Validation of Modern JSON Schema: Formalization and Complexity

JSON Schema is the de-facto standard schema language for JSON data. The language went through many minor revisions, but the most recent versions of the language, starting from Draft 2019-09, added two novel features, dynamic references and annotation-dependent validation, that change the evaluation model. Modern JSON Schema is the name used to indicate all versions from Draft 2019-09, which are characterized by these new features, while Classical JSON Schema is used to indicate the previous versions. These new "modern"features make the schema language quite difficult to understand and have generated many discussions about the correct interpretation of their official specifications; for this reason, we undertook the task of their formalization. During this process, we also analyzed the complexity of data validation in Modern JSON Schema, with the idea of confirming the polynomial complexity of Classical JSON Schema validation, and we were surprised to discover a completely different truth: data validation, which is expected to be an extremely efficient process, acquires, with Modern JSON Schema features, a PSPACE complexity. In this paper, we give the first formal description of Modern JSON Schema, which we have discussed with the community of JSON Schema tool developers, and which we consider a central contribution of this work. We then prove that its data validation problem is PSPACE-complete. We prove that the origin of the problem lies in the Draft 2020-12 version of dynamic references, and not in annotation-dependent validation. We study the schema and data complexities, showing that the problem is PSPACE-complete with respect to the schema size even with a fixed instance but is in P when the schema is fixed and only the instance size is allowed to vary. Finally, we run experiments that show that there are families of schemas where the difference in asymptotic complexity between dynamic and static references is extremely visible, even with small schemas.