[Paper Review] Towards Refinement Strategy Planning for Event-B

Tsutomu Kobayashi, Shinichi Honiden|arXiv (Cornell University)|Oct 26, 2012

Distributed systems and fault tolerance6 references3 citations

TL;DR

This paper proposes a systematic method for planning refinement strategies in Event-B by analyzing semantic constraints and relationships between system elements, enabling non-experts to construct well-structured, complexity-mitigated models through automated ordering of artifact and phenomenon introduction. The approach uses a cost-based ranking system to prioritize introduction sequences that minimize verification burden while respecting typing and consistency constraints.

ABSTRACT

Event-B is a formal approach oriented to system modeling and analysis. It supports refinement mechanism that enables stepwise modeling and verification of a system. By using refinement, the complexity of verification can be spread and mitigated. In common development using Event-B, a specification written in a natural language is examined before modeling in order to plan the modeling and refinement strategy. After that, starting from a simple abstract model, concrete models in several different abstraction levels are constructed by gradually introducing complex structures and concepts. Although users of Event-B have to plan how to abstract the specification for the construction of each model, guidelines for such a planning have not been suggested. Specifically, some elements in a model often require that other elements are included in the model because of semantics constraints of Event-B. As such requirements introduces many elements at once, non-experts of Event-B often make refinement rough though rough refinement does not mitigate the complexity of verification well. In response to the problem, a method is proposed to plan what models are constructed in each abstraction level. The method calculates plans that mitigate the complexity well considering the semantics constraints of Event-B and the relationships between elements in a system.

Motivation & Objective

• To address the challenge of ineffective refinement strategy planning in Event-B, where non-experts often create overly coarse refinements that fail to reduce verification complexity.
• To identify and model semantic constraints in Event-B that govern the order in which system elements (artifacts, phenomena, sets, variables) must be introduced.
• To provide a systematic, automated approach that supports non-expert users in constructing stepwise, consistent, and complexity-minimized refinement paths.
• To formalize the relationship between artifact introduction and the required underlying phenomena, ensuring type consistency and proof obligation manageability.
• To enable more systematic and accessible use of Event-B by reducing reliance on expert knowledge in refinement planning.

Proposed method

• The method models system specifications as artifacts (natural language statements) and their corresponding formal expressions in Event-B as invariants.
• It identifies phenomena—such as sets, constants, variables, and events—that are required to express each artifact, based on semantic and typing constraints.
• A cost function is defined to evaluate the complexity of introducing each artifact, based on the number of new phenomena required, with a focus on minimizing cumulative complexity.
• The algorithm uses a priority-based search to explore all possible introduction orders of artifacts, pruning suboptimal sequences using a 'CertainlyBetter' function that compares candidate plans.
• It employs a recursive search with pruning to efficiently explore and rank introduction sequences, ensuring only non-dominated plans are retained at each step.
• The method integrates proof obligation considerations implicitly by ensuring type consistency and avoiding invalid refinements through constraint checking.

Experimental results

Research questions

• RQ1 How can refinement strategy planning in Event-B be formalized to reduce the burden on non-expert users?
• RQ2 What semantic constraints in Event-B necessitate specific ordering of phenomenon and artifact introduction?
• RQ3 How can the complexity of verification be minimized through systematic planning of refinement steps?
• RQ4 What criteria can be used to compare and rank different refinement sequences for optimality?
• RQ5 How can the method support the construction of consistent, type-safe models across multiple abstraction levels?

Key findings

• The proposed method successfully generates a ranked list of optimal refinement sequences that respect Event-B's typing and consistency constraints.
• The method reduces verification complexity by ensuring that artifacts are introduced only after all required phenomena are available, preventing type errors and proof failures.
• The approach enables non-experts to construct effective refinement paths without deep expertise in formal methods or proof obligations.
• The algorithm efficiently prunes suboptimal sequences using the 'CertainlyBetter' function, maintaining computational feasibility even for moderate-sized specifications.
• The method was validated on a library management system, demonstrating that certain introduction orders (e.g., {a}, {b}, {c}) are significantly more effective than others (e.g., {b}, {a}, {c}) in minimizing complexity.
• The results show that the number of new phenomena introduced per step is a critical factor in determining the overall complexity of refinement, and optimal ordering can reduce this burden substantially.