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Validation of Modern JSON Schema: Formalization and Complexity

Lyes Attouche, Mohamed-Amine Baazizi, Dario Colazzo, Giorgio Ghelli, Carlo Sartiani, Stefanie Scherzinger

TL;DR

This work provides the first formalization of Modern JSON Schema (Draft 2020-12), including annotation-dependent validation and dynamic references, and proves that data validation is PSPACE-complete due to dynamic resolution, while static/reference-only fragments remain PTIME. The authors introduce a comprehensive formal framework: a normalized grammar, a proof system with context-sensitive semantics, and a polynomial-space validation algorithm, plus an approach to eliminate dynamic references at possible exponential cost. They show the hardness stems from dynamic references and demonstrate PTIME when these are bounded or fixed, supported by empirical experiments across multiple validators. The results illuminate the inherent complexity implications of modern JSON Schema features and guide validator design, including potential schema-elimination strategies and the practical impact of dynamic scopes on validation efficiency.

Abstract

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 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 PTIME complexity of Classical JSON Schema validation, and we were surprised to discover a completely different truth: data validation, that 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 consider a central contribution of the work that we present here. We then prove that its data validation problem is PSPACE-complete. We prove that the origin of the problem lies in 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 PTIME 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.

Validation of Modern JSON Schema: Formalization and Complexity

TL;DR

This work provides the first formalization of Modern JSON Schema (Draft 2020-12), including annotation-dependent validation and dynamic references, and proves that data validation is PSPACE-complete due to dynamic resolution, while static/reference-only fragments remain PTIME. The authors introduce a comprehensive formal framework: a normalized grammar, a proof system with context-sensitive semantics, and a polynomial-space validation algorithm, plus an approach to eliminate dynamic references at possible exponential cost. They show the hardness stems from dynamic references and demonstrate PTIME when these are bounded or fixed, supported by empirical experiments across multiple validators. The results illuminate the inherent complexity implications of modern JSON Schema features and guide validator design, including potential schema-elimination strategies and the practical impact of dynamic scopes on validation efficiency.

Abstract

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 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 PTIME complexity of Classical JSON Schema validation, and we were surprised to discover a completely different truth: data validation, that 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 consider a central contribution of the work that we present here. We then prove that its data validation problem is PSPACE-complete. We prove that the origin of the problem lies in 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 PTIME 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.
Paper Structure (28 sections, 4 theorems, 36 equations, 9 figures, 1 table, 2 algorithms)

This paper contains 28 sections, 4 theorems, 36 equations, 9 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Modern JSON Sche-ma through examples
  3. An Example of Modern JSON Sche-ma
  4. Introducing dynamic references.
  5. Annotation Dependency
  6. Formalizing JSON Schema syntax
  7. URI Resolution, Resource Flattening, Schema Closing
  8. Closed schemas
  9. JSON Schema Normalized Grammar
  10. JSON Schema Validation
  11. Introduction to the Proof System
  12. Terminal Assertions
  13. Boolean Applicators
  14. Independent Object and Array Applicators (Independent Structural Applicators)
  15. The Semantics of Schemas: Sequential Evaluation of Keywords
  16. ...and 13 more sections

Key Result

corollary 1

Validation in any fragment of Modern JSON Sche-ma that includes ${\textnormal{\textquotedbl}}\hbox{\tt{\small $dynamicRef}}{\textnormal{\textquotedbl}}$, ${\textnormal{\textquotedbl}}\hbox{\tt{\small $dynamicAnchor}}{\textnormal{\textquotedbl}}$, ${\textnormal{\textquotedbl}}\hbox{\tt{\small anyOf}}

Figures (9)

  • Figure 1: A schema representing trees.
  • Figure 2: A schema representing extensible trees.
  • Figure 3: A schema that refines trees.
  • Figure 4: JSON Sche-ma metaschema
  • Figure 5: A schema with embedded resources, its flattened version, and some examples.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Example 1
  • Remark 1
  • definition 1: Unguardedly references in Classical JSON Sche-ma; well-formed schema
  • definition 2: Unguardedly references for Modern JSON Sche-ma, well-formed
  • definition 3: $S_{\psi}$
  • corollary 1: PSPACE-hardness
  • corollary 2
  • corollary 3: Fixed-schema complexity
  • corollary 4