Complete Test Suites for Automata in Monoidal Closed Categories

TL;DR

This paper develops a general framework for creating complete test suites for automata within monoidal closed categories, extending classical methods and deriving new test suites for various automata types.

Contribution

It introduces a unified theoretical framework for proving test suite completeness across diverse automata models, generalizing the W-method.

Findings

Recovered the W-method for classical automata

Derived new complete test suites for weighted automata

Extended the framework to nominal automata

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.