Luciana Foss

Specification patterns for properties over reachable states of graph grammars

Essential characteristics of the behavior of a system may be described by properties. These descriptions must be precise and unambiguous to enable verification through (semi-)automated tools. There are many appropriate mathematical languages for writing system requirements, but they are often difficult to be applied by user without a good mathematical background. Patterns for property specifications capture recurring solutions for common problems, simplifying this task. This paper presents specification patterns for properties over reachable states of graph grammars, that is, properties of complex graph structures. This proposal may be used to aid the verification of systems where states are represented as graphs.

Graph Grammars: A Comparison between Verification Methods

Graph grammars are a formal specification language well-suited to applications in which states have a complex topology (involving not only many types of elements, but also different types of relations between them) and in which behaviour is essentially data-driven, that is, events are triggered basically by particular configurations of the state. Many reactive systems are examples of this class of applications, such as protocols for distributed and mobile systems, simulation of biological systems, and many others. Graph grammars can be analysed through model-checking and theorem proving. Each verification technique has arguments for and against its use, but we can say that model-checking and theorem proving are complementary. The main aim of this paper is to present the main existing approaches for the analysis of graph grammars considering each one of these techniques, describing a brief comparative between them.

Theorem Proving Graph Grammars: Strategies for Discharging Proof Obligations

One way of developing reliable systems is through the use of Formal Methods. A Graph Grammar specification is visual and based in a simple mechanism of rewriting rules. On the other hand, verification through theorem proving allows the proof of properties for systems with huge (and infinite) state space. There is a previously proposed approach that has allowed the application of theorem proving technique to graph grammars. One of the disadvantages of such an approach (and theorem proving in general) is the specific mathematical knowledge required from the user for concluding the proofs. This paper proposes proof strategies in order to help the developer in the verification process through theorem proving, when adopting graph grammar as specification language.

Correct transformation: From object-based graph grammars to PROMELA

Model transformation is an approach that, among other advantages, enables the reuse of existing analysis and implementation techniques, languages and tools. The area of formal verification makes wide use of model transformation because the cost of constructing efficient model checkers is extremely high. There are various examples of translations from specification and programming languages to the input languages of prominent model checking tools, like SPIN. However, this approach provides a safe analysis method only if there is a guarantee that the transformation process preserves the semantics of the original specification/program, that is, that the transformation is correct. Depending on the source and/or target languages, this notion of correctness is not easy to achieve. In this paper, we tackle this problem in the context of Object-Based Graph Grammars (OBGG). OBGG is a formal language suitable for the specification of distributed systems, with a variety of tools and techniques centered around the transformation of OBGG models. We describe in details the model transformation from OBGG models to PROMELA, the input language of the SPIN model checker. Amongst the contributions of this paper are: (a) the correctness proof of the transformation from OBGG models to PROMELA; (b) a generalization of this process in steps that may be used as a guide to prove the correctness of transformations from different specification/programming languages to PROMELA.

From UML to SIMULINK CAAM: Formal Specification and Transformation Analysis

UML and Simulink are attractive languages for embedded systems design and modeling. An automatic mapping from UML models to Simulink would be an interesting resource in a seamless design flow, allowing designers to use UML as modeling language for the whole system and at same time to use facilities for code generation based on Simulink. In a previous work, the UML to Simulink translation was prototyped using a Java implementation. In this paper, we present the formal definition of this translation using graph grammars, as well as its automation, which is supported by the AGG system. With the formalization of the metamodels and translation rules, we can guarantee the correctness of the translation. We also illustrate the effectiveness of our methodology by means of a case study.

Towards robustness and duality analysis of intuitionistic fuzzy aggregations

This paper studies the robustness of intuitionistic fuzzy connectives in fuzzy reasoning. Starting with an evaluation of the sensitivity in representable fuzzy negations, we apply the results in the intuitionistic (S, N)-implication class and its dual construction. As the main contribution, the paper formally states that the robustness preserves the projection functions in this class and corresponding dual operators.

Aproximating static list schedules in dynamic multithreaded applications

List scheduling algorithms are known to be efficient when the application to be executed can be described statically as a Directed Acyclic Graph (DAG) of tasks. Regardless of knowing the entire DAG beforehand, obtaining an optimal schedule in a parallel machine is a NP-hard problem. Moreover, many programming tools propose the use of scheduling techniques based on list strategies. This paper presents an analysis of scheduling algorithms for multithread programs in a dynamic scenario where threads are created and destroyed during execution. We introduce an algorithm to convert DAGs, describing applications as tasks, into Directed Cyclic Graphs (DCGs) describing the same application designed in a multithread programming interface. Our algorithm covers case studies described in previous works, successfully mapping from the abstract level of graphs to the application environment. These mappings preserve the guarantees offered by the abstract model, providing efficient scheduling of dynamic programs that follow the intended multithread model. We conclude the paper presenting some performance results we obtained by list schedulers in dynamic multithreaded environments. We also compare these results with the best scheduling we could obtain with similar static task schedulers.

Correlation coefficient analysis based on fuzzy negations and representable automorphisms

This paper aims to study the correlation between Atanassovs intuitionistic fuzzy sets (A-IFSs) obtained as image of strong intuitionistic fuzzy negations. We consider the action of strong fuzzy negations in order to verify the conditions under which the correlation coefficient related to such A-IFSs and their corresponding conjugate constructions are obtained. We attempt to present algebraic expressions of correlation relationship by considering representable intuitionistic automorphisms.

Robustness of f- and g-generated Fuzzy (Co)Implications

This paper studies the robustness of intuitionistic fuzzy implications in fuzzy reasoning based on Atanassovs intuitionistic fuzzy logic. Starting with an evaluation of the sensitivity in representable fuzzy negations, we apply the results in the Yagers classes of fuzzy implications called the f- and g-generated fuzzy implications. The paper formally states that the robustness preserves the projection functions in such class and also discusses their corresponding dual operators.

Aggregating fuzzy implications based on OWA-operators

This paper presents the fuzzy (S, N)- QL- and D-subimplication classes, which are obtained by OWA operators performed over the families of triangular subnorms and sub-conorms along with fuzzy negations. Since these classes of subim-plications are explicitly represented by such connectives, the corresponding (S, N)- QL- and D-subimplicatios are characterized by the generalized associativity and distributive properties together with extensions of the exchange and neutrality principles. As the main results, these families of subimplications extend related implications by preserving their corresponding properties.