Reactive Safety

TL;DR

This paper explores reactive safety in systems with environment interactions, showing it encompasses a broader class of properties than standard safety, and provides algorithms for verification and synthesis.

Contribution

It introduces reactive safety as a larger class than standard safety and offers algorithms for checking and translating reactive safety properties.

Findings

Reactive safety is strictly larger than standard safety.

Algorithms for checking reactive safety properties.

Extensions of verification and synthesis methods.

Abstract

The distinction between safety and liveness properties is a fundamental classification with immediate implications on the feasibility and complexity of various monitoring, model checking, and synthesis problems. In this paper, we revisit the notion of safety for reactive systems, i.e., for systems whose behavior is characterized by the interplay of uncontrolled environment inputs and controlled system outputs. We show that reactive safety is a strictly larger class of properties than standard safety. We provide algorithms for checking if a property, given as a temporal formula or as a word or tree automaton, is a reactive safety property and for translating such properties into safety automata. Based on this construction, the standard verification and synthesis algorithms for safety properties immediately extend to the larger class of reactive safety.