{"acknowledgement":"This research was supported in part by the Office of Naval Research Young Investigator Award N00014-95-1-0520, by the National Science Foundation CAREER award CCR-9501708, by the National Science Foundation Grant CCR-9504469, by the Air Force Office of Scientific Research Contract F49620-93-1-0056, by the Army Research Office MURI Grant DAAH-04-96-1-0341, by the Army Research Office Contract DAAH-04-94-G-0026, by the Defense Advanced Research Projects Agency Grant NAG2-892, and by the California PATH program.","quality_controlled":"1","publist_id":"237","language":[{"iso":"eng"}],"title":"What's decidable about hybrid automata?","oa_version":"Published Version","publication":"Journal of Computer and System Sciences","day":"01","month":"01","issue":"1","publisher":"Elsevier","doi":"10.1006/jcss.1998.1581","year":"1998","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_published":"1998-01-01T00:00:00Z","abstract":[{"text":"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 a boundary between decidability and undecidability for the reachability problem of 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 independent 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 theω-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.","lang":"eng"}],"date_created":"2018-12-11T12:09:08Z","date_updated":"2022-08-23T14:29:15Z","type":"journal_article","oa":1,"citation":{"mla":"Henzinger, Thomas A., et al. “What’s Decidable about Hybrid Automata?” <i>Journal of Computer and System Sciences</i>, vol. 57, no. 1, Elsevier, 1998, pp. 94–124, doi:<a href=\"https://doi.org/10.1006/jcss.1998.1581\">10.1006/jcss.1998.1581</a>.","short":"T.A. Henzinger, P. Kopke, A. Puri, P. Varaiya, Journal of Computer and System Sciences 57 (1998) 94–124.","ama":"Henzinger TA, Kopke P, Puri A, Varaiya P. What’s decidable about hybrid automata? <i>Journal of Computer and System Sciences</i>. 1998;57(1):94-124. doi:<a href=\"https://doi.org/10.1006/jcss.1998.1581\">10.1006/jcss.1998.1581</a>","chicago":"Henzinger, Thomas A, Peter Kopke, Anuj Puri, and P. Varaiya. “What’s Decidable about Hybrid Automata?” <i>Journal of Computer and System Sciences</i>. Elsevier, 1998. <a href=\"https://doi.org/10.1006/jcss.1998.1581\">https://doi.org/10.1006/jcss.1998.1581</a>.","ieee":"T. A. Henzinger, P. Kopke, A. Puri, and P. Varaiya, “What’s decidable about hybrid automata?,” <i>Journal of Computer and System Sciences</i>, vol. 57, no. 1. Elsevier, pp. 94–124, 1998.","apa":"Henzinger, T. A., Kopke, P., Puri, A., &#38; Varaiya, P. (1998). What’s decidable about hybrid automata? <i>Journal of Computer and System Sciences</i>. Elsevier. <a href=\"https://doi.org/10.1006/jcss.1998.1581\">https://doi.org/10.1006/jcss.1998.1581</a>","ista":"Henzinger TA, Kopke P, Puri A, Varaiya P. 1998. What’s decidable about hybrid automata? Journal of Computer and System Sciences. 57(1), 94–124."},"_id":"4492","publication_identifier":{"isbn":["0022-0000"]},"volume":57,"intvolume":"        57","page":"94 - 124","article_processing_charge":"No","author":[{"last_name":"Henzinger","first_name":"Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Henzinger, Thomas A","orcid":"0000−0002−2985−7724"},{"full_name":"Kopke, Peter","last_name":"Kopke","first_name":"Peter"},{"last_name":"Puri","first_name":"Anuj","full_name":"Puri, Anuj"},{"full_name":"Varaiya, P.","last_name":"Varaiya","first_name":"P."}],"publication_status":"published","article_type":"original","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0022000098915811","open_access":"1"}],"extern":"1","status":"public"}