On the limitations of analysing worst-case dynamic energy of processing

TL;DR

This paper investigates the challenges in accurately analyzing the worst-case dynamic energy consumption of software on embedded microprocessors, revealing computational hardness and limitations of existing models.

Contribution

It proves that calculating exact worst-case energy is NP-hard and demonstrates the impossibility of tight, safe bounds, highlighting fundamental limitations in current energy modeling approaches.

Findings

Finding exact worst-case energy is NP-hard.

Tight bounds cannot be guaranteed to be safe.

Energy models must trade safety for tightness.

Abstract

This paper examines dynamic energy consumption caused by data during software execution on deeply embedded microprocessors, which can be significant on some devices. In worst-case energy consumption analysis, energy models are used to find the most costly execution path. Taking each instruction's worst case energy produces a safe but overly pessimistic upper bound. Algorithms for safe and tight bounds would be desirable. We show that finding exact worst-case energy is NP-hard, and that tight bounds cannot be approximated with guaranteed safety. We conclude that any energy model targeting tightness must either sacrifice safety or accept overapproximation proportional to data-dependent energy.