Modal Interface Automata

TL;DR

This paper introduces Modal Interface Automata (MIA), a new interface theory that extends existing frameworks by adding conjunction, disjunction, and compositional operators, addressing prior limitations in interface specification formalisms.

Contribution

It defines conjunction and disjunction for IA and disjunctive MTS, and introduces MIA with explicit output-must-transitions, fixing previous shortcomings without requiring determinism.

Findings

Defines conjunction and disjunction operators for IA and disjunctive MTS.

Introduces Modal Interface Automata (MIA) with enhanced features.

Proves correctness of the new operators as greatest lower bounds and least upper bounds.

Abstract

De Alfaro and Henzinger's Interface Automata (IA) and Nyman et al.'s recent combination IOMTS of IA and Larsen's Modal Transition Systems (MTS) are established frameworks for specifying interfaces of system components. However, neither IA nor IOMTS consider conjunction that is needed in practice when a component shall satisfy multiple interfaces, while Larsen's MTS-conjunction is not closed and Bene\v{s} et al.'s conjunction on disjunctive MTS does not treat internal transitions. In addition, IOMTS-parallel composition exhibits a compositionality defect. This article defines conjunction (and also disjunction) on IA and disjunctive MTS and proves the operators to be 'correct', i.e., the greatest lower bounds (least upper bounds) wrt. IA- and resp. MTS-refinement. As its main contribution, a novel interface theory called Modal Interface Automata (MIA) is introduced: MIA is a rich subset of IOMTS featuring explicit output-must-transitions while input-transitions are always allowed implicitly, is equipped with compositional parallel, conjunction and disjunction operators, and allows a simpler embedding of IA than Nyman's. Thus, it fixes the shortcomings of related work, without restricting designers to deterministic interfaces as Raclet et al.'s modal interface theory does.