Opacity problems in multi-energy timed automata

TL;DR

This work introduces guarded multi-energy timed automata as an extension of timed automata with multiple energy variables and guards over such variables, and establishes positive results over a number of subclasses.

Abstract

Cyber-physical systems can be subject to information leakage; in the presence of continuous variables such as time and energy, these leaks can be subtle to detect. We study here the verification of opacity problems over systems with observation over both timing and energy information. We introduce guarded multi-energy timed automata as an extension of timed automata with multiple energy variables and guards over such variables. Despite undecidability of this general formalism, we establish positive results over a number of subclasses, notably when the attacker observes the final energy and/or the execution time, but also when they have access to the value of the energy variables every time unit.