Quotient of Acceptance Specifications Under Reachability Constraints

Abstract

Abstract. The quotient operation, which is dual to the composition, is crucial in specification theories as it allows the synthesis of missing specifications and thus enables incremental design. In this paper, we consider a specification theory based on marked acceptance specifications (MAS) which are automata enriched with variability information encoded by acceptance sets and with reachability constraints on states. We define a sound and complete quotient for MAS hence ensuring reachability properties by construction.

MAccS: A Tool for Reachability by Design

“…In order to enable the concurrent implementation of MAS while guaranteeing some reachability constraints, we have proposed in [1] a compatible reachability criterion which is a precondition for the computation of S 1 ⊗ S 2 and allows to check if a pair of marked states is always reachable in the product of any two models of the MAS. For example, the MAS Server given in Fig.…”

“…The tool MoTRAS [13] also proposes a complete specification theory for MTS, which are less expressive than MAS. MoTRAS allows for LTL model-checking of specifications but this is not enough to go along with reachability constraints as advocated in [1]. Several non-deterministic MTS variants, namely Disjunctive MTS [14], Boolean MTS and Parametric MTS [15], which have a similar expressive power as acceptance specifications (without marked states), are also under the scope of MoTRAS, but only for a reduced set of operations: there is no quotient for DMTS and only refinement and the deterministic hull for BMTS and PMTS.…”

“…The tool MAccS implements a specification theory based on marked acceptance specifications (MAS) [1]. As an example of MAS, consider the specification Server shown in Fig.…”

“…Now Fig. 2 depicts two models of Server (for a formal definition of satisfaction, see [1]). In each state of the model, the set of outgoing transitions must be an element of the acceptance set of the specification.…”