### Abstract

We present an algebra of discrete timed input/output automata that may execute in the context of different clock granularities - which we call timed machines; this algebra includes a refinement operator through which a machine can be extended with new states and transitions in order to accommodate a finer clock granularity as required to interoperate with other machines, and an extension of the traditional product of timed input-output automata to the situation in which the granularities of the two machines are not the same. Over this algebra, we then define an algebra of networks of timed machines that includes operations through which networks can be modified at run time, thus offering a model for systems of interconnected components that can dynamically bind to other systems and, therefore, cannot be adjusted at design time to ensure that they operate in a timed homogeneous setting. We investigate important properties of timed machines such as consistency - in the sense that a machine can be ensured to generate a non-empty language, and feasibility - in the sense that a machine can be ensured to generate a non-empty language no matter what inputs it receives, and propose techniques for checking if timed machines are consistent or are feasible. We generalise those properties to networks of timed machines, and investigate how consistency and feasibility of networks can be proved through properties that can be checked at design time without having to compute, at run time, the product of the machines that operate on those networks, which would not be practical.

Original language | English |
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Pages (from-to) | 800-855 |

Number of pages | 56 |

Journal | Mathematical Structures in Computer Science |

Volume | 28 |

Issue number | 6 |

Early online date | 24 May 2017 |

DOIs | |

Publication status | Published - Jun 2018 |

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## Cite this

*Mathematical Structures in Computer Science*,

*28*(6), 800-855. https://doi.org/10.1017/S0960129517000135