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Deep networks can usually depend on extracting more structural information to improve denoising results. However, they may ignore correlation between pixels from an image to pursue better denoising performance. Window transformer can use long- and short-distance modeling to interact pixels to address mentioned problem. To make a tradeoff between distance modeling and denoising time, we propose a heterogeneous window transformer (HWformer) for image denoising. HWformer first designs heterogeneous global windows to capture global context information for improving denoising effects. To build a bridge between long and short-distance modeling, global windows are horizontally and vertically shifted to facilitate diversified information without increasing denoising time. To prevent the information loss phenomenon of independent patches, sparse idea is guided a feed-forward network to extract local information of neighboring patches. The proposed HWformer only takes 30% of popular Restormer in terms of denoising time.

This paper studies the problem of increasing the connectivity of an ad-hoc peer-to-peer network subject to cyber-attacks targeting the agents in the network. The adopted strategy involves the design of local interaction rules for the agents to locally modify the graph topology by adding and removing links with neighbors. Two distributed protocols are presented to boost the algebraic connectivity of the network graph beyond $k-2\sqrt{k-1}$ where $k\in \mathbb{N}$ is a free design parameter; these two protocols are achieved through the distributed construction of random (approximate) regular graphs. One protocol leverages coordinated actions between pairs of neighboring agents and is mathematically proven to converge to the desired graph topology. The other protocol relies solely on the uncoordinated actions of individual agents and it is validated by a spectral analysis through Monte-Carlo simulations. Numerical simulations offer a comparative analysis with other state-of-the-art algorithms, showing the ability of both proposed protocols to maintain high levels of connectivity despite attacks carried out with full knowledge of the network structure, and highlighting their superior performance.

In this paper, we investigate the verification and enforcement of strong state-based opacity (SBO) in discrete-event systems modeled as partially-observed (nondeterministic) finite-state automata, including strong K-step opacity (K-SSO), strong current-state opacity (SCSO), strong initial-state opacity (SISO), and strong infinite-step opacity (Inf-SSO). They are stronger versions of four widely-studied standard opacity notions, respectively. We firstly propose a new notion of K-SSO, and then we construct a concurrent-composition structure that is a variant of our previously-proposed one to verify it. Based on this structure, a verification algorithm for the proposed notion of K-SSO is designed. Also, an upper bound on K in the proposed K-SSO is derived. Secondly, we propose a distinctive opacity-enforcement mechanism that has better scalability than the existing ones (such as supervisory control). The basic philosophy of this new mechanism is choosing a subset of controllable transitions to disable before an original system starts to run in order to cut off all its runs that violate a notion of strong SBO of interest. Accordingly, the algorithms for enforcing the above-mentioned four notions of strong SBO are designed using the proposed two concurrent-composition structures. In particular, the designed algorithm for enforcing Inf-SSO has lower time complexity than the existing one in the literature, and does not depend on any assumption. Finally, we illustrate the applications of the designed algorithms using examples., Comment: 30 pages, 20 figures, partial results in Section 3 were presented at IEEE Conference on Decision and Control, 2022. arXiv admin note: text overlap with arXiv:2204.04698

Opacity is a property that captures security concerns in cyber-physical systems and its verification plays a significant role. This paper investigates the verifications of K-step and infinite-step weak and strong opacity for partially observed nondeterministic finite state automata. K-step weak opacity is checked by constructing, for some states in the observer, appropriate state-trees, to propose a necessary and sufficient condition. Based on the relation between K-step weak and infinite-step weak opacity, a condition that determines when a system is not infinite-step weak opaque is presented. Regarding K-step and infinite-step strong opacity, we develop a secret-involved projected automaton, based on which we construct secret-unvisited state trees to derive a necessary and sufficient condition for K-step strong opacity. Furthermore, an algorithm is reported to compute a verifier that can be used to obtain a necessary and sufficient condition for infinite-step strong opacity. It is argued that, in some particular cases, the proposed methods achieve reduced complexity compared with the state of the art.

Inspired by privacy problems where the behavior of a system should not be revealed to an external curious observer, we investigate event concealment and concealability enforcement in discrete event systems modeled as non-deterministic finite automata under partial observation. Given a subset of secret events in a given system, concealability holds if the occurrence of all secret events remains hidden to a curious observer (an eavesdropper). A secret event is said to be (at least under some executions) unconcealable (inferable) if its occurrence can be indirectly determined with certainty after a finite number of observations. When concealability of a system does not hold (i.e., one or more secret events are unconcealable), we analyze how a defender, placed at the interface of the system with the eavesdropper, can be used to enforce concealability. The defender takes as input each observed event of the system and outputs a carefully modified event sequence (seen by the eavesdropper) using event deletion, insertion, or replacement. The defender is said to be C-enforceable if, following the occurrence of the secret events and regardless of subsequent activity generated by the system, it can always deploy a strategy to manipulate observations and conceal the events perpetually. We discuss systematic procedures to detect the presence of unconcealable secret events and verify C-Enforceability using techniques from state estimation and event diagnosis. We also propose a polynomial complexity construction for obtaining one necessary and one sufficient condition for C-Enforceability.

In this paper, we revisit the verification of strong K-step opacity (K-SSO) for partially-observed discrete-event systems modeled as nondeterministic finite-state automata. As a stronger version of the standard K-step opacity, K-SSO requires that an intruder cannot make sure whether or not a secret state has been visited within the last K observable steps. To efficiently verify K-SSO, we propose a new concurrent-composition structure, which is a variant of our previously- proposed one. Based on this new structure, we design an algorithm for deciding K-SSO and prove that the proposed algorithm not only reduces the time complexity of the existing algorithms, but also does not depend on the value of K. Furthermore, a new upper bound on the value of K in K-SSO is derived, which also reduces the existing upper bound on K in the literature. Finally, we illustrate the proposed algorithm by a simple example., Comment: 6 pages, 2 figures, submitted to IEEE CDC on March 28, 2022

Opacity, as an important property in information-flow security, characterizes the ability of a system to keep some secret information from an intruder. In discrete-event systems, based on a standard setting in which an intruder has the complete knowledge of the system's structure, the standard versions of current-state opacity and initial-state opacity cannot perfectly characterize high-level privacy requirements. To overcome such a limitation, in this paper we propose two stronger versions of opacity in partially-observed discrete-event systems, called \emph{strong current-state opacity} and \emph{strong initial-state opacity}. Strong current-state opacity describes that an intruder never makes for sure whether a system is in a secret state at the current time, that is, if a system satisfies this property, then for each run of the system ended by a secret state, there exists a non-secret run whose observation is the same as that of the previous run. Strong initial-state opacity captures that the visit of a secret state at the initial time cannot be inferred by an intruder at any instant. Specifically, a system is said to be strongly initial-state opaque if for each run starting from a secret state, there exists a non-secret run of the system that has the same observation as the previous run has. To verify these two properties, we propose two information structures using a novel concurrent-composition technique, which has exponential-time complexity $O(|X|^4|\Sigma_o||\Sigma_{uo}||\Sigma|2^{|X|})$, where $|X|$ (resp., $|\Sigma|$, $|\Sigma_o|$, $|\Sigma_{uo}|$) is the number of states (resp., events, observable events, unobservable events) of a system., Comment: 10 pages, 11 figures

In this paper we investigate multi-agent discrete-event systems with partial observation. The agents can be divided into several groups in each of which the agents have similar (isomorphic) state transition structures, and thus can be relabeled into the same template. Based on the template a scalable supervisor whose state size and computational cost are independent of the number of agents is designed for the case of partial observation. The scalable supervisor under partial observation does not need to be recomputed regardless of how many agents are added to or removed from the system. We generalize our earlier results to partial observation by proposing sufficient conditions for safety and maximal permissiveness of the scalable least restrictive supervisor on the template level. An example is provided to illustrate the proposed scalable supervisory synthesis.

In this paper, we study the problem of non-blockingness verification by tapping into the basis reachability graph (BRG). Non-blockingness is a property that ensures that all pre-specified tasks can be completed, which is a mandatory requirement during the system design stage. In this paper we develop a condition of transition partition of a given net such that the corresponding conflict-increase BRG contains sufficient information on verifying non-blockingness of its corresponding Petri net. Thanks to the compactness of the BRG, our approach possesses practical efficiency since the exhaustive enumeration of the state space can be avoided. In particular, our method does not require that the net is deadlock-free., Comment: This article is an extended version of the paper "C. Gu, Z. Ma, Z. Li and A. Giua. Non-blockingness verification of bounded Petri nets using basis reachability graphs. IEEE Control Systems Letters, doi:10.1109/LCSYS.2021.3087937, 2021" with benchmarks

This paper deals with the state estimation problem in discrete-event systems modeled with nondeterministic finite automata, partially observed via a sensor measuring unit whose measurements (reported observations) may be vitiated by a malicious attacker. The attacks considered in this paper include arbitrary deletions, insertions, or substitutions of observed symbols by taking into account a bounded number of attacks or, more generally, a total cost constraint (assuming that each deletion, insertion, or substitution bears a positive cost to the attacker). An efficient approach is proposed to describe possible sequences of observations that match the one received by the measuring unit, as well as their corresponding state estimates and associated total costs. We develop an algorithm to obtain the least-cost matching sequences by reconstructing only a finite number of possible sequences, which we subsequently use to efficiently perform state estimation. We also develop a technique for verifying tamper-tolerant diagnosability under attacks that involve a bounded number of deletions, insertions, and substitutions (or, more generally, under attacks of bounded total cost) by using a novel structure obtained by attaching attacks and costs to the original plant. The overall construction and verification procedure have complexity that is of O(|X|^2 C^2),where |X| is the number of states of the given finite automaton and C is the maximum total cost that is allowed for all the deletions, insertions, and substitutions. We determine the minimum value of C such that the attacker can coordinate its tampering action to keep the observer indefinitely confused while utilizing a finite number of attacks. Several examples are presented to demonstrate the proposed methods.

G-images refer to image data defined on irregular graph domains. This work elaborates a similarity-preserving Fuzzy C-Means (FCM) algorithm for G-image segmentation and aims to develop techniques and tools for segmenting G-images. To preserve the membership similarity between an arbitrary image pixel and its neighbors, a Kullback-Leibler divergence term on membership partition is introduced as a part of FCM. As a result, similarity-preserving FCM is developed by considering spatial information of image pixels for its robustness enhancement. Due to superior characteristics of a wavelet space, the proposed FCM is performed in this space rather than Euclidean one used in conventional FCM to secure its high robustness. Experiments on synthetic and real-world G-images demonstrate that it indeed achieves higher robustness and performance than the state-of-the-art FCM algorithms. Moreover, it requires less computation than most of them., Comment: This paper has been withdrawn by the author since some statements are not right as raised by other researchers

Traditional clustering methods are limited when dealing with huge and heterogeneous groups of gene expression data, which motivates the development of bi-clustering methods. Bi-clustering methods are used to mine bi-clusters whose subsets of samples (genes) are co-regulated under their test conditions. Studies show that mining bi-clusters of consistent trends and trends with similar degrees of fluctuations from the gene expression data is essential in bioinformatics research. Unfortunately, traditional bi-clustering methods are not fully effective in discovering such bi-clusters. Therefore, we propose a novel bi-clustering method by involving here the theory of Granular Computing. In the proposed scheme, the gene data matrix, considered as a group of time series, is transformed into a series of ordered information granules. With the information granules we build a characteristic matrix of the gene data to capture the fluctuation trend of the expression value between consecutive conditions to mine the ideal bi-clusters. The experimental results are in agreement with the theoretical analysis, and show the excellent performance of the proposed method.

Opacity is a confidentiality property that holds when certain secret strings of a given system cannot be revealed to an outside observer under any system activity. Opacity violations stimulate the study of opacity enforcement strategies. Among other methodologies, opacity has been enforced using insertion mechanisms, i.e., output obfuscation mechanisms that are allowed to insert fictitious output symbols before actual system outputs, in order to preserve opacity. This paper studies and analyzes more powerful extended insertion mechanisms, which can insert symbols before and after an actual system output, thus, providing opacity to a wider class of systems. In order to address practical considerations, the paper also introduces event insertion constraints (i.e., the case when only specific symbols can be inserted before and/or after an actual system output). For each case, we construct an appropriate verifier that can be used to obtain necessary and sufficient conditions for checking opacity enforceability.

This paper focuses on the problem of cyber attacks for discrete event systems under supervisory control. In more detail, the goal of the supervisor, who has a partial observation of the system evolution, is that of preventing the system from reaching a set of unsafe states. An attacker may act in two different ways: he can corrupt the observation of the supervisor editing the sensor readings, and can enable events that are disabled by the supervisor. This is done with the aim of leading the plant to an unsafe state, and keeping the supervisor unaware of that before the unsafe state is reached. A special automaton, called attack structure is constructed as the parallel composition of two special structures. Such an automaton can be used by the attacker to select appropriate actions (if any) to reach the above goal, or equivalently by the supervisor, to validate its robustness with respect to such attacks., Comment: This work has been presented at 15th European Workshop on Advanced Control and Diagnosis, ACD 2019