To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. Examples of knowledge representation formalisms include semantic nets, systems architecture, frames, rules, and ontologies. The modern theory is formulated in various specially developed mathematical formalisms. This can be shown under various mathematical formalisms for quantum mechanics. Other formalisms include the geometric algebra formulation and a matrix representation of Maxwell's equations. Numerous mathematical formalisms have been established to handle the case of an interacting system. Bonding is often described using the formalisms of molecular orbital theory. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. It can be included in heterogeneous design systems with various input formalisms and output languages. Most formalisms provide the following operations to construct regular expressions. A rather different set of formalisms and notation are used in this case. Among them formalisms which allow to have changing model structures while the simulation time evolves. The languages generated by these formalisms properly lie between the context-free and context-sensitive languages. The design of languages and formalisms involves a trade-off between expressive power and analyzability. The relationships can be represented using a variety of formalisms/languages.