Reachability in timed automata with diagonal constraints
Abstract
We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in the form of a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test "is-Z-simulated-by-Z' ?" which ascertains that zone Z does not reach more states than zone Z', and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. In this paper, we propose a simulation relation LU-d for timed automata with diagonal constraints. On the negative side, we show that deciding Z-is-not-LU-d-simulated-by-Z' is NP-complete. On the positive side, we identify a witness for non-simulation and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.11007
- arXiv:
- arXiv:1806.11007
- Bibcode:
- 2018arXiv180611007G
- Keywords:
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- Computer Science - Logic in Computer Science;
- 68Q60
- E-Print:
- Shorter version of this article appears in CONCUR 2018