Complete FSM testing using strong separability

Hierons, R.M. orcid.org/0000-0002-4771-1446 and Mousavi, M.R. (2026) Complete FSM testing using strong separability. In: Bertrand, N. and Milius, S., (eds.) Foundations of Software Science and Computation Structures: 29th International Conference, FoSSaCS 2026, Held as Part of the International Joint Conferences on Theory and Practice of Software, ETAPS 2026, Turin, Italy, April 11–16, 2026, Proceedings. 29th International Conference, FoSSaCS 2026, Held as Part of the International Joint Conferences on Theory and Practice of Software, ETAPS 2026, 11-16 Apr 2026, Turin, Italy. Lecture Notes in Computer Science, vol. LNCS 16503. Springer, pp. 328-349. ISBN: 9783032227294. ISSN: 0302-9743. EISSN: 1611-3349.

Abstract

Apartness is a concept developed in constructive mathematics, which has resurfaced in the areas 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, the Harmonized State Identifiers (HSI) method, to adopt 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.

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Item Type:	Proceedings Paper
Authors/Creators:	Hierons, R.M. https://orcid.org/0000-0002-4771-1446 Mousavi, M.R.
Editors:	Bertrand, N. Milius, S.
Copyright, Publisher and Additional Information:	© 2026 The Author(s). Except as otherwise noted, this author-accepted version of a conference paper published in Foundations of Software Science and Computation Structures: 29th International Conference, FoSSaCS 2026, Held as Part of the International Joint Conferences on Theory and Practice of Software, ETAPS 2026, Turin, Italy, April 11–16, 2026, Proceedings is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ © The Editor(s) (if applicable) and The Author(s), 2026. Open Access. This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits any noncommercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if you modified the licensed material. You do not have permission under this license to share adapted material derived from this chapter or parts of it. The images or other third party material in this chapter are included in the chapter’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Keywords:	Finite state machine testing; cyber-physical systems; apartness; strong separability
Dates:	Accepted: 22 December 2025 Published (online): 15 April 2026 Published: 16 April 2026
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield)
Funding Information:	Funder Grant number UK Research and Innovation EP/V026801/2
Date Deposited:	16 Jan 2026 16:09
Last Modified:	17 Apr 2026 11:23
Status:	Published
Publisher:	Springer
Series Name:	Lecture Notes in Computer Science
Refereed:	Yes
Identification Number:	10.1007/978-3-032-22730-0_16
Related URLs:	Conference
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:236622

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Complete FSM testing using strong separability

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