The concept of a regular memory area of an artificial intelligence system defined. Semantic hierarchies are considered as a uniform and universal format for structural descriptions of knowledge representations. An infinite saturated binary tree, the vertices of which are binary sequences, implements a single memory format. Finite saturated binary trees with labeled vertices represent individual knowledge in infinite memory. Regular expressions are used as a specification for the memory areas in question. Regular memory domains generalize the system of morphism domain class developed for semantic hierarchy formalisms. The study of regular memory structures and the choice of special tools for modeling memory and thought processes in artificial intelligence systems carried out. The structure of regular memory is associated with classes of knowledge processing operations, as well as the goals of classifying, storing and applying knowledge of a given structure in such systems. Applications of regular memory structures creates conditions for a deep formalization of the tools of constructing memory structures and modeling thought processes in intelligent systems. Associating regular expressions with state machines allows using them as a parameter for effective modeling of the intelligent processes.