A Graph Rewriting Approach for Transformational Design of Digital Systems

Transformational design integrates design and verification. It combines “correctness by construction” and design creativity by the use of pre-proven behaviour preserving transformations as design steps. The formal aspects of this methodology are hidden in the transformations. A constraint is the availability of a design representation with a compositional formal semantics. Graph representations are useful design representations because of their visualisation of design information. In this paper graph rewriting theory, as developed in the last twenty years in mathematics, is shown to be a useful basis for a formal framework for transformational design. The semantic aspects of graphs which are no part of graph rewriting theory are included by the use of attributed graphs. The used attribute algebra, table algebra, is a relation algebra derived from database theory. The combination of graph rewriting, table algebra and transformational design is new

Integrated Structure and Semantics for Reo Connectors and Petri Nets

In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models. For this purpose, we introduce a notion of connectors which consist of a number of interconnected, user-defined primitives with fixed behavior. While the structure of connectors resembles hypergraphs, their semantics is given in terms of so-called port automata. We define both models in a categorical setting where composition operations can be elegantly defined and integrated. Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks. We then define a semantical functor from the connector to the port automata category which preserves this composition. We further show how to encode Reo connectors and Petri nets into this model and indicate applications to dynamic reconfigurations modeled using double pushout graph transformation

Prospects for Declarative Mathematical Modeling of Complex Biological Systems

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. The potential advantages are particularly relevant in the case of developmental modeling, wherein complex spatial structures exhibit dynamics at molecular, cellular, and organogenic levels to relate genotype to multicellular phenotype. Multiscale modeling can benefit from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects; we define semantics-preserving implementation and semantics-approximating model reduction transformations; and we outline a "meta-hierarchy" for organizing declarative models and the mathematical methods that can fruitfully manipulate them

An agent-based model studying the acquisition of a language system of logical constructions

This paper presents an agent-based model that studies the emergence and evolution of a language system of logical constructions, i.e. a vocabulary and a set of grammatical constructions that allows the expression of logical combinations of categories. The model assumes the agents have a common vocabulary for basic categories, the ability to construct logical combinations of categories using Boolean functions, and some general purpose cognitive capacities for invention, adoption, induction and adaptation. But it does not assume the agents have a vocabulary for Boolean functions nor grammatical constructions for expressing such logical combinations of categories through language. The results of the experiments we have performed show that a language system of logical constructions emerges as a result of a process of selforganisation of the individual agents’ interactions when these agents adapt their preferences for vocabulary and grammatical constructions to those they observe are used more often by the rest of the population, and that such a language system is transmitted from one generation to the next.Peer ReviewedPostprint (published version

From Separate Formal Specifications to Certified Integrated Visual Modelling Techniques and Environments - Position Statement

In this position statement we discuss the state of the art and role of formal specification and modelling techniques in different periods with special focus on the work of the TFS-group at TU-Berlin. In the past (1970 – 1990) single formal specification techniques have been developed with little impact on practical software development. In the present (1990 – 2010) integrated and visual modelling techniques have gained more and more importance. For the future (2010 – 2020) we try to sketch the idea of a Certified Integrated Visual Modelling Technique and Environment based on an integration of graph theory, graph transformation and Petri net theory, short Dynamic Graph and Net Theory

Distributed Port Automata

Dynamic reconfigurations are a powerful approach for the adaption of component-based or service-oriented software systems at runtime. Important issues in this area are the problems of state transfer and state consistency, i.e., to determine the system state after a reconfiguration and to ensure that it is valid. To deal with these problems, we introduce distributed port automata in this paper. Distributed port automata combine structural and behavioral system properties and therefore allow to reason about dynamic reconfigurations. In our approach, we use an automata-based model for describing the behavior of the primitive building blocks in a system, and a graph-based model for describing its structure in terms of a network. We demonstrate how to derive the system semantics of a distributed port automaton and show that it is compositional. We consider an encoding of the coordination language Reo and show a new result on compositionality of flattening for distributed graphs

The design and implementation of Object Grammars

An Object Grammar is a variation on traditional BNF grammars, where the notation is extended to support declarative bidirectional mappings between text and object graphs. The two directions for interpreting Object Grammars are parsing and formatting. Parsing transforms text into an object graph by recognizing syntactic features and creating the corresponding object structure. In the reverse direction, formatting recognizes object graph features and generates an appropriate textual presentation. The key to Object Grammars is the expressive power of the mapping, which decouples the syntactic structure from the graph structure. To handle graphs, Object Grammars support declarative annotations for resolving textual names that refer to arbitrary objects in the graph structure. Predicates on the semantic structure provide additional control over the mapping. Furthermore, Object Grammars are compositional so that languages may be defined in a modular fashion. We have implemented our approach to Object Grammars as one of the foundations of the Ens (o) over bar system and illustrate the utility of our approach by showing how it enables definition and composition of domain-specific languages (DSLs). (C) 2014 Elsevier B.V. All rights reserved.</p