arXiv subjects

Jakub Večeřa

Publications and source records attributed to Jakub Večeřa.

3 recordsLinked to original sources

arXiv2026

On the Secret Protection Problem in Discrete-Event Systems

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 $Σ_{2}^{P}$-complete.

cs.FL↗

arXiv2025

Secret Protection in Labeled Petri Nets

We study the secret protection problem (SPP), where the objective is to find a policy of minimal cost ensuring that every execution path from an initial state to a secret state contains a sufficient number of protected events. The problem was originally introduced and studied in the setting of finite automata. In this paper, we extend the framework to labeled Petri nets. We consider two variants of the problem: the Parikh variant, where all occurrences of protected events along an execution path contribute to the security requirement, and the indicator variant, where each protected event is counted only once per execution path. We show that both variants can be solved in exponential space for labeled Petri nets, and that their decision versions are ExpSpace-complete. As a consequence, there is no polynomial-time or polynomial-space algorithm for these problems.

cs.FL↗

arXiv2020

Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A byproduct of our approach is a new uniqueness result for Gibbs particle processes.

math.PR↗