NCT00778102.

Sesqui-pushout (SqPO) rewriting - "sesqui" means "one and a half" in Latin - is a new algebraic approach to abstract rewriting in any category. SqPO rewriting is a deterministic and conservative extension of double-pushout (DPO) rewriting, which allows to model "deletion in unknown context", a typical feature of single-pushout (SPO) rewriting, as well as cloning. After illustrating the expressiveness of the proposed approach through a case study modelling an access control system, we discuss sufficient conditions for the existence of final pullback complements and we analyze the relationship between SqPO and the classical DPO and SPO approaches

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Abstract. A bidirectional transformation (BX) keeps a pair of interrelated models synchronized. Symmetric BXs are those for which neither model in the pair fully determines the other. We build two algebraic frameworks for symmetric BXs, with one correctly implementing the other, and both being delta-based generalizations of known state-based frameworks. We identify two new algebraic laws-weak undoability and weak invertibility, which capture important semantics of BX and are useful for both state-and delta-based settings. Our approach also provides a flexible tool architecture adaptable to different user's needs.