Graph-Based Shape Analysis Beyond Context-Freeness

We develop a shape analysis for reasoning about relational properties of data structures. Both the concrete and the abstract domain are represented by hypergraphs. The analysis is parameterized by user-supplied indexed graph grammars to guide concretization and abstraction. This novel extension of context-free graph grammars is powerful enough to model complex data structures such as balanced binary trees with parent pointers, while preserving most desirable properties of context-free graph grammars. One strength of our analysis is that no artifacts apart from grammars are required from the user; it thus offers a high degree of automation. We implemented our analysis and successfully applied it to various programs manipulating AVL trees, (doubly-linked) lists, and combinations of both

On the equivalence, containment, and covering problems for the regular and context-free languages

We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Turing machine computations exponential in the size of the grammar is used to prove several exponential lower bounds. These lower bounds include exponential time for testing equivalence of grammars generating finite sets, and exponential space for testing equivalence of non-self-embedding grammars. Several problems which might be complex because of this encoding are shown to simplify for linear grammars. Other problems considered include grammatical covering and structural equivalence for right-linear, linear, and arbitrary grammars

Graph Transformations and Game Theory: A Generative Mechanism for Network Formation

Many systems can be described in terms of networks with characteristic structural properties. To better understand the formation and the dynamics of complex networks one can develop generative models. We propose here a generative model (named dynamic spatial game) that combines graph transformations and game theory. The idea is that a complex network is obtained by a sequence of node-based transformations determined by the interactions of nodes present in the network. We model the node-based transformations by using graph grammars and the interactions between the nodes by using game theory. We illustrate dynamic spatial games on a couple of examples: the role of cooperation in tissue formation and tumor development and the emergence of patterns during the formation of ecological networks

Towards Theorem Proving Graph Grammars using Event-B

Graph grammars may be used as specification technique for different kinds of systems, specially in situations in which states are complex structures that can be adequately modeled as graphs (possibly with an attribute data part) and in which the behavior involves a large amount of parallelism and can be described as reactions to stimuli that can be observed in the state of the system. The verification of properties of such systems is a difficult task due to many aspects: in many situations the systems have an infinite number of states; states themselves are complex and large; there are a number of different computation possibilities due to the fact that rule applications may occur in parallel. There are already some approaches to verification of graph grammars based on model checking, but in these cases only finite state systems can be analyzed. Other approaches propose over- and/or under-approximations of the state-space, but in this case it is not possible to check arbitrary properties. In this work, we propose to use the Event-B formal method and its theorem proving tools to analyze graph grammars. We show that a graph grammar can be translated into an Event-B specification preserving its semantics, such that one can use several theorem provers available for Event-B to analyze the reachable states of the original graph grammar. The translation is based on a relational definition of graph grammars, that was shown to be equivalent to the Single-Pushout approach to graph grammars

Phrase structure grammars as indicative of uniquely human thoughts

I argue that the ability to compute phrase structure grammars is indicative of a particular kind of thought. This type of thought that is only available to cognitive systems that have access to the computations that allow the generation and interpretation of the structural descriptions of phrase structure grammars. The study of phrase structure grammars, and formal language theory in general, is thus indispensable to studies of human cognition, for it makes explicit both the unique type of human thought and the underlying mechanisms in virtue of which this thought is made possible

Developmental constraints on learning artificial grammars with fixed, flexible and free word order

Human learning, although highly flexible and efficient, is constrained in ways that facilitate or impede the acquisition of certain systems of information. Some such constraints, active during infancy and childhood, have been proposed to account for the apparent ease with which typically developing children acquire language. In a series of experiments, we investigated the role of developmental constraints on learning artificial grammars with a distinction between shorter and relatively frequent words (‘function words,’ F-words) and longer and less frequent words (‘content words,’ C-words). We constructed 4 finite-state grammars, in which the order of F-words, relative to C-words, was either fixed (F-words always occupied the same positions in a string), flexible (every F-word always followed a C-word), or free. We exposed adults (N = 84) and kindergarten children (N = 100) to strings from each of these artificial grammars, and we assessed their ability to recognize strings with the same structure, but a different vocabulary. Adults were better at recognizing strings when regularities were available (i.e., fixed and flexible order grammars), while children were better at recognizing strings from the grammars consistent with the attested distribution of function and content words in natural languages (i.e., flexible and free order grammars). These results provide evidence for a link between developmental constraints on learning and linguistic typology

Ten virtues of structured graphs

This paper extends the invited talk by the first author about the virtues of structured graphs. The motivation behind the talk and this paper relies on our experience on the development of ADR, a formal approach for the design of styleconformant, reconfigurable software systems. ADR is based on hierarchical graphs with interfaces and it has been conceived in the attempt of reconciling software architectures and process calculi by means of graphical methods. We have tried to write an ADR agnostic paper where we raise some drawbacks of flat, unstructured graphs for the design and analysis of software systems and we argue that hierarchical, structured graphs can alleviate such drawbacks