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The Formal Design Models of Digraph Architectures and Behaviors

The Formal Design Models of Digraph Architectures and Behaviors

Yingxu Wang, Aderemi Adewumi
Copyright: © 2012 |Volume: 4 |Issue: 1 |Pages: 30
ISSN: 1942-9045|EISSN: 1942-9037|EISBN13: 9781466614192|DOI: 10.4018/jssci.2012010105
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MLA

Wang, Yingxu, and Aderemi Adewumi. "The Formal Design Models of Digraph Architectures and Behaviors." IJSSCI vol.4, no.1 2012: pp.100-129. http://doi.org/10.4018/jssci.2012010105

APA

Wang, Y. & Adewumi, A. (2012). The Formal Design Models of Digraph Architectures and Behaviors. International Journal of Software Science and Computational Intelligence (IJSSCI), 4(1), 100-129. http://doi.org/10.4018/jssci.2012010105

Chicago

Wang, Yingxu, and Aderemi Adewumi. "The Formal Design Models of Digraph Architectures and Behaviors," International Journal of Software Science and Computational Intelligence (IJSSCI) 4, no.1: 100-129. http://doi.org/10.4018/jssci.2012010105

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Abstract

Graphs are one of the most fundamental and widely used non-linear hierarchical structures of linked nodes. Problems in sciences and engineering can be formulated and solved by the graph model. This paper develops a comprehensive design pattern of formal digraphs using the Doubly-Linked List (DLL) architecture. The most complicated form of graphs known as the weighted digraph is selected as a general graph model, based on it simple graphs such as nondirected and/or nonweighted ones can be easily derived and tailored. A rigorous denotational mathematics, Real-Time Process Algebra (RTPA), is adopted, which allows both architectural and behavioral models of digraphs to be rigorously designed and implemented in a top-down approach. The architectural models of digraphs are created using RTPA architectural modeling methodologies known as the Unified Data Models (UDMs). The physical model of digraphs is implemented using nodes of DLL dynamically created in the memory. The behavioral models of digraphs are specified and refined by a set of 18 Unified Process Models (UPMs) in three categories namely the management operations, traversal operations, and node manipulation operations. This work has been applied in a number of real-time and nonreal-time system designs and specifications such as a Real-Time Operating System (RTOS+), graph-based and tree-based applications, and the ADT library for an RTPA-based automatic code generation tool.

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