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Knowledge graphs have come a long way from a simple set of RDF triples to systems for acquiring new knowledge. While in previous years, the primary application of knowledge graphs used to be semantic search, nowadays, knowledge graphs are permeating all areas of modern industry. This paper presents a survey of new knowledge graph variants, such as virtual knowledge graphs, dynamic knowledge graphs, and executable knowledge graphs used in modern industrial applications, as well as their primary application: cognitive digital twins. The paper also briefly examines methods for constructing knowledge graphs using large language models and improving the performance of large language models through the use of knowledge graphs.

The intention of the paper is to present a framework for developing, studying and comparing testing equivalences in interleaving, step, partial-order and combined semantics with reverse, in the context of safe Dense-Time Petri Nets (TPNs). For representation of behavior of TPNs partial-order semantic of time causal processes are used. Reversibility means that single or concurrent actions can be undone only after caused actions are undone or not done yet. As result we establish relationships between testing equivalences under consideration.

Reversible computing, which has been widely studied in recent years, is an unconventional form of computing that can be performed in both directions: forward and backward. Any sequence of actions performed by the system can be later canceled for any reason (for example, in case of an error), allowing one to restore the system to its previous state, as if the canceled actions had never performed. Event structures are a fundamental model in concurrency theory, allowing us to comprehend the behavior of concurrent systems by describing system events and their relations. In the literature, there are two main approaches to constructing the semantics of transition systems for event structure models. One approach is based on configurations, i.e. sets of already executed events, and the other relies on residuals, i.e. model fragments that have not yet been executed. Configuration-based transition systems are mainly used to represent semantics and equivalences of concurrent models. Residual-based transition systems are actively involved to demonstrate the consistency between the operational and denotational semantics of algebraic calculi for concurrent processes, as well as to visualize the behavior of models. This article provides a category-theoretic characterization of these types of transition systems semantics for cause-respecting reversible prime event structures, and establishes the relationship between the semantics, which can be useful in constructing algebraic descriptions of the composition of reversible concurrent processes.