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Abstract: Inspired by decomposition problems in rule-based formalisms in ComputationalSystems Biology and recent work on compositionality in graph transformation,this paper proposes to use arbitrary colimits to -deconstruct- models ofreactions in which states are represented as objects of adhesive categories.The fundamental problem is the decomposition of complex reactions of largestates into simpler reactions of smaller states.The paper defines the local decomposition problem for transformations. Tosolve this problem means to -reconstruct- a given transformation as the colimitof -smaller- ones where the shape of the colimit and the decomposition of thesource object of the transformation are fixed in advance. The first result isthe soundness of colimit decomposition for arbitrary double pushouttransformations in any category, which roughly means that several -local-transformations can be combined into a single -global- one. Moreover, asolution for a certain class of local decomposition problems is given, whichgeneralizes and clarifies recent work on compositionality in graphtransformation.



Author: Tobias Heindel Universt├Ąt Duisburg-Essen, Germany

Source: https://arxiv.org/







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