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Incrementally Modular Abstraction Hierarchy Using Algebraic Topology

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Transactions on Computational Science XXIII

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 8490))

Abstract

We have introduced a new design method called incrementally modular abstraction hierarchy (IMAH). IMAH is based on algebraic topology and it provides seven levels of abstraction hierarchy. Using IMAH, designers can begin their development at any level of the abstraction hierarchy. By ascending the hierarchy, they can generalize their design. By descending it, they can specialize their development. When complete, they are able to consider the entire conceptual and physical view of what they have achieved through their work. Though IMAH is a powerful tool, it requires only a simple explanation to be accepted by most researchers and developers. In this paper, we will use basic mathematical concepts, pushouts and pullbacks, to show how systems can be designed in both bottom-up and top-down fashions.

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Ohmori, K., Kunii, T.L. (2014). Incrementally Modular Abstraction Hierarchy Using Algebraic Topology. In: Gavrilova, M.L., Tan, C.J.K., Mao, X., Hong, L. (eds) Transactions on Computational Science XXIII. Lecture Notes in Computer Science, vol 8490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43790-2_1

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  • DOI: https://doi.org/10.1007/978-3-662-43790-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43789-6

  • Online ISBN: 978-3-662-43790-2

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