Checking Thorough Refinement on Modal Transition Systems Is EXPTIME-Complete
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Proceedings |
| Conference | Theoretical Aspects of Computing - ICTAC 2009, 6th International Colloquium, Kuala Lumpur, Malaysia, August 16-20, 2009. Proceedings |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-642-03466-4_7 |
| Field | Informatics |
| Keywords | compositional verification; modal transition systems; refinement |
| Attached files | |
| Description | Modal transition systems (MTS), a specification formalism introduced more than 20 years ago, has recently received a considerable attention in several different areas. Many of the fundamental questions related to MTSs have already been answered. However, the problem of the exact computational complexity of thorough refinement checking between two finite MTSs remained unsolved and was repeatedly stated as an open problem. We settle down this question by showing EXPTIME-completeness of thorough refinement checking on finite MTSs. The upper-bound result relies on a novel algorithm running in single exponential time providing a direct goal-oriented way to decide thorough refinement. If the right-hand side MTS is moreover deterministic, or has a fixed size, the running time of the algorithm becomes polynomial. The lower-bound proof is achieved by reduction from the acceptance problem of alternating linear bounded automata and the problem remains EXPTIME-hard even if the left-hand side MTS is fixed. |
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