Modeling Graph Languages with Grammars Extracted via Tree Decompositions

Work on probabilistic models of natural language tends to focus on strings and trees, but there is increasing interest in more general graph-shaped structures since they seem to be better suited for representing natural language semantics, ontologies, or other varieties of knowledge structures. However, while there are relatively simple approaches to defining generative models over strings and trees, it has proven more challenging for more general graphs. This paper describes a natural generalization of the n-gram to graphs, making use of Hyperedge Replacement Grammars to define generative models of graph languages.9 page(s

Expressive Power of Hypergraph Lambek Grammars

Hypergraph Lambek grammars (HL-grammars) is a novel logical approach to generating graph languages based on the hypergraph Lambek calculus. In this paper, we establish a precise relation between HL-grammars and hypergraph grammars based on the double pushout (DPO) approach: we prove that HL-grammars generate the same class of languages as DPO grammars with the linear restriction on lengths of derivations. This can be viewed as a complete description of the expressive power of HL-grammars and also as an analogue of the Pentus theorem, which states that Lambek grammars generate the same class of languages as context-free grammars. As a corollary, we prove that HL-grammars subsume contextual hyperedge replacement grammars

Generating Correctness-Preserving Editing Operations for Diagram Editors

In previous work it has already been shown that syntax-directed and free-hand editing can be gainfully integrated into a single diagram editor. That way, the user can arrange diagram components on the screen without any restrictions in free-hand editing mode, whereas syntax-directed editing operations provide powerful assistance. So far, editing operations had to be specified or programmed by the editor developer. In contrast, this paper proposes an approach where diagram-specific editing operations are generated on the fly during the editing process and without any additional specification effort. These operations provably preserve the correctness of the diagram. The proposed approach requires a specification of the visual language by a hypergraph grammar

Parsing of Hyperedge Replacement Grammars with Graph Parser Combinators

Graph parsing is known to be computationally expensive. For this reason the construction of special-purpose parsers may be beneficial for particular graph languages. In the domain of string languages so-called parser combinators are very popular for writing efficient parsers. Inspired by this approach, we have proposed graph parser combinators in a recent paper, a framework for the rapid development of special-purpose graph parsers. Our basic idea has been to define primitive graph parsers for elementary graph components and a set of combinators for the flexible construction of more advanced graph parsers. Following this approach, a declarative, but also more operational description of a graph language can be given that is a parser at the same time. In this paper we address the question how the process of writing correct parsers on top of our framework can be simplified by demonstrating the translation of hyperedge replacement grammars into graph parsers. The result are recursive descent parsers as known from string parsing with some additional nondeterminism

Probabilistic regular graphs

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Parallel Communicating String - Graph P System

The concept of parallel communicating grammar systems generating string languages is extended to string-graph P systems and their generative power is studied. It is also established that for every language L generated by a parallel communicating grammar system there exists an equivalent parallel communicating string-graph P system generating the string-graph language corresponding to L

From Double Pushout Grammars to Hypergraph Lambek Grammars With and Without Exponential Modality

We study how to relate well-known hypergraph grammars based on the double pushout (DPO) approach and grammars over the hypergraph Lambek calculus HL (called HL-grammars). It turns out that DPO rules can be naturally encoded by types of HL using methods similar to those used by Kanazawa for multiplicative-exponential linear logic. In order to generalize his reasonings we extend the hypergraph Lambek calculus by adding the exponential modality, which results in a new calculus HMEL0; then we prove that any DPO grammar can be converted into an equivalent HMEL0-grammar. We also define the conjunctive Kleene star, which behaves similarly to this exponential modality, and establish a similar result. If we add neither the exponential modality nor the conjunctive Kleene star to HL, then we can still use the same encoding and show that any DPO grammar with a linear restriction on the length of derivations can be converted into an equivalent HL-grammar.Comment: In Proceedings TERMGRAPH 2022, arXiv:2303.1421