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arXiv · 2509.14372

On the Secret Protection Problem in Discrete-Event Systems

Tomáš Masopust·Jakub Večeřa
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Abstract

The secret protection problem (SPP) seeks to synthesize a minimum-cost policy ensuring that every execution from an initial state to a secret state includes a sufficient number of protected events. The problem is solvable in polynomial time under the assumption that transitions are uniquely labeled. When this assumption is relaxed, the problem becomes weakly \NP-hard. We first strengthen the result by showing that the problem is strongly \NP-hard even if all parameters are restricted to binary values. We then propose a formulation of SPP as an integer linear programming (ILP) problem, and empirically evaluate the scalability and effectiveness of the ILP-based approach on relatively large systems. Finally, we examine the complexity of a variant of SPP in which only distinct protected events contribute to clearance and show that its decision version is $\Sigma_{2}^{P}$-complete.

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Tomáš Masopust, Jakub Večeřa. 2025-09-17. On the Secret Protection Problem in Discrete-Event Systems. https://arxiv.org/abs/2509.14372

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