Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of the ACM (JACM)
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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 ε-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.