This work presents a technique to compute symbolic polynomial approximations of the amount of dynamic memory required to safely execute a method without running out of memory, for Javalike imperative programs. We consider object allocations and deallocations made by the method and the methods it transitively calls. More precisely, given an initial configuration of the stack and the heap, the peak memory consumption is the maximum space occupied by newly created objects in all states along a run from it. We over-approximate the peak memory consumption using a scopedmemory management where objects are organized in regions associated with the lifetime of methods. We model the problem of computing the maximum memory occupied by any region configuration as a parametric polynomial optimization problem over a polyhedral domain and resort to Bernstein basis to solve it. We apply the developed tool to several benchmarks.

The peak heap consumption of a program is the maximum size of the live data on the heap during the execution of the program, i.e., the minimum amount of heap space needed to run the program without exhausting the memory. It is well-known that garbage collection (GC) makes the problem of predicting the memory required to run a program difficult. This paper presents, the best of our knowledge, the first live heap space analysis for garbage-collected languages which infers accurate upper bounds on the peak heap usage of a program’s execution that are not restricted to any complexity class, i.e., we can infer exponential, logarithmic, polynomial, etc., bounds. Our analysis is developed for an (sequential) object-oriented bytecode language with a scoped-memory manager that reclaims unreachable memory when methods return. We also show how our analysis can accommodate other GC schemes which are closer to the ideal GC which collects objects as soon as they become unreachable. The practicality of our approach is experimentally evaluated on a prototype implementation. We demonstrate that it is fully automatic, reasonably accurate and efficient by inferring live heap space bounds for a standardized set of benchmarks, the JOlden suite.

Memory requirement estimation is an important issue in the development of embedded systems, since memory directly influences performance, cost and power consumption. It is therefore crucial to have tools that automatically compute accurate estimates of the memory requirements of programs to better control the development process and avoid some catastrophic execution exceptions. Many important memory issues can be expressed as the problem of maximizing a parametric polynomial defined over a parametric convex domain. Bernstein expansion is a technique that has been used to compute upper bounds on polynomials defined over intervals and parametric “boxes”. In this paper, we propose an extension of this theory to more general parametric convex domains and illustrate its applicability to the resolution of memory issues with several application examples.

Abstract. This work presents a technique to compute symbolic nonlinear approximations of the amount of dynamic memory required to safely run a method in (Java-like) imperative programs. We do that for scoped-memory management where objects are organized in regions associated with the lifetime of methods. Our approach resorts to a symbolic non-linear optimization problem which is solved using Bernstein basis. 1

This paper presents an analysis that derives a formula describing the worst-case live heap space usage of programs in a functional language with automated memory management (garbage collection). First, the given program is automatically transformed into bound functions that describe upper bounds on the live heap space usage and other related space metrics in terms of the sizes of function arguments. The bound functions are simplified and rewritten to obtain recurrences, which are then solved to obtain the desired formulas characterizing the worst-case space usage. These recurrences may be difficult to solve due to uses of the maximum operator. We give methods to automatically solve categories of such recurrences. Our analysis determines and exploits monotonicity and monotonicity-like properties of bound functions to derive upper bounds on heap usage, without considering behaviors of the program that cannot lead to maximal space usage.