1. State Digrams in UML: A Formal Senmatics using Graph Transformations
Xiyao Yin

2. Overview Introduction of UML Features of UML State Diagrams
Process of Deriving Graphs
Graph Transformation Systems
Transitions to Nested States
Conclusion

3. Introduction
The Unified Modeling Language (UML) is a general-purpose visual modeling language that is designed to specify, visualize, construct and document the artifacts of software systems.
Description of UML diagrams:
abstract syntax
well-formedness rules for the abstract syntax
semantics

4. UML State Diagrams

5. UML State Diagrams

6. Deriving Graphs
The process of state expansion in nested state diagrams is explained by graph transformations in three steps:
(1) adding boundary nodes introducing a precise interface for the state to be expanded
(2) expanding the state
(3) removing the boundary nodes

7. Deriving Graphs

8. Deriving Graphs

9. Graph Transformation Systems
Definition Let C = (CA, CN ) be a pair of color alphabets.
A C-colored graph G is a six-tuple (GA, GN, s, t, mA, mN ), consisting of:
1. sets GA and GN , called the set of arcs and the set of nodes;
2. source and target mappings s: GA →GN ; t : GA→GN;
3. arcs and nodes coloring mappings mA : GA→CA ; mN : GN→CN

10. Transitions to Nested States

11. Transitions to Nested States

12. Transitions to Nested States

13. Transitions to Nested States

14. Conclusion
The general idea of the overall approach is to rewrite UML diagrams to canonical graph representation. We achieve a normal form for nested UML state diagrams by means of graph transformations.
The main advantage of the graph transformation approach is the closeness between the mathematical graph representation and the UML diagram representation.
This approach is applicable to other forms of UML diagrams as well.

15. Thank you!