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In previous work, we have introduced multi-version models for model-driven software engineering, which allow checking well-formedness and finding merge conflicts for multiple versions of the same model at once. However, situations where different models are linked via automatic model transformations also have to be handled for multi-version models. In this paper, we propose a technique for jointly handling the transformation of multiple versions of a source model into corresponding versions of a target model. This enables the use of a more compact representation that may afford improved execution time of both the transformation and further analysis. Our approach is based on the well-known formalism of triple graph grammars and the aforementioned encoding of model version histories called multi-version models. In addition to batch transformation of an entire history, the technique covers incremental synchronization of changes in the framework of multi-version models. Our solution is complemented by a dedicated pattern matching technique for multi-version models. We show the correctness of our approach with respect to the standard semantics of triple graph grammars and conduct an empirical evaluation to investigate the performance of our technique regarding execution time and memory consumption. Our results indicate that the proposed solution affords lower memory consumption and may improve execution time for batch transformation of large version histories, but can also come with computational overhead in unfavorable cases.<\/jats:p>","DOI":"10.1007\/s10270-024-01238-1","type":"journal-article","created":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T02:16:59Z","timestamp":1731723419000},"page":"1699-1736","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Incremental model transformations with triple graph grammars for multi-version models and multi-version pattern matching"],"prefix":"10.1007","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1138-2425","authenticated-orcid":false,"given":"Matthias","family":"Barkowsky","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4723-730X","authenticated-orcid":false,"given":"Holger","family":"Giese","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,16]]},"reference":[{"issue":"4","key":"1238_CR1","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1007\/s10270-009-0146-z","volume":"9","author":"A Seibel","year":"2010","unstructured":"Seibel, A., Neumann, S., Giese, H.: Dynamic hierarchical mega models: comprehensive traceability and its efficient maintenance. 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