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Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-free Languages (2312.00458v1)

Published 1 Dec 2023 in cs.FL

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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