Abstract
The Structure Design is generated with Data Flow Diagrams (DFD). DFD have been used for more than ten years, and they are still popular. The main drawback of DFD is the lack of mathematical foundation. The great demand for bigger and more sophisticated computer systems makes necessary the formulation of a formal theory for DFD. This theory will provide a way of checking consistency and completeness. Universal Algebra has become a useful and important tool in theoretical computer science. Universal Algebra is used in this paper to represent DFD, to generate DFD, to prove consistency and completeness and to define complete DFD. A process decomposition is defined in strict mathematical way; the famous Birkoff's Variety Theorem is used to prove consistency in the process decomposition; a definition of minimal DFD is given; a relation between Universal Algebra concepts and DFD is defined; and a definition of complete (well-defined) DFD is given. The DFD are defined using basic concepts of Universal Algebra theory. The results from this paper can be incorporated in any of the CASE tools used to generate DFD.
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