Incremental Quantitative Analysis on Dynamic Costs

Abstract: In quantitative program analysis, values are assigned to execution traces to represent a quality measure. Such analyses cover important applications, e.g. resource usage. Examining all traces is well known to be intractable and therefore traditional algorithms reason over an over-approximated set. Typically, inaccuracy arises due to inclusion of infeasible paths in this set. Thus path-sensitivity is one cure. However, there is another reason for the inaccuracy: that the cost model, i.e., the way in which the analysis of each trace is quantified, is dynamic. That is, the cost of a trace is dependent on the context in which the trace is executed. Thus the goal of accurate analysis, already challenged by path-sensitivity, is now further challenged by context-sensitivity. In this paper, we address the problem of quantitative analysis defined over a dynamic cost model. Our algorithm is an "anytime" algorithm: it generates an answer quickly, but if the analysis resource budget allows, it progressively produces better solutions via refinement iterations. The result of each iteration remains sound, but importantly, must converge to an exact analysis when given an unlimited resource budget. In order to be scalable, our algorithm is designed to be incremental. We finally give evidence that a new level of practicality is achieved by an evaluation on a realistic collection of benchmarks.