Compositionality, Decompositionality and Refinement in Input/Output Conformance Testing - Technical Report

TL;DR

This paper introduces a formal conformance testing framework using Modal Interface Automata with Input Refusals, enabling precise specification, compositional reasoning, and decompositional analysis for component-based systems.

Contribution

It presents a novel behavioral formalism IR-MIA and a conformance relation modal-irioco that support positive/negative testing, compositionality, and decompositionality in input/output conformance testing.

Findings

Modal-irioco is preserved under modal refinement.

Modal-irioco is a preorder under certain restrictions.

The quotient operator enables decompositional testing.

Abstract

We propose an input/output conformance testing theory utilizing Modal Interface Automata with Input Refusals (IR-MIA) as novel behavioral formalism for both the specification and the implementation under test. A modal refinement relation on IR-MIA allows distinguishing between obligatory and allowed output behaviors, as well as between implicitly underspecified and explicitly forbidden input behaviors. The theory therefore supports positive and negative conformance testing with optimistic and pessimistic environmental assumptions. We further show that the resulting conformance relation on IR-MIA, called modal-irioco, enjoys many desirable properties concerning component-based behaviors. First, modal-irioco is preserved under modal refinement and constitutes a preorder under certain restrictions which can be ensured by a canonical input completion for IR-MIA. Second, under the same restrictions, modal-irioco is compositional with respect to parallel composition of IR-MIA with multi-cast and hiding. Finally, the quotient operator on IR-MIA, as the inverse to parallel composition, facilitates decompositionality in conformance testing to solve the unknown-component problem.