Modal Interface Automata

Abstract

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 Beneš et al.'s conjunction on disjunctive MTS does not treat internal transitions. In addition, IOMTSparallel 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.

Nondeterministic Modal Interfaces

“…Interface theories [2,7,8,16,17,22] support the component-based design of concurrent systems and offer a semantic framework for, e.g., software contracts [1] and web services [5]. Several such theories are based on de Alfaro and Henzinger's Interface Automata (IA) [11], whose distinguishing feature is a parallel composition on labelled transition systems with inputs and outputs, where receiving an unexpected input is regarded as an error, i.e., a communication mismatch.…”

“…In a refinement of an interface, all required behaviour must be preserved and no disallowed behaviour may be added. Whereas in IA outputs are optional, they may now be enforced in theories combining IA and MTS, such as Nyman et al's IOMTS [16], Bauer et al's MIO [2], Raclet et al 's Modal Interfaces (MI) [22] and our Modal Interface Automata (MIA) [17,18]. In this paper we extend MI to nondeterministic systems, yielding the most general approach to date and permitting new applications, e.g., for dealing with races in networks.…”

“…In contrast to the somewhat related demonic completion as used, e.g., in [12], we do not enforce input-enabledness. With the new feature, our interface theory allows for a proper distinction between may-and must-transitions for inputs, unlike [17,18]. This enables us to define conjunction also on interfaces with dissimilar alphabets via alphabet extension.…”

Observational Refinement and Merge for Disjunctive MTSs

“…Merge has been investigated in the literature for MTSs as well as for DMTSs, for strong, observational and alphabet refinements [3,4,10,12,13,19,20]. It was shown that MTSs are not closed for merge under strong refinement [10,13] (which implies that they are not closed under observational and alphabet merges as well, since observational merge must agree with strong merge when no τ -transitions are involved).…”

“…For DMTSs, a strong merge algorithm was given in [4]. Observational merge however, was only considered for the restricted subset of dMTS where τ -labels are allowed on possible transitions only [19].…”