Formal Derivation of Concurrent Garbage Collectors

Concurrent garbage collectors are notoriously difficult to implement correctly. Previous approaches to the issue of producing correct collectors have mainly been based on posit-and-prove verification or on the application of domain-specific templates and transformations. We show how to derive the upper reaches of a family of concurrent garbage collectors by refinement from a formal specification, emphasizing the application of domain-independent design theories and transformations. A key contribution is an extension to the classical lattice-theoretic fixpoint theorems to account for the dynamics of concurrent mutation and collection.Comment: 38 pages, 21 figures. The short version of this paper appeared in the Proceedings of MPC 201

Rough set decision algorithms for modeling with uncertainty

The use of decision rules allows to extract information and to infer conclusions from relational databases in a reliable way, thanks to some indicators like support and certainty. Moreover, decision algorithms collect a group of decision rules that satisfies desirable properties to describe the relational system. However, when a decision table is considered within a fuzzy environment, it is necessary to extend all notions related to decision algorithms to this framework. This paper presents a generalization of these notions, highlighting the new definitions of indicators of relevance to describe decision rules and decision algorithm

Generating a Catalog of Unanticipated Schemas in Class Hierarchies using Formal Concept Analysis

International audienceContext: Inheritance is the cornerstone of object-oriented development, supporting conceptual modeling, subtype polymorphism and software reuse. But inheritance can be used in subtle ways that make complex systems hard to understand and extend, due to the presence of implicit dependencies in the inheritance hierarchy. Objective: Although these dependencies often specify well-known schemas (i.e., recurrent design or coding patterns, such as hook and template methods), new unanticipated dependency schemas arise in practice, and can consequently be hard to recognize and detect. Thus, a developer making changes or extensions to an object-oriented system needs to understand these implicit contracts defined by the dependencies between a class and its subclasses, or risk that seemingly innocuous changes break them. Method: To tackle this problem, we have developed an approach based on Formal Concept Analysis. Our FoCARE methodology (Formal Concept Analysis based-Reverse Engineering) identifies undocumented hi- erarchical dependencies in a hierarchy by taking into account the existing structure and behavior of classes and subclasses. Results: We validate our approach by applying it to a large and non-trivial case study, yielding a catalog of Hierarchy Schemas, each one composed of a set of dependencies over methods and attributes in a class hierarchy. We show how the discovered dependency schemas can be used not only to identify good design practices, but also to expose bad smells in design, thereby helping developers in initial reengineering phases to develop a first mental model of a system. Although some of the identified schemas are already documented in existing literature, with our approach based on Formal Concept Analysis (FCA), we are also able to identify previously unidentified schemas

Rough sets based on Galois connections

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately. different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks