Language and semantics of expressions for Grafcet model synthesis in a MDE environment

The GRAphe Fonctionnel de Commande Étapes Transitions (GRAFCET) is a powerful graphical modeling language for the pecification of controllers in discrete event systems.It uses expressions to express the conditions of transitions and conditional actions as well as the logical and arithmetic expressions assigned to stored actions. However, several research works has focused on the transformation of Grafcet specifications (including expressions) into control code for embedded systems. To make it easier to edit valid Grafcet models and generate code, it is necessary to propose a formalization of the Grafcet expression language permitting to validate its constructs and provide an appropriate semantics. For this, we propose a context-free grammar that generates the whole set of Grafcet expressions, by extending the usual grammars of logical and arithmetic expressions. We also propose a metamodel and an associated semantics of Grafcet expressions to facilitate the implementation of the Grafcet language. A parser of the expressions Grafcet emph G7Expr is then obtained thanks to the generator of parsers ANTLR, while the metamodel is implemented in the Eclipse EMF Model Driven Engineering (MDE) environment. The combination of the two tools makes it possible to analyze and automatically build Grafcet expressions when editing and synthesizing Grafcet models. Le GRAphe Fonctionnel de Commande Étapes Transitions (GRAFCET) est un puissant lan-gage de modélisation graphique pour la spécification de contrôleurs dans des systèmes à événe-ments discrets. Il fait usage des expressions pour exprimer les conditions de franchissement des transitions et des actions conditionnelles ainsi que les expressions logiques et arithmétiques assi-gnées aux actions stockées. Cependant, de nombreux travaux se sont penchés sur la transformation de spécifications Grafcet (y compris les expressions) en code de contrôle pour systèmes embar-qués. Pour faciliter l'édition de modèles Grafcet valides et la génération du code de contrôle, il est judicieux de proposer une formalisation du langage des expressions Grafcet, permettant de valider ses constructions et d'en pourvoir une sémantique appropriée. Pour cela, nous proposons une gram-maire hors-contexte qui génère tout l'ensemble des expressions Grafcet, en étendant les grammaires usuelles des expressions arithmétiques et logiques. Nous proposons également un métamodèle et une sémantique associée des expressions Grafcet pour faciliter la mise en oeuvre du langage Grafcet sous la forme d'un parseur des expressions Grafcet G7Expr obtenu grce au générateur d'analyseurs syntaxiques ANTLR, alors que le métamodèle est mis en oeuvre dans l'environnement d'Ingénie-rie Dirigée par les Modèles (IDM) Eclipse EMF. L'association des deux outils permet d'analyser et de construire automatiquement les expressions Grafcet lors de l'édition et la synthèse des modèles Grafcet.

MODELING OF MAXIMALLY PARALLEL STRUCTURES OF ALGORITHMS FOR SOLVING THERMAL PROBLEMS

The paper demonstrates the possibility of creating a maximum parallel form of computational algorithms to solve thermal problems and their mapping to the architecture of multiprocessor systems based on solving thermal problems of mathematical physics. It is shown that an effective tool for studying heat and mass transfer problems in metallurgical production could be parallel computing technologies on distributed cluster systems with a relatively low cost and reasonably easily scalable both in the number of processors and in the amount of RAM. Tridiagonal structure systems' parallelization was implemented by a numerical-analytical approach, which predetermined their maximally parallel algorithmic form. That approach is facilitated by the minimum possible implementation time of the developed algorithm on parallel computing systems. Furthermore, during the arithmetic expressions parallel computations, the developed algorithm separates the error in the output data from rounding operations. Thus, the parallelization of tridiagonal systems based on numerical-analytical discretization methods does not impose any restrictions on the topology of the mesh nodes of the computational domain.Furthermore, as applied to the parallel computation of arithmetic expressions, it separates the initial data error from a real PC's rounding operations. That approach eliminates the recurrent structure of computing the sought-for decision vectors, which, as a rule, leads to the round-off errors accumulation. Such a parallel form of the constructed algorithm is maximal and has the shortest possible implementation time of the algorithm on parallel computing systems. The developed approach to parallelizing the mathematical model is stable for various types of input data. It has the most parallel form and is distinguished by the minimum time for solving the problem as applied to multiprocessor computing systems. That is explained as follows. If it is hypothesized that one processor can be assigned to one processor and one processor can be assigned to one node of the computational mesh domain, the computations can be processed in parallel and simultaneously for all nodes of the computational mesh domain. The simulation process was implemented on a PC cluster. It follows from the simulation results analysis that the developed method for solving the heat conduction problem effectively minimizes residuals.

A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes

In this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of $(m+1)$ ( m + 1 ) -point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The $C^{0}$ C 0 , $C^{1}$ C 1 and $C^{2}$ C 2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.

Numerical Markov Logic Network: A Scalable Probabilistic Framework for Hybrid Knowledge Inference

In recent years, the Markov Logic Network (MLN) has emerged as a powerful tool for knowledge-based inference due to its ability to combine first-order logic inference and probabilistic reasoning. Unfortunately, current MLN solutions cannot efficiently support knowledge inference involving arithmetic expressions, which is required to model the interaction between logic relations and numerical values in many real applications. In this paper, we propose a probabilistic inference framework, called the Numerical Markov Logic Network (NMLN), to enable efficient inference of hybrid knowledge involving both logic and arithmetic expressions. We first introduce the hybrid knowledge rules, then define an inference model, and finally, present a technique based on convex optimization for efficient inference. Built on decomposable exp-loss function, the proposed inference model can process hybrid knowledge rules more effectively and efficiently than the existing MLN approaches. Finally, we empirically evaluate the performance of the proposed approach on real data. Our experiments show that compared to the state-of-the-art MLN solution, it can achieve better prediction accuracy while significantly reducing inference time.

Third Grade Students’ Use of Relational Thinking

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

Modelovanje ekvivalencije matematičkih izraza u početnoj nastavi

The notion of expression equivalence is one of the terms that has been recognized in the literature as key to understanding algebraic ideas. To understand this term, the context used as a basis for developing meaning is important, as well as the language in which generalizations are expressed. The aim of this paper is twofold: a) to examine whether the context of a textual task and modeling activities influence the understanding of the transformation of expressions into equivalent forms; b) determine whether the understanding of the equivalence of the expression is affected by the level of abstractness of the expression (algebraic or arithmetic). The research is of a quasi-experimental design with two experimental groups and one control group. The sample consists of 148 fourth-graders. The existence of statistically significant differences between the students of the experimental groups and the control group suggests that the modeling process influences the development of the notion of expression equivalence. This research did not show any differences in the results of the students who were taught using algebraic or arithmetic expressions. This implies that the understanding of equivalence developed through the modeling process is not related to the level of abstractness of the mathematical language used, but that, based on understanding the meaning of the term, students can transform arithmetic and algebraic expressions with equal success.

Latent Compositional Representations Improve Systematic Generalization in Grounded Question Answering

Answering questions that involve multi-step reasoning requires decomposing them and using the answers of intermediate steps to reach the final answer. However, state-of-the-art models in grounded question answering often do not explicitly perform decomposition, leading to difficulties in generalization to out-of-distribution examples. In this work, we propose a model that computes a representation and denotation for all question spans in a bottom-up, compositional manner using a CKY-style parser. Our model induces latent trees, driven by end-to-end (the answer) supervision only. We show that this inductive bias towards tree structures dramatically improves systematic generalization to out-of- distribution examples, compared to strong baselines on an arithmetic expressions benchmark as well as on C losure, a dataset that focuses on systematic generalization for grounded question answering. On this challenging dataset, our model reaches an accuracy of 96.1%, significantly higher than prior models that almost perfectly solve the task on a random, in-distribution split.