Control-flow refinement and progress invariants for bound analysis

Abstract

Symbolic complexity bounds help programmers understand the performance characteristics of their implementations. Existing work provides techniques for statically determining bounds of procedures with simple control-flow. However, procedures with nested loops or multiple paths through a single loop are challenging.In this paper we describe two techniques, control-flow refinement and progress invariants, that together enable estimation of precise bounds for procedures with nested and multi-path loops. Control-flow refinement transforms a multi-path loop into a semantically equivalent code fragment with simpler loops by making the structure of path interleaving explicit. We show that this enables non-disjunctive invariant generation tools to find a bound on many procedures for which previous techniques were unable to prove termination. Progress invariants characterize relationships between consecutive states that can arise at a program location. We further present an algorithm that uses progress invariants to compute precise bounds for nested loops. The utility of these two techniques goes beyond our application to symbolic bound analysis. In particular, we discuss applications of control-flow refinement to proving safety properties that otherwise require disjunctive invariants.We have applied our methodology to over 670,000 lines of code of a significant Microsoft product and were able to find symbolic bounds for 90% of the loops. We are not aware of any other published results that report experiences running a bound analysis on a real code-base.

Static Analysis

“…The third and last connection with previous work is related to the WCCC computation. The method of Gulwani et al [24,23] for proving termination and bounding the complexity consists in creating counters -new variables which are incremented when traversing some transitions -and asking an invariant generator for bounds on the counter values. An elaborate system is proposed for selecting the transitions to be counted, which necessitates repeated calls to the invariant generator.…”

“…As our ranking function shows, the "outer" counter should be placed either on the transition from lbl 5 to lbl 6 or on the transition from lbl 6 to lbl 10 . Or the graph must be transformed as proposed in [23], but with a risk of complexity increase. We believe that our work bridges the gap between techniques based on the placement of counters and the use of abstract interpretation to bound them, and techniques based on global ranking functions to derive complexity bounds.…”

Quantitative dynamic‐memory analysis for Java

“…[8,9,14,21,22]), on one hand, and quantitative analysis (e.g. [11,12,[23][24][25][26]), on the other, are currently subject of intensive research (see [27] for a detailed account). Nevertheless, we are not aware of any other integrated tool-suite, like ours, able to generate scoped-memory regions and method-level certificates of memory usage.…”

“…The closest related works are those of Chin et al [25,28], Albert et al [23,24], and Gulwani et al [26,29]. The work of Chin relies on a type system and Presburger arithmetic.…”

Software bloat analysis

“…Finding such inefficiencies can be naturally thought of as a testing problem, where special test strategies (e.g., worst-case complexity testing [7]) may need to be created to evaluate how efficient a specific implementation is. It is also possible to employ sophisticated program analysis techniques, such as those developed in the SPEED project [11,15,14,12,13], to compute symbolic resource bounds for program components, which can provide useful insights into how they perform as a function of their inputs and can produce early warnings about potential performance problems.…”