Formal definition and verification of data flow diagrams

Abstract

Data flow diagrams (DFD) are widely used to specify large complex software systems. A DFD is visual and informal, hence, easy to learn and use. However, its informality makes it difficult to conduct formal verification of the consistency and completeness of a DFD specification. The objective of this article is to provide a formal basis for the DFD. A DFD is defined as a diagraph together with a binary relation, called the precedence relation. The nodes of the digraph represent the processes, data stores, and external entities, and the directed edges represent the data flows. The precedence relation for a DFD is an abstraction of the functional semantics and specifies the “is-used-to-produce” relationships among the data flows. Based on this definition, the notion of consistency in process decomposition is defined. The child DFD that results from decomposition is consistent with the parent process if the child DFD preserves the precedence relation for the parent process and does not introduce additional precedence relationships between the input and output flows of the parent process. This consistency criterion is shown to be stronger than those found in the literature. Moreover, a number of completeness criteria are discussed and formalized. The results of this paper can be easily incorporated into some existing CASE tools.