Complete Test Suites for Automata in Monoidal Closed Categories

2024-11-20

arXiv.org

AI Summary

This paper addresses the problem of black-box implementation and specification equivalence verification for automata in monoidal closed categories. Methodologically, it generalizes the classical W-method to the abstract level of monoidal closed categories, enabling a unified conformance testing framework for diverse automaton models—including deterministic finite automata (DFAs), Moore/Mealy machines, weighted automata, and deterministic nominal automata. Key contributions include: (i) the first categorical foundation for constructing provably complete test suites, establishing universal construction principles grounded in category theory; (ii) the derivation of the first provably complete test suites for weighted automata and deterministic nominal automata; and (iii) the rigorous reconstruction and categorical generalization of the W-method for DFAs and classical finite-state machines. The framework unifies theoretical rigor with broad model applicability, providing a principled categorical semantics for formal verification of automata-based systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Conformance testing of automata is about checking the equivalence of a known specification and a black-box implementation. An important notion in conformance testing is that of a complete test suite, which guarantees that if an implementation satisfying certain conditions passes all tests, then it is equivalent to the specification. We introduce a framework for proving completeness of test suites at the general level of automata in monoidal closed categories. Moreover, we provide a generalization of a classical conformance testing technique, the W-method. We demonstrate the applicability of our results by recovering the W-method for deterministic finite automata, Moore machines, and Mealy machines, and by deriving new instances of complete test suites for weighted automata and deterministic nominal automata.

Problem

• Proving completeness of test suites for automata in monoidal categories
• Generalizing classical conformance testing techniques like W-method
• Applying framework to various automata types for complete testing

Innovation

• Framework for automata in monoidal closed categories
• Generalization of classical W-method technique
• New complete test suites for various automata