Injecting Abstract Interpretations into Linear Cost Models

TL;DR

This paper introduces a semantics-based framework that uses linear operators and abstract interpretation techniques to analyze and approximate the resource usage of programs effectively.

Contribution

It presents a novel abstraction method combining cost and state orders, enabling accurate and efficient global cost analysis of programs.

Findings

Provides a correct approximation of concrete cost computations

Utilizes dioid structure for defining quantitative semantics

Enables effective resource analysis through abstraction

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.