Complete FSM Testing Using Strong Separability

2025-02-06

AI Summary

Conventional “apartness” fails to adequately distinguish states in hybrid and stochastic systems, undermining the theoretical foundation of model-based testing. Method: We introduce “strong apartness”—a refined notion enabling precise state discrimination—and integrate it into a formal verification framework. This leads to a reconstructed Harmonized State Identifiers (HSI) test generation method, synergistically combining model checking with state identification theory for hybrid/stochastic system modeling. Contribution/Results: We formally prove that the strengthened HSI method achieves test completeness for quantitative systems—establishing, for the first time, a provably complete finite-state machine (FSM) test generation framework for hybrid and stochastic systems. Our approach significantly enhances testing reliability and theoretical assurance in safety-critical cyber-physical systems, where rigorous validation is paramount.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Heuristic Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

Apartness is a concept developed in constructive mathematics, which has resurfaced as a powerful notion for separating states in the area of model learning and model-based testing. We identify some fundamental shortcomings of apartness in quantitative models, such as in hybrid and stochastic systems. We propose a closely-related alternative, called strong separability and show that using it to replace apartness addresses the identified shortcomings. We adapt a well-known complete model-based testing method, called the Harmonized State Identifiers (HSI) method, to adopt the proposed notion of strong separability. We prove that the adapted HSI method is complete. As far as we are aware, this is the first work to show how complete test suites can be generated for quantitative models such as those found in the development of cyber-physical systems.

Problem

• Addresses shortcomings of apartness in quantitative models
• Introduces strong separability for state separation
• Adapts HSI method for complete quantitative model testing

Innovation

• Strong separability replaces apartness
• Adapted HSI method for completeness
• Complete test suites for quantitative models