Formula omitted]; unlocking the potential of compositional static average-case analysis

Abstract

Compositionality is the “golden key” to static analysis and plays a central role in static worst-case time analysis. We show that compositionality, combined with the capacity for tracking data distributions, unlocks a useful novel technique for average-case analysis.The applicability of the technique has been demonstrated via the static average-case analysis tool DISTRI. The tool automatically extracts average-case time from source code of programs implemented in the novel programming language MOQA1MOdular Quantitative Analysis.1. MOQA enables the prediction of the average number of basic steps performed in a computation, paving the way for static analysis of complexity measures such as average time or average power use. MOQA has as a unique feature a guaranteed average-case timing compositionality.The compositionality property brings a strong advantage for the programmer. The capacity to combine parts of code, where the average-time is simply the sum of the times of the parts, is a very helpful advantage in static analysis, something which is not available in current languages. Moreover, re-use is a key factor in the MOQA approach: once the average time is determined for a piece of code, then this time will hold in any context. Hence it can be re-used and the timing impact is always the same. Compositionality also improves precision of static average-case analysis, supporting the determination of accurate estimates on the average number of basic operations of MOQA programs.The MOQA “language” essentially consists of a suite of data-structuring operations together with conditionals, for-loops and recursion. As such MOQA can be incorporated in any traditional programming language, importing all of its benefits in a familiar context2MOQA is implemented at CEOL in Java 5.0 as MOQA-java.2.Compositionality for average-case is subtle and one may easily be tempted to conclude that compositionality “comes for free”. For genuine compositional reasoning however, one needs to be able to track data and their distribution throughout computations; a non-trivial problem. The lack of an efficient method to track distributions has plagued all prior static average-case analysis approaches. We show how MOQA enables the finitary representation and tracking of the distribution of data states throughout computations. This enables one to unlock the true potential of compositional reasoning. Links with reversible computing are discussed. The highly visual aspect of this novel and unified approach to the Analysis of Algorithms also has a pedagogical advantage, providing students with useful insights in the nature of algorithms and their analysis.