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This paper studies the problem of synthesizing (lexicographic) polynomial ranking functions for loops that can be described in polynomial arithmetic over integers and reals. While the analogous ranking function synthesis problem for linear arithmetic is decidable, even checking whether a given function ranks an integer loop is undecidable in the nonlinear setting. We side-step the decidability barrier by working within the theory of linear integer/real rings (LIRR) rather than the standard model of arithmetic. We develop a termination analysis that is guaranteed to succeed if a loop (expressed as a formula) admits a (lexicographic) polynomial ranking function. In contrast to template-based ranking function synthesis in real arithmetic, our completeness result holds for lexicographic ranking functions of unbounded dimension and degree, and effectively subsumes linear lexicographic ranking function synthesis for linear integer loops., Comment: The arXiv version corrects some errors in the published version of the paper in the proceedings of CAV 2024

Deep Neural Networks (DNNs) have recently made significant progress in many fields. However, studies have shown that DNNs are vulnerable to adversarial examples, where imperceptible perturbations can greatly mislead DNNs even if the full underlying model parameters are not accessible. Various defense methods have been proposed, such as feature compression and gradient masking. However, numerous studies have proven that previous methods create detection or defense against certain attacks, which renders the method ineffective in the face of the latest unknown attack methods. The invisibility of adversarial perturbations is one of the evaluation indicators for adversarial example attacks, which also means that the difference in the local correlation of high-frequency information in adversarial examples and normal examples can be used as an effective feature to distinguish the two. Therefore, we propose an adversarial example detection framework based on a high-frequency information enhancement strategy, which can effectively extract and amplify the feature differences between adversarial examples and normal examples. Experimental results show that the feature augmentation module can be combined with existing detection models in a modular way under this framework. Improve the detector's performance and reduce the deployment cost without modifying the existing detection model.

Deep Neural Networks have been widely used in many fields. However, studies have shown that DNNs are easily attacked by adversarial examples, which have tiny perturbations and greatly mislead the correct judgment of DNNs. Furthermore, even if malicious attackers cannot obtain all the underlying model parameters, they can use adversarial examples to attack various DNN-based task systems. Researchers have proposed various defense methods to protect DNNs, such as reducing the aggressiveness of adversarial examples by preprocessing or improving the robustness of the model by adding modules. However, some defense methods are only effective for small-scale examples or small perturbations but have limited defense effects for adversarial examples with large perturbations. This paper assigns different defense strategies to adversarial perturbations of different strengths by grading the perturbations on the input examples. Experimental results show that the proposed method effectively improves defense performance. In addition, the proposed method does not modify any task model, which can be used as a preprocessing module, which significantly reduces the deployment cost in practical applications.

This paper presents a theory of non-linear integer/real arithmetic and algorithms for reasoning about this theory. The theory can be conceived as an extension of linear integer/real arithmetic with a weakly-axiomatized multiplication symbol, which retains many of the desirable algorithmic properties of linear arithmetic. In particular, we show that the conjunctive fragment of the theory can be effectively manipulated (analogously to the usual operations on convex polyhedra, the conjunctive fragment of linear arithmetic). As a result, we can solve the following consequence-finding problem: given a ground formula F, find the strongest conjunctive formula that is entailed by F. As an application of consequence-finding, we give a loop invariant generation algorithm that is monotone with respect to the theory and (in a sense) complete. Experiments show that the invariants generated from the consequences are effective for proving safety properties of programs that require non-linear reasoning.

Localization and mapping is a key technology for bridging the virtual and physical worlds in augmented reality (AR). Localization and mapping works by creating and querying maps made of anchor points that enable the overlay of these two worlds. As a result, information about the physical world is captured in the map and naturally gives rise to concerns around who can map physical spaces as well as who can access or modify the virtual ones. This paper discusses how we can provide access controls over virtual maps as a basic building block to enhance security and privacy of AR systems. In particular, we propose VACMaps: an access control system for localization and mapping using formal methods. VACMaps defines a domain-specific language that enables users to specify access control policies for virtual spaces. Access requests to virtual spaces are then evaluated against relevant policies in a way that preserves confidentiality and integrity of virtual spaces owned by the users. The precise semantics of the policies are defined by SMT formulas, which allow VACMaps to reason about properties of access policies automatically. An evaluation of VACMaps is provided using an AR testbed of a single-family home. We show that VACMaps is scalable in that it can run at practical speeds and that it can also reason about access control policies automatically to detect potential policy misconfigurations.

Adding perturbations to images can mislead classification models to produce incorrect results. Recently, researchers exploited adversarial perturbations to protect image privacy from retrieval by intelligent models. However, adding adversarial perturbations to images destroys the original data, making images useless in digital forensics and other fields. To prevent illegal or unauthorized access to sensitive image data such as human faces without impeding legitimate users, the use of reversible adversarial attack techniques is increasing. The original image can be recovered from its reversible adversarial examples. However, existing reversible adversarial attack methods are designed for traditional imperceptible adversarial perturbations and ignore the local visible adversarial perturbation. In this paper, we propose a new method for generating reversible adversarial examples based on local visible adversarial perturbation. The information needed for image recovery is embedded into the area beyond the adversarial patch by the reversible data hiding technique. To reduce image distortion, lossless compression and the B-R-G (bluered-green) embedding principle are adopted. Experiments on CIFAR-10 and ImageNet datasets show that the proposed method can restore the original images error-free while ensuring good attack performance.

This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear integer arithmetic has a best model as a deterministic affine transition system. Second, we show that for any linear dynamical system $f$ with integer eigenvalues and any integer arithmetic formula $G$, there is a linear integer arithmetic formula that holds exactly for the states of $f$ for which $G$ is eventually invariant. Combining the two, we develop a monotone conditional termination analysis for general loops.

Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances (e.g., complete synthesis of linear ranking functions for polyhedral loops [Podelski and Rybalchenko, 2004]), and (2) algorithms that are widely applicable, but have weak behavioral guarantees (e.g., Terminator [Cook et al., 2006]). This paper investigates the space in between: how can we design practical termination analyzers with useful behavioral guarantees? This paper presents a termination analysis that is both compositional (the result of analyzing a composite program is a function of the analysis results of its components) and monotone ("more information into the analysis yields more information out"). The paper has two key contributions. The first is an extension of Tarjan's method for solving path problems in graphs to solve infinite path problems. This provides a foundation upon which to build compositional termination analyses. The second is a collection of monotone conditional termination analyses based on this framework. We demonstrate that our tool ComPACT (Compositional and Predictable Analysis for Conditional Termination) is competitive with state-of-the-art termination tools while providing stronger behavioral guarantees.