Injecting Abstract Interpretations into Linear Cost Models

Abstract

We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs. The dioid structure of the set of costs allows for defining the quantitative semantics as a linear operator. We then present an abstraction technique inspired from abstract interpretation in order to effectively compute global cost information from the program. Abstraction has to take two distinct notions of order into account: the order on costs and the order on states. We show that our abstraction technique provides a correct approximation of the concrete cost computations.

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

“…Among the applications of such an approach we mention the verification of resource consumption properties in the setting of semirings [132], data flow analysis [61] and precision analysis [62] in the setting of the probabilistic While imperative language. An analogous approach very close in principle is adopted to analyze quantitative properties with regard to the use of resources such as time and memory [41]. An alternative approach, aiming to improve scalability, is based on the abstract interpretation of a probabilistic automaton semantics for a simple imperative language [130].…”