[Paper Review] Rule-based Graph Repair using Minimally Restricted Consistency-Improving Transformations

Alexander Lauer|arXiv (Cornell University)|Jul 18, 2023

Model-Driven Software Engineering TechniquesComputer Science3 citations

TL;DR

This paper introduces a novel rule-based graph repair approach using minimally restricted consistency-improving transformations, enabling fine-grained repair of inconsistent models by distinguishing between consistency-maintaining and consistency-increasing rule applications at specific nesting levels. The key contribution is a framework with less complex, layer-specific application conditions—especially for basic increasing rules—enabling efficient, direct repair of circular conflict-free constraints and sets of constraints.

ABSTRACT

Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them. These models must satisfy certain sets of constraints. An example are the multiplicities of a class structure. During the development process, a change to a model may result in an inconsistent model that must at some point be repaired. This problem is called model repair. In particular, we will consider rule-based graph repair which is defined as follows: Given a graph $G$, a constraint $c$ such that $G$ does not satisfy $c$, and a set of rules $R$, use the rules of $\mathcal{R}$ to transform $G$ into a graph that satisfies $c$. Known notions of consistency have either viewed consistency as a binary property, either a graph is consistent w.r.t. a constraint $c$ or not, or only viewed the number of violations of the first graph of a constraint. In this thesis, we introduce new notions of consistency, which we call consistency-maintaining and consistency-increasing transformations and rules, respectively. This is based on the possibility that a constraint can be satisfied up to a certain nesting level. We present constructions for direct consistency-maintaining or direct consistency-increasing application conditions, respectively. Finally, we present an rule-based graph repair approach that is able to repair so-called \emph{circular conflict-free constraints}, and so-called circular conflict-free sets of constraints. Intuitively, a set of constraint $C$ is circular conflict free, if there is an ordering $c_1, \ldots, c_n$ of all constraints of $C$ such that there is no $j <i></i>

Motivation & Objective

• Address the limitation of existing model repair approaches that treat consistency as a binary property or only consider first-level violations.
• Introduce a fine-grained notion of consistency that evaluates model repair based on the nesting level of constraint violations.
• Develop direct consistency-maintaining and consistency-increasing rules at layer to prevent new violations during transformation.
• Construct application conditions for general and basic increasing rules that are less complex and restrictive than prior methods.
• Enable repair of circular conflict-free constraints and sets of constraints through a structured, layered transformation process.

Proposed method

• Define consistency-maintaining and consistency-increasing transformations based on the first unsatisfied nesting level of constraints.
• Introduce 'direct' variants that prohibit any new violations, ensuring stronger consistency guarantees.
• Propose two types of application conditions: one for general rules and a simpler variant for 'basic increasing rules' that only require checking for violation removal.
• Use derived rules to ensure that basic rules can be applied even when their left-hand side does not initially contain the required constraint layer.
• Apply the repair process to circular conflict-free constraints, where no repair of a later constraint introduces a violation in an earlier one.
• Construct application conditions using sets of overlaps (P_C') and conditions on existence and removal of violations to ensure correctness and minimality.

Experimental results

Research questions

• RQ1 How can consistency be measured beyond a binary state, allowing for incremental improvement in model repair?
• RQ2 What conditions ensure that a rule application does not introduce new violations while improving consistency at a given nesting level?
• RQ3 Can application conditions be simplified for specific rule types, such as basic increasing rules, to reduce complexity and restrictiveness?
• RQ4 Under what structural conditions on constraints is a rule-based repair process guaranteed to terminate and maintain consistency?
• RQ5 How can the repair of multiple constraints be coordinated when they are interdependent, especially in the presence of circular conflicts?

Key findings

• The proposed notion of consistency-increasing at layer allows for finer-grained repair by focusing on the first unsatisfied nesting level, enabling detection of minimal changes like single edge or node insertions/deletions.
• Application conditions for basic increasing rules are significantly less complex and restrictive than those for general rules, as they only require verifying that at least one violation is removed.
• Derived rules ensure that the requirement for a rule's left-hand side to contain a specific constraint layer does not limit the applicability of basic increasing rules.
• The framework successfully enables repair of circular conflict-free constraints and sets of constraints, where no repair of a later constraint causes a violation in an earlier one.
• The application conditions for consistency-maintaining and consistency-increasing rules are formally constructed and proven to ensure correctness, with potential for further optimization by combining violation-removal and no-violation-inserted components.
• The approach provides a foundation for extending repair to all satisfiable nested constraints, including those with Boolean operators, though this remains future work.