A Characterization on Necessary Conditions of Realizability for Reactive System Specifications

This paper focuses on verification for reactive system specifications. A reactive system is an open system that continuously interacts with an uncontrollable external environment, and it must often be highly safe and reliable. However, realizability checking for a given specification is very costly, so we need effective methods to detect and analyze defects in unrealizable specifications to refine them efficiently. We introduce a systematic characterization on necessary conditions of realizability. This characterization is based on quantifications for inputs and outputs in early and late behaviors and reveals four essential aspects of realizability: exhaustivity, strategizability, preservability and stability. Additionally, the characterization derives new necessary conditions, which enable us to classify unrealizable specifications systematically and hierarchically.