### Abstract

The spider diagram logic forms a fragment of constraint diagram logic and is designed to be primarily used as a diagrammatic software specification tool. Our interest is in using the logical basis of spider diagrams and the existing known equivalences between certain logics, formal language theory classes and some automata to inform the development of diagrammatic logic. Such developments could have many advantages, one of which would be aiding software engineers who are familiar with formal languages and automata to more intuitively understand diagrammatic logics. In this paper we consider relationships between spider diagrams of order (an extension of spider diagrams) and the star-free subset of regular languages. We extend the concept of the language of a spider diagram to encompass languages over arbitrary alphabets. Furthermore, the product of spider diagrams is introduced. This operator is the diagrammatic analogue of language concatenation.We establish that star-free languages are denable by spider diagrams of order equipped with the product operator and, based on this relationship, spider diagrams of order are as expressive as rst order monadic logic of order.

Original language | English |
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Title of host publication | Proceedings of the 5th international conference on the theory and application of diagrams |

Place of Publication | Berlin Heidelberg |

Publisher | Springer-Verlag |

Pages | 172-187 |

Number of pages | 16 |

Volume | 5223 |

ISBN (Electronic) | 9783540877301 |

ISBN (Print) | 9783540877295 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

Event | Proceedings of the 5th international conference on the theory and application of diagrams - Herrsching, Germany, 19-21 September, 2008 Duration: 1 Jan 2008 → … |

### Publication series

Name | Lecture Notes in Computer Science |
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### Conference

Conference | Proceedings of the 5th international conference on the theory and application of diagrams |
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Period | 1/01/08 → … |

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## Cite this

Delaney, A., Taylor, J., & Thompson, S. (2008). Spider diagrams of order and a hierarchy of star-free regular languages. In

*Proceedings of the 5th international conference on the theory and application of diagrams*(Vol. 5223, pp. 172-187). (Lecture Notes in Computer Science). Springer-Verlag. https://doi.org/10.1007/978-3-540-87730-1_18