# Specifying Graph Languages with Type Graphs

## TL;DR

This paper explores formal methods for defining graph languages using type graphs, including logic and annotations, analyzing their decidability and closure properties to advance graph specification techniques.

## Contribution

It introduces three novel formalisms for specifying graph languages with type graphs, extending the basic approach with logic and annotations, and analyzes their theoretical properties.

## Key findings

- Decidability results for each formalism
- Closure properties of the graph language classes
- Relationships between restriction graphs and type graphs

## Abstract

We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped homomorphically to a given type graph. In this context, we also study languages specified by restriction graphs and their relation to type graphs. Second, we extend this basic approach to a type graph logic and, third, to type graphs with annotations. We present decidability results and closure properties for each of the formalisms.