Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Avoiding Unnecessary Information Loss: Correct and Efficient Model Synchronization Based on Triple Graph Grammars

Model synchronization, i.e., the task of restoring consistency between two interrelated models after a model change, is a challenging task. Triple Graph Grammars (TGGs) specify model consistency by means of rules that describe how to create consistent pairs of models. These rules can be used to automatically derive further rules, which describe how to propagate changes from one model to the other or how to change one model in such a way that propagation is guaranteed to be possible. Restricting model synchronization to these derived rules, however, may lead to unnecessary deletion and recreation of model elements during change propagation. This is inefficient and may cause unnecessary information loss, i.e., when deleted elements contain information that is not represented in the second model, this information cannot be recovered easily. Short-cut rules have recently been developed to avoid unnecessary information loss by reusing existing model elements. In this paper, we show how to automatically derive (short-cut) repair rules from short-cut rules to propagate changes such that information loss is avoided and model synchronization is accelerated. The key ingredients of our rule-based model synchronization process are these repair rules and an incremental pattern matcher informing about suitable applications of them. We prove the termination and the correctness of this synchronization process and discuss its completeness. As a proof of concept, we have implemented this synchronization process in eMoflon, a state-of-the-art model transformation tool with inherent support of bidirectionality. Our evaluation shows that repair processes based on (short-cut) repair rules have considerably decreased information loss and improved performance compared to former model synchronization processes based on TGGs.Comment: 33 pages, 20 figures, 3 table

A Solution to the Flowgraphs Case Study using Triple Graph Grammars and eMoflon

After 20 years of Triple Graph Grammars (TGGs) and numerous actively maintained implementations, there is now a need for challenging examples and success stories to show that TGGs can be used for real-world bidirectional model transformations. Our primary goal in recent years has been to increase the expressiveness of TGGs by providing a set of pragmatic features that allow a controlled fallback to programmed graph transformations and Java. Based on the Flowgraphs case study of the Transformation Tool Contest (TTC 2013), we present (i) attribute constraints used to express complex bidirectional attribute manipulation, (ii) binding expressions for specifying arbitrary context relationships, and (iii) post-processing methods as a black box extension for TGG rules. In each case, we discuss the enabled trade-off between guaranteed formal properties and expressiveness. Our solution, implemented with our metamodelling and model transformation tool eMoflon (www.emoflon.org), is available as a virtual machine hosted on Share.Comment: In Proceedings TTC 2013, arXiv:1311.753

Strong Effects of Network Architecture in the Entrainment of Coupled Oscillator Systems

Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization. However, the entrainment is significantly facilitated if the networks are directionally biased, i.e., closer to the feedforward networks. Furthermore, we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes. The neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results.Comment: 15 pages, 11 figures, RevTe

Iteration Algebras for UnQL Graphs and Completeness for Bisimulation

This paper shows an application of Bloom and Esik's iteration algebras to model graph data in a graph database query language. About twenty years ago, Buneman et al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation. However, no mathematical semantics of UnQL/UnCAL graphs has been developed. In this paper, we give an equational axiomatisation and algebraic semantics of UnCAL graphs. The main result of this paper is to prove that completeness of our equational axioms for UnCAL for the original bisimulation of UnCAL graphs via iteration algebras. Another benefit of algebraic semantics is a clean characterisation of structural recursion on graphs using free iteration algebra.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Bidirectional Transformation "bx" (Dagstuhl Seminar 11031)

Bidirectional transformations bx are a mechanism for maintaining the consistency of two (or more) related sources of information. Researchers from many different areas of computer science including databases (DB), graph transformations (GT), software engineering (SE), and programming languages (PL) are actively investigating the use of bx to solve a diverse set of problems. Although researchers have been actively working on bidirectional transformations in the above mentioned communities for many years already, there has been very little cross-discipline interaction and cooperation so far. The purpose of a first International Meeting on Bidirectional Transformations (GRACE-BX), held in December 2008 near Tokyo, was therefore to bring together international elites, promising young researchers, and leading practitioners to share problems, discuss solutions, and open a dialogue towards understanding the common underpinnings of bx in all these areas. While the GRACE-BX meeting provided a starting point for exchanging ideas in different communities and confirmed our believe that there is a considerable overlap of studied problems and developed solutions in the identified communities, the Dagstuhl Seminar 11031 on ``Bidirectional Transformations\u27\u27 also aimed at providing a place for working together to define a common vocabulary of terms and desirable properties of bidirectional transformations, develop a suite of benchmarks, solve some challenging problems, and launch joint efforts to form a living bx community of cooperating experts across the identified subdisciplines. This report documents the program and the outcomes of Dagstuhl Seminar 11031 with abstracts of tutorials, working groups, and presentations on specific research topics

Task-based acceleration of bidirectional recurrent neural networks on multi-core architectures

This paper proposes a novel parallel execution model for Bidirectional Recurrent Neural Networks (BRNNs), B-Par (Bidirectional-Parallelization), which exploits data and control dependencies for forward and reverse input computations. B-Par divides BRNN workloads across different parallel tasks by defining input and output dependencies for each RNN cell in both forward and reverse orders. B-Par does not require per-layer barriers to synchronize the parallel execution of BRNNs. We evaluate B-Par considering the TIDIGITS speech database and the Wikipedia data-set. Our experiments indicate that B-Par outperforms the state-of-the-art deep learning frameworks TensorFlow-Keras and Pytorch by achieving up to 2.34× and 9.16× speed-ups, respectively, on modern multi-core CPU architectures while preserving accuracy. Moreover, we analyze in detail aspects like task granularity, locality, or parallel efficiency to illustrate the benefits of B-Par.This work is partially supported by the Generalitat de Catalunya (contract 2017-SGR-1414) and the Spanish Ministry of Science and Technology through the PID2019- 107255GB project. Marc Casas has been supported by the Spanish Ministry of Economy, Industry and Competitiveness under the Ramon y Cajal fellowship No. RYC-2017-23269.Peer ReviewedPostprint (author's final draft