What's decidable about hybrid automata?

T.A. Henzinger, P. Kopke, A. Puri, P. Varaiya, in:, ACM, 1995, pp. 373–382.

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Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify the precise boundary between decidability and undecidability of the reachability problem for hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical significance for verification, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular automata. The translation also preserves the omega-languages of initialized rectangular automata with bounded nondeterminism. On the negative side, we show that several slight generalizations of initialized rectangular automata lead to an undecidable reachability problem. In particular, we prove that the reachability problem is undecidable for timed automata augmented with a single stopwatch.
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Date Published
1995-01-01
Page
373 - 382
Conference
STOC: Symposium on the Theory of Computing
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Henzinger TA, Kopke P, Puri A, Varaiya P. What’s decidable about hybrid automata? In: ACM; 1995:373-382. doi:10.1145/225058.225162
Henzinger, T. A., Kopke, P., Puri, A., & Varaiya, P. (1995). What’s decidable about hybrid automata? (pp. 373–382). Presented at the STOC: Symposium on the Theory of Computing, ACM. https://doi.org/10.1145/225058.225162
Henzinger, Thomas A, Peter Kopke, Anuj Puri, and P. Varaiya. “What’s Decidable about Hybrid Automata?,” 373–82. ACM, 1995. https://doi.org/10.1145/225058.225162.
T. A. Henzinger, P. Kopke, A. Puri, and P. Varaiya, “What’s decidable about hybrid automata?,” presented at the STOC: Symposium on the Theory of Computing, 1995, pp. 373–382.
Henzinger TA, Kopke P, Puri A, Varaiya P. 1995. What’s decidable about hybrid automata? STOC: Symposium on the Theory of Computing 373–382.
Henzinger, Thomas A., et al. What’s Decidable about Hybrid Automata? ACM, 1995, pp. 373–82, doi:10.1145/225058.225162.

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