From Jinja bytecode to term rewriting: A complexity reflecting transformation

Abstract

In this paper we show how the runtime complexity of imperative programs can be analysed fully automatically by a transformation to term rewrite systems, the complexity of which can then be automatically verified by existing complexity tools. We restrict to well-formed Jinja bytecode programs that only make use of non-recursive methods. The analysis can handle programs with cyclic data only if the termination behaviour is independent thereof.We exploit a term-based abstraction of programs within the abstract interpretation framework. The proposed transformation encompasses two stages. For the first stage we perform a combined control and data flow analysis by evaluating program states symbolically, which is shown to yield a finite representation of all execution paths of the given program through a graph, dubbed computation graph. In the second stage we encode the (finite) computation graph as a term rewrite system. This is done while carefully analysing complexity preservation and reflection of the employed transformations such that the complexity of the obtained term rewrite system reflects on the complexity of the initial program. Finally, we show how the approach can be automated and provide ample experimental evidence of the advantages of the proposed analysis.