Mutations on Brauer configurations are introduced and associated with some suitable automata to solve generalizations of the Chicken McNugget problem. Additionally, based on marked order polytopes, the new Diophantine equations called Gelfand–Tsetlin equations are also solved. The approach allows algebraic descriptions of some properties of the AES key schedule via some Brauer configuration algebras and suitable non-deterministic finite automata (NFA).

Since its introduction, researching malware has had two main goals. On the one hand, malware writers have been focused on developing software that can cause more damage to a targeted host for as long as possible. On the other hand, malware analysts have as one of their main purposes the development of tools such as malware detection systems (MDS) or network intrusion detection systems (NIDS) to prevent and detect possible threats to the informatic systems. Obfuscation techniques, such as the encryption of the virus’s code lines, have been developed to avoid their detection. In contrast, shallow machine learning and deep learning algorithms have recently been introduced to detect them. This paper is devoted to some theoretical implications derived from these investigations. We prove that hidden algebraic structures as equipped posets and their categories of representations are behind the research of some infections. Properties of these categories are given to provide a better understanding of different infection techniques.