Traditional algebraic frameworks for bidirectional transformations are state-based: the input and output are states of data. But actual implementations are delta-based: the synchronizer tries to understand what is the delta resulted from the update, and then try to propagate the delta.

We show that state-based algebraic framework has several drawbacks, and build delta-based algebraic frameworks for both the asymmetric case and the symmetric case.

"Correctness of Model Synchronization Based on Triple Graph Grammars",
*ACM/IEEE 14th International Conference on Model Driven Engineering Languages and Systems*: Springer, 10/2011.
[pdf]

"From State- to Delta-based Bidirectional Model Transformations: the Symmetric Case",
*ACM/IEEE 14th International Conference on Model Driven Engineering Languages and Systems*: Springer, 10/2011.
[pdf][pdf]

"From State- to Delta-Based Bidirectional Model Transformations: the Asymmetric Case",
*Journal of Object Technology*, vol. 10, 2011.

"From State-Based to Delta-Based Bidirectional Model Transformation",
*3rd International Conference on Model Transformation*, Malaga, Spain, Springer, pp. 61-76, 06/2010.
[pdf][ppt]