On the validation of complex systems operating in open contexts

Poddey, Alexander; Brade, Tino; Stellet, Jan Erik; Branz, Wolfgang · 2019 · OpenAlex-citations

DOI: 10.48550/arxiv.1902.10517

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Summary

This paper addresses the fundamental challenges of validating complex autonomous systems, such as automated vehicles and mobile robots, that operate in unstructured, public real-world environments characterized as "open contexts." The authors argue that the infinite complexity of these environments, combined with the emergent behavior of technical systems, creates a serious safety risk and a significant regulatory hurdle. Existing validation approaches often fail to address crucial aspects of this problem, risking societal rejection and financial loss. The paper aims to formalize the validation problem and propose a holistic strategy for achieving "valid" systems—those bearing no unreasonable risk—rather than "perfectly" valid ones, which are theoretically impossible to define or prove in open contexts. The authors introduce the "validation triangle," consisting of three interdependent aspects: Purpose (P), Context (C), and Realization (R). They argue that none of these aspects can be expressed in a formally complete manner due to "implicit infinite complexity." The development process involves iterative deductions that map this infinite reality into finite models ($\bar{T}$). However, these deductions create a "deductive gap" between the model and the effective reality ($T^\dagger$), potentially leading to systematic failures or "unacceptable losses." The paper critiques the reliance on verification alone, noting that a system can meet specifications yet fail to fulfill its intended purpose due to these gaps. To address this, the authors propose a systematic, system-view-based approach to validation (sys2val), which emphasizes making assumptions explicit and providing evidence for their validity at every step of the development process. Key findings include the identification of specific risks arising from the deductive gap, such as "misleading arguments" where tests appear to validate a hypothesis due to shared approximations in both the test design and interpretation. The authors demonstrate that once a relevant subspace is neglected during a deduction step, it cannot be reintroduced in subsequent steps; therefore, errors in early development phases require redesign at higher abstraction levels. The paper concludes that the development goal is not to achieve a perfectly valid system but to find an optimum between implicit and explicit complexity that robustly prevents unacceptable losses. This requires "ongoing validation" post-release to continuously check assumptions against evolving contexts. The authors integrate these concepts with existing standards like ISO 26262 and ISO/PAS 21448 (SOTIF), arguing that a holistic, iterative approach is necessary to manage the safety of autonomous systems in open environments.

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• Applied Guidance: standards test procedures