Open Access

Ferenc Bujtor, Walter Vogler

• De Alfaro and Henzinger advocated interface automata to model and study behavioural types, which describe communication patterns of systems while abstracting e.g. from data. They come with a specific parallel composition: if, in some state, one component tries to make an output, which the other one cannot receive, the state is regarded as an error. Error states are removed along with some states leading to them. As refinement relation an alternating simulation is introduced. In this report, we study to what degree this refinement relation is justified by the desires to avoid error states and to support modular refinement. For this, we leave the error states in place and mark them as such instead of removing them in the composition. Our Error-I-O-Transition systems are slightly more general than Interface automata, which are restricted to input determinism. Our basic requirement is: an implementation must be error free, if the specification is. For two different notions of errorDe Alfaro and Henzinger advocated interface automata to model and study behavioural types, which describe communication patterns of systems while abstracting e.g. from data. They come with a specific parallel composition: if, in some state, one component tries to make an output, which the other one cannot receive, the state is regarded as an error. Error states are removed along with some states leading to them. As refinement relation an alternating simulation is introduced. In this report, we study to what degree this refinement relation is justified by the desires to avoid error states and to support modular refinement. For this, we leave the error states in place and mark them as such instead of removing them in the composition. Our Error-I-O-Transition systems are slightly more general than Interface automata, which are restricted to input determinism. Our basic requirement is: an implementation must be error free, if the specification is. For two different notions of error freeness, we determine the coarsest precongruences contained in the respective basic refinement relations. We characterize these best refinement relations meeting our desirables with trace sets. Thus our precongruences are less discriminating than simulation-based ones. Along the way we point out an error in an early paper by de Alfaro and Henzinger.…