Author:
Richard Banach
Affiliation:
University of Manchester, United Kingdom
Keyword(s):
Model based Frameworks, Event-B, Stochastic Extensions, Invariants, Martingales.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Cross-Feeding between Data and Software Engineering
;
Formal Methods
;
Knowledge Management and Information Sharing
;
Knowledge-Based Systems
;
Model-Driven Engineering
;
Requirements Engineering
;
Simulation and Modeling
;
Software Engineering
;
Software Engineering Methods and Techniques
;
Symbolic Systems
Abstract:
In conventional formal model based development frameworks, invariants play a key role in controlling the
behaviour of the model (when they contribute to the definition of the model) or in verifying the model’s
properties (when the model, independently defined, is required to preserve the invariants). However, when
variables take values distributed according to some probability distribution, the possibility of verifying that
system behaviour is, in the long term, confined to some acceptable set of states can be severely diminished
because the system might, in fact, with low probability fail to be thus confined. This short paper proposes
martingales as suitable analogues of invariants for capturing suitable properties of non-terminating systems
whose behaviour is with high probability good, yet where a small chance of poor behaviour remains. The idea
is explored in the context of the well-known Event-B framework.