## Abstract

Modal and mixed transition systems are specification formalisms that allow the mixing of over- and under-approximation. We discuss three fundamental decision problems for such specifications:

— whether a set of specifications has a common implementation;

— whether an individual specification has an implementation; and

— whether all implementations of an individual specification are implementations of another one.

For each of these decision problems we investigate the worst-case computational complexity for the modal and mixed cases. We show that the first decision problem is EXPTIME-complete for both modal and mixed specifications. We prove that the second decision problem is EXPTIME-complete for mixed specifications (it is known to be trivial for modal ones). The third decision problem is also shown to be EXPTIME-complete for mixed specifications.

— whether a set of specifications has a common implementation;

— whether an individual specification has an implementation; and

— whether all implementations of an individual specification are implementations of another one.

For each of these decision problems we investigate the worst-case computational complexity for the modal and mixed cases. We show that the first decision problem is EXPTIME-complete for both modal and mixed specifications. We prove that the second decision problem is EXPTIME-complete for mixed specifications (it is known to be trivial for modal ones). The third decision problem is also shown to be EXPTIME-complete for mixed specifications.

Originalsprog | Engelsk |
---|---|

Tidsskrift | Mathematical Structures in Computer Science |

Vol/bind | 20 |

Sider (fra-til) | 75-103 |

ISSN | 0960-1295 |

Status | Udgivet - 2010 |

## Emneord

- Modal Transition Systems
- Mixed Transition Systems
- Specification Formalisms
- EXPTIME-complete
- Decision Problems