Adhesive categories provide an abstract setting for the double-pushout approach to rewriting, generalising classical approaches to graph transformation. Fundamental results about parallelism and confluence, including the local Church-Rosser theorem, can be proven in adhesive categories, provided that one restricts to linear rules. We identify a class of categories, including most adhesive categories used in rewriting, where those same results can be proven in the presence of rules that are merely left-linear, i.e., rules which can merge different parts of a rewritten object. Such rules naturally emerge, e.g., when using graphical encodings for modelling the operational semantics of process calculi. © 2011 Springer-Verlag GmbH.
CITATION STYLE
Baldan, P., Gadducci, F., & Sobociński, P. (2011). Adhesivity is not enough: Local Church-Rosser revisited. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 48–59). https://doi.org/10.1007/978-3-642-22993-0_8
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