Proof Tactics for Theorem Proving Graph Grammars through Rodin

Graph grammar is a formal language suitable for the specification of distributed and concurrent systems. Theorem proving is a technique that allows the verification of systems with huge (and infinite) state space. One of the disadvantages of theorem proving graph grammars (and theorem proving in general) is the specific mathematical knowledge required from the user for concluding the proofs. Previous works have proposed proof strategies to help the developer in the verification process when adopting such approach, firstly establishing proof tactics for some properties and after proposing a visual representation for them. This paper extends the set of proposed tactics, with the aim of expanding the available strategies and encouraging the use of such a technique

A Graph Grammar to Transform a Dataflow Graph into a Multithread Graph and its Application in Task Scheduling

The scheduling of tasks in a parallel program is an NP-complete problem, where scheduling tasks over multiple processing units requires an effective strategy to maximize the exploitation of the parallel hardware. Several studies focus on the scheduling of parallel programs described into DAGs (Directed Acyclic Graphs). However, this representation does not describe a multithreaded program suitably. This paper shows the structure and semantics of a DCG, an abstraction which describes a multithreaded program, and proposes standards to map structures found in DAGs into segments of a DCG. A graph grammar has been developed to perform the proposed transformation and case studies using DAGs found in the literature validate the transformation process. Besides the automatic translation and precise definition of the mapping, the use of a formal language also allowed the verification of the existence and uniqueness of the out coming model.

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 asmodeling 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 theeffectiveness of our methodology by means of a case study

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear un derstanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5–7 vast areas of the tropics remain understudied.8–11 In the American tropics, Amazonia stands out as the world’s most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepre sented in biodiversity databases.13–15 To worsen this situation, human-induced modifications16,17 may elim inate pieces of the Amazon’s biodiversity puzzle before we can use them to understand how ecological com munities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple or ganism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region’s vulnerability to environmental change. 15%–18% of the most ne glected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lostinfo:eu-repo/semantics/publishedVersio

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

Abordagem relacional de gramática de grafos

Gramática de grafos é uma linguagem formal bastante adequada para sistemas cujos estados possuem uma topologia complexa (que envolvem vários tipos de elementos e diferentes tipos de relações entre eles) e cujo comportamento é essencialmente orientado pelos dados, isto é, eventos são disparados por configurações particulares do estado. Vários sistemas reativos são exemplos desta classe de aplicações, como protocolos para sistemas distribuídos e móveis, simulação de sistemas biológicos, entre outros. A verificação de gramática de grafos através da técnica de verificação de modelos já é utilizada por diversas abordagens. Embora esta técnica constitua um método de análise bastante importante, ela tem como desvantagem a necessidade de construir o espaço de estados completo do sistema, o que pode levar ao problema da explosão de estados. Bastante progresso tem sido feito para lidar com esta dificuldade, e diversas técnicas têm aumentado o tamanho dos sistemas que podem ser verificados. Outras abordagens propõem aproximar o espaço de estados, mas neste caso não é possível a verificação de propriedades arbitrárias. Além da verificação de modelos, a prova de teoremas constitui outra técnica consolidada para verificação formal. Nesta técnica tanto o sistema quanto suas propriedades são expressas em alguma lógica matemática. O processo de prova consiste em encontrar uma prova a partir dos axiomas e lemas intermediários do sistema. Cada técnica tem argumentos pró e contra o seu uso, mas é possível dizer que a verificação de modelos e a prova de teoremas são complementares. A maioria das abordagens utilizam verificadores de modelos para analisar propriedades de computações, isto é, sobre a seqüência de passos de um sistema. Propriedades sobre estados alcançáveis só são verificadas de forma restrita. O objetivo deste trabalho é prover uma abordagem para a prova de propriedades de grafos alcançáveis de uma gramática de grafos através da técnica de prova de teoremas. Propõe-se uma tradução (da abordagem Single-Pushout) de gramática de grafos para uma abordagem lógica e relacional, a qual permite a aplicação de indução matemática para análise de sistemas com espaço de estados infinito. Definiu-se gramática de grafos utilizando estruturas relacionais e aplicações de regras com linguagens lógicas. Inicialmente considerou-se o caso de grafos (tipados) simples, e então se estendeu a abordagem para grafos com atributos e gramáticas com condições negativas de aplicação. Além disso, baseado nesta abordagem, foram estabelecidos padrões para a definição, codificação e reuso de especificações de propriedades. O sistema de padrões tem o objetivo de auxiliar e simplificar a tarefa de especificar requisitos de forma precisa. Finalmente, propõe-se implementar definições relacionais de gramática de grafos em estruturas de event-B, de forma que seja possível utilizar os provadores disponíveis para event-B para demonstrar propriedades de gramática de grafos.Graph grammars are a formal 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. The verification of graph grammar models through model-checking is currently supported by various approaches. Although model-checking is an important analysis method, it has as disadvantage the need to build the complete state space, which can lead to the state explosion problem. Much progress has been made to deal with this difficulty, and many techniques have increased the size of the systems that may be verified. Other approaches propose to over- and/or under-approximate the state-space, but in this case it is not possible to check arbitrary properties. Besides model checking, theorem proving is another wellestablished approach for verification. Theorem proving is a technique where both the system and its desired properties are expressed as formulas in some mathematical logic. A logical description defines the system, establishing a set of axioms and inference rules. The process of verification consists of finding a proof of the required property from the axioms or intermediary lemmas of the system. Each verification technique has arguments for and against its use, but we can say that model-checking and theorem proving are complementary. Most of the existing approaches use model checkers to analyse properties of computations, that is, properties over the sequences of steps a system may engage in. Properties about reachable states are handled, if at all possible, only in very restricted ways. In this work, our main aim is to provide a means to prove properties of reachable graphs of graph grammar models using the theorem proving technique. We propose an encoding of (the Single-Pushout approach of) graph grammar specifications into a relational and logical approach which allows the application of the mathematical induction technique to analyse systems with infinite state-spaces. We have defined graph grammars using relational structures and used logical languages to model rule applications. We first consider the case of simple (typed) graphs, and then we extend the approach to the non-trivial case of attributed-graphs and grammars with negative application conditions. Besides that, based on this relational encoding, we establish patterns for the presentation, codification and reuse of property specifications. The pattern has the goal of helping and simplifying the task of stating precise requirements to be verified. Finally, we propose to implement relational definitions of graph grammars in event-B structures, such that it is possible to use the event-B provers to demonstrate properties of a graph grammar

Abordagem relacional de gramática de grafos

Gramática de grafos é uma linguagem formal bastante adequada para sistemas cujos estados possuem uma topologia complexa (que envolvem vários tipos de elementos e diferentes tipos de relações entre eles) e cujo comportamento é essencialmente orientado pelos dados, isto é, eventos são disparados por configurações particulares do estado. Vários sistemas reativos são exemplos desta classe de aplicações, como protocolos para sistemas distribuídos e móveis, simulação de sistemas biológicos, entre outros. A verificação de gramática de grafos através da técnica de verificação de modelos já é utilizada por diversas abordagens. Embora esta técnica constitua um método de análise bastante importante, ela tem como desvantagem a necessidade de construir o espaço de estados completo do sistema, o que pode levar ao problema da explosão de estados. Bastante progresso tem sido feito para lidar com esta dificuldade, e diversas técnicas têm aumentado o tamanho dos sistemas que podem ser verificados. Outras abordagens propõem aproximar o espaço de estados, mas neste caso não é possível a verificação de propriedades arbitrárias. Além da verificação de modelos, a prova de teoremas constitui outra técnica consolidada para verificação formal. Nesta técnica tanto o sistema quanto suas propriedades são expressas em alguma lógica matemática. O processo de prova consiste em encontrar uma prova a partir dos axiomas e lemas intermediários do sistema. Cada técnica tem argumentos pró e contra o seu uso, mas é possível dizer que a verificação de modelos e a prova de teoremas são complementares. A maioria das abordagens utilizam verificadores de modelos para analisar propriedades de computações, isto é, sobre a seqüência de passos de um sistema. Propriedades sobre estados alcançáveis só são verificadas de forma restrita. O objetivo deste trabalho é prover uma abordagem para a prova de propriedades de grafos alcançáveis de uma gramática de grafos através da técnica de prova de teoremas. Propõe-se uma tradução (da abordagem Single-Pushout) de gramática de grafos para uma abordagem lógica e relacional, a qual permite a aplicação de indução matemática para análise de sistemas com espaço de estados infinito. Definiu-se gramática de grafos utilizando estruturas relacionais e aplicações de regras com linguagens lógicas. Inicialmente considerou-se o caso de grafos (tipados) simples, e então se estendeu a abordagem para grafos com atributos e gramáticas com condições negativas de aplicação. Além disso, baseado nesta abordagem, foram estabelecidos padrões para a definição, codificação e reuso de especificações de propriedades. O sistema de padrões tem o objetivo de auxiliar e simplificar a tarefa de especificar requisitos de forma precisa. Finalmente, propõe-se implementar definições relacionais de gramática de grafos em estruturas de event-B, de forma que seja possível utilizar os provadores disponíveis para event-B para demonstrar propriedades de gramática de grafos.Graph grammars are a formal 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. The verification of graph grammar models through model-checking is currently supported by various approaches. Although model-checking is an important analysis method, it has as disadvantage the need to build the complete state space, which can lead to the state explosion problem. Much progress has been made to deal with this difficulty, and many techniques have increased the size of the systems that may be verified. Other approaches propose to over- and/or under-approximate the state-space, but in this case it is not possible to check arbitrary properties. Besides model checking, theorem proving is another wellestablished approach for verification. Theorem proving is a technique where both the system and its desired properties are expressed as formulas in some mathematical logic. A logical description defines the system, establishing a set of axioms and inference rules. The process of verification consists of finding a proof of the required property from the axioms or intermediary lemmas of the system. Each verification technique has arguments for and against its use, but we can say that model-checking and theorem proving are complementary. Most of the existing approaches use model checkers to analyse properties of computations, that is, properties over the sequences of steps a system may engage in. Properties about reachable states are handled, if at all possible, only in very restricted ways. In this work, our main aim is to provide a means to prove properties of reachable graphs of graph grammar models using the theorem proving technique. We propose an encoding of (the Single-Pushout approach of) graph grammar specifications into a relational and logical approach which allows the application of the mathematical induction technique to analyse systems with infinite state-spaces. We have defined graph grammars using relational structures and used logical languages to model rule applications. We first consider the case of simple (typed) graphs, and then we extend the approach to the non-trivial case of attributed-graphs and grammars with negative application conditions. Besides that, based on this relational encoding, we establish patterns for the presentation, codification and reuse of property specifications. The pattern has the goal of helping and simplifying the task of stating precise requirements to be verified. Finally, we propose to implement relational definitions of graph grammars in event-B structures, such that it is possible to use the event-B provers to demonstrate properties of a graph grammar