### Abstract

Random graphs have the property that they are very predictable. Even by exploring a small part reliable observations are possible regarding their structure and size. An unfortunate observation is that standard models for random graphs, such as the Erdös-Rényi model, do not reflect the structure of the graphs that describe distributed systems and protocols. In this paper we propose to use the parallel composition of such random graphs to model ‘real’ state spaces. We show how we can use this structure to predict the size of state spaces, and we can use it to explain that software bugs are in practice far easier to find than predicted by the standard random graph models. By some practical experiments we show that our new random model is an improvement over the standard model in predicting properties of transition systems representing realistic systems.
Keywords: Random graph, P-parallel random transition system, state space size

Original language | English |
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Title of host publication | 14th International Workshop on Automated Verification of Critical Systems (AVOCS14, Enschede, The Netherlands, September 24-26, 2014. Pre-proceedings) |

Editors | M. Huisman, J.C. Pol, van de |

Publisher | CTIT |

Pages | 141-156 |

Publication status | Published - 2014 |

Event | 14th International Workshop on Automated Verification of Critical Systems (AVoCS 2014) - University of Twente, Enschede, Netherlands Duration: 24 Sep 2014 → 26 Sep 2014 Conference number: 14 |

### Publication series

Name | CTIT Workshop Proceedings Series |
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Volume | WP 14-01 |

ISSN (Print) | 1574-0846 |

### Conference

Conference | 14th International Workshop on Automated Verification of Critical Systems (AVoCS 2014) |
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Abbreviated title | AVoCS 2014 |

Country | Netherlands |

City | Enschede |

Period | 24/09/14 → 26/09/14 |

Other | 14th International Workshop on Automated Verification of Critical Systems |

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## Cite this

Groote, J. F., van der Hofstad, R. W., & Raffelsieper, M. (2014). On the random structure of behavioural transition systems. In M. Huisman, & J. C. Pol, van de (Eds.),

*14th International Workshop on Automated Verification of Critical Systems (AVOCS14, Enschede, The Netherlands, September 24-26, 2014. Pre-proceedings)*(pp. 141-156). (CTIT Workshop Proceedings Series; Vol. WP 14-01). CTIT.