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arXiv · 2312.00458

Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-free Languages

Thomas Brihaye·Sophie Pinchinat·Alexandre Terefenko
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Abstract

We present a mathematical setting for attack-defense trees, a classic graphical model to specify attacks and countermeasures. We equip attack-defense trees with (trace) language semantics allowing to have an original dynamic interpretation of countermeasures. Interestingly, the expressiveness of attack-defense trees coincides with star-free languages, and the nested countermeasures impact the expressiveness of attack-defense trees. With an adequate notion of countermeasure-depth, we exhibit a strict hierarchy of the star-free languages that does not coincides with the classic one. Additionally, driven by the use of attack-defense trees in practice, we address the decision problems of trace membership and of non-emptiness, and study their computational complexities parameterized by the countermeasure-depth.

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Thomas Brihaye, Sophie Pinchinat, Alexandre Terefenko. 2023-12-01. Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-free Languages. https://arxiv.org/abs/2312.00458

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