State Digrams in UML: A Formal Senmatics using Graph Transformations

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State Digrams in UMLA Formal Senmatics using
Graph Transformations

• Xiyao Yin

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Overview

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

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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

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UML State Diagrams
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UML State Diagrams
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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

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Deriving Graphs
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Deriving Graphs
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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

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Transitions to Nested States
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Transitions to Nested States
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Transitions to Nested States
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Transitions to Nested States
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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.

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Thank you!