Parametrised Modal Interface Automata

Abstract

Interface theories (ITs) enable us to analyse the compatibility interfaces and refine them while preserving their compatibility. However, most ITs are for finite state interfaces, whereas computing systems are often parametrised involving components, the number of which cannot be fixed. We present, to our knowledge, the first IT that allows us to specify a parametric number of interfaces. Moreover, we provide a fully algorithmic procedure, implemented in a tool, for checking the compatibility of and refinement between parametrised interfaces. Finally, we show that the restrictions of the technique are necessary; removing any of them renders the refinement checking problem undecidable.

An optimal cut-off algorithm for parameterised refinement checking

“…As the main result of this section, we prove Proposition 31 which says that a finite basis of a parameterised system is a cut-off set. Results similar to Lemma 25 as well as Lemmata 26 and 29 are proved in [1] and [17,18,16], respectively, but here we also provide the full proofs which were not included in [1]. The main result, Proposition 31, is new.…”

“…Our approach is based on the precongruence reduction (PR) technique previously used to prove static cut-offs for PLTSs with predicates defined in the universal fragment (∀ * ) of FOL [17] and for PLTSs with special quorum functions [16]. The technique is also adapted to parameterised modal interface automata without predicates [18]. In general, the PR technique applies to parameterised systems with a finite basis, meaning that any (big) system instance can be represented as a composition of finitely many (small) system instances.…”

Dynamic Cut-Off Algorithm for Parameterised Refinement Checking

“…Results similar to Prop. 15 are proved in [24,23,21] but the main result, Thm 23, the supporting lemmata, Lemmata 20 and 22, and the related dynamic cut-off algorithm are completely new.…”

“…The novelty of the algorithm is in its generality; it not only combines existing static cut-off techniques but also extends their application domain beyond known decidable fragments. In future, we aim to extend the algorithm to other process algebraic formalisms such as modal interface automata [23].…”

“…Our approach is based on the precongruence reduction (PR) technique previously used to prove static cut-offs for PLTSs with predicates defined in the universal fragment (∀ * ) of FOL [24] and for PLTSs with special quorum functions [21]. The technique is also adapted to parameterised modal interface automata without predicates [23]. In general, the PR technique applies to implementation-specification pairs the topology of which is downward-closed in the sense that any (big) instance can be represented as a composition of smaller instances.…”