{"paper":{"title":"Notions of Centralized and Decentralized Opacity in Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.SY","authors_text":"Bhaskar Ramasubramanian, Rance Cleaveland, Steven I. Marcus","submitted_at":"2019-03-16T02:59:12Z","abstract_excerpt":"We formulate notions of opacity for cyberphysical systems modeled as discrete-time linear time-invariant systems. A set of secret states is $k$-ISO with respect to a set of nonsecret states if, starting from these sets at time $0$, the outputs at time $k$ are indistinguishable to an adversarial observer. Necessary and sufficient conditions to ensure that a secret specification is $k$-ISO are established in terms of sets of reachable states. We also show how to adapt techniques for computing under-approximations and over-approximations of the set of reachable states of dynamical systems in orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06869","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}