Abstract
Abstract Decomposition is one of the useful methods for investigating complex systems. In this paper, we use some universal algebraic concepts and formulate the most primary system, that is, a transition system as a universal algebra. The reason why we need the universal algebraic approach is that it makes easy to solve the preservation problems of properties of systems by using the model theoretic results. After formulating a transition system as a universal algebra (S-algebra), we discuss the PR-decomposition of S-algebras, which is a generalization of the well-known decomposition of state automata. Moreover, we solve the serial decomposition and the parallel decomposition problems of S-algebras.
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