem because memory footprint does not monotonically increase during program execution (i.e., due to memory recycling).…”

LOOPUS - A Tool for Computing Loop Bounds for C Programs

“…Loopus can also be seen as contribution towards solving the termination problem for C programs as it provides a conceptually simpler alternative to recently proposed methods [1]. The underlying reasoning of Loopus builds on earlier work of the second author [2] of which we give a short description below. In contrast to [2] which is targeted at .NET programs, our tool analyzes programs written in C, which pose a different challenge to static analyses.…”