Abstract Separation-logic proofs of heap-manipulating programs require careful accounting of objects and pointers in memory. On paper, these proofs are often accompanied by heap-memory diagrams that help authors and readers track the evolution of the program’s abstract state. However, users of interactive theorem provers must instead work with plain-text notations that obscure object relationships. This paper presents the first automatic visualization library for separation-logic heap predicates, mimicking hand-drawn diagrams found in published materials. Four key features make the library practical. First, it supports animating across proof steps. Second, it offers users a DSL to specify how custom predicates should be visualized. Third, it is straightforward to port to new separation logic frameworks. And fourth, it can be used in browsers and IDEs, during and after proof development. We demonstrate these features by implementing support for CFML and Iris and integrating with Alectryon and VsRocq.

Most separation logics hide container-internal pointers for modularity. This makes it difficult to specify container APIs that temporarily expose those pointers to the outside, and to verify programs that use these APIs.

The strategies for important node detection according to topological structures are widely explored in complex networks. The diameter is a very important topological parameter among various network topological indicators. However, it is seldom utilized in important node searching methods. In this study, we defined the nodes on the diameter paths as central nodes and proposed a Diameter Center Detection (DCD) method to search the central nodes. In the experiments, the DCD method is applied to three deterministic networks, a series of small-world networks, scale-free networks and five real networks, respectively. The experimental results show that the central nodes searched by DCD have advantages over the nodes of the whole network in the evaluations of various centrality measures, e.g. Betweenness Centrality (BC), Closeness Centrality (CC), Degree Centrality (DC) and k-shell decomposition results. In addition, after deleting central nodes, the network structure changes a lot on the perspective from both diameter and giant component. Furthermore, the experimental results show that the edge deleting policy based on DCD is effective in the way that deleting fewer edges disrupting more node pair connectivity.

There is a growing interest in multilabel image classification. In this study, we proposed a novel texture classification approach combining the fractal theory and the LBP complex networks (FLCN). The complex networks were constructed based on the LBP features and the pixel relationships of the image. The suitable parameters and the combination of statistical properties on the complex networks were investigated to represent the texture of the image. The experimental results show that the FLCN method has good performance in the classifications of the segmented images and the biomedical images. In addition, the approach is more robust compared with other methods.