Approximate Data Exchange

We introduce approximate data exchange, by relaxing classical data exchange problems such as Consistency and Typechecking to their approximate versions based on Property Testing. It provides a natural framework for consistency and safety questions, which first considers approximate solutions and then exact solutions obtained with a Corrector. We consider a model based on transducers of words and trees, and study ε-Consistency, i.e., the problem of deciding whether a given source instance I is 2-close to a source I , whose image by a transducer is also ε-close to a target schema. We prove that ε-Consistency has an ε-tester, i.e. can be solved by looking at a constant fraction of the input I. We also show that ε-Typechecking on words can be solved in polynomial time, whereas the exact problem is PSPACE-complete. Moreover, data exchange settings can be composed when they are close.