{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T19:56:47Z","timestamp":1743105407350,"version":"3.40.3"},"publisher-location":"Cham","reference-count":36,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030500856"},{"type":"electronic","value":"9783030500863"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-50086-3_9","type":"book-chapter","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T12:03:09Z","timestamp":1591704189000},"page":"150-168","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Probabilistic Timed Automata with One Clock and Initialised Clock-Dependent Probabilities"],"prefix":"10.1007","author":[{"given":"Jeremy","family":"Sproston","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,8]]},"reference":[{"key":"9_CR1","unstructured":"Akshay, S., Bouyer, P., Krishna, S.N., Manasa, L., Trivedi, A.: Stochastic timed games revisited. In: Faliszewski, P., Muscholl, A., Niedermeier, R., (eds.) Proceedings of MFCS 2016 LIPIcs, vol. 58, pp. 8:1\u20138:14. Leibniz-Zentrum f\u00fcr Informatik (2016)"},{"issue":"2","key":"9_CR2","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0304-3975(94)90010-8","volume":"126","author":"R Alur","year":"1994","unstructured":"Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183\u2013235 (1994)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR3","volume-title":"Principles of Model Checking","author":"C Baier","year":"2008","unstructured":"Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)"},{"key":"9_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/978-3-030-18744-6_4","volume-title":"Reliability, Safety, and Security of Railway Systems. Modelling, Analysis, Verification, and Certification","author":"N Bertrand","year":"2019","unstructured":"Bertrand, N., Bordais, B., H\u00e9lou\u00ebt, L., Mari, T., Parreaux, J., Sankur, O.: Performance evaluation of metro regulations using probabilistic model-checking. In: Collart-Dutilleul, S., Lecomte, T., Romanovsky, A. (eds.) RSSRail 2019. LNCS, vol. 11495, pp. 59\u201376. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-18744-6_4"},{"issue":"4","key":"9_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2168\/LMCS-10(4:6)2014","volume":"10","author":"N Bertrand","year":"2014","unstructured":"Bertrand, N., et al.: Stochastic timed automata. Log. Methods Comput. Sci. 10(4), 1\u201373 (2014)","journal-title":"Log. Methods Comput. Sci."},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/978-3-319-10696-0_25","volume-title":"Quantitative Evaluation of Systems","author":"N Bertrand","year":"2014","unstructured":"Bertrand, N., Brihaye, T., Genest, B.: Deciding the value 1 problem for reachability in 1-clock decision stochastic timed automata. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 313\u2013328. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-10696-0_25"},{"key":"9_CR7","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/978-3-319-10575-8_29","volume-title":"Handbook of Model Checking","author":"P Bouyer","year":"2018","unstructured":"Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Ouaknine, J., Worrell, J.: Model checking real-time systems. In: Clarke, E.M., Henzinger, T.A., Veith, H., Bloem, R. (eds.) Handbook of Model Checking, pp. 1001\u20131046. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-10575-8_29"},{"issue":"2","key":"9_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2168\/LMCS-4(2:9)2008","volume":"4","author":"P Bouyer","year":"2008","unstructured":"Bouyer, P., Larsen, K.G., Markey, N.: Model checking one-clock priced timed automata. Log. Methods Comput. Sci. 4(2), 1\u201328 (2008)","journal-title":"Log. Methods Comput. Sci."},{"key":"9_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1007\/978-3-319-18579-8_3","volume-title":"Analytical and Stochastic Modelling Techniques and Applications","author":"S Chakraborty","year":"2015","unstructured":"Chakraborty, S., Katoen, J.-P.: Model checking of open interval markov chains. In: Gribaudo, M., Manini, D., Remke, A. (eds.) ASMTA 2015. LNCS, vol. 9081, pp. 30\u201342. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-18579-8_3"},{"key":"9_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-540-78499-9_22","volume-title":"Foundations of Software Science and Computational Structures","author":"K Chatterjee","year":"2008","unstructured":"Chatterjee, K., Sen, K., Henzinger, T.A.: Model-checking $$\\omega $$-regular properties of interval Markov chains. In: Amadio, R. (ed.) FoSSaCS 2008. LNCS, vol. 4962, pp. 302\u2013317. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-78499-9_22"},{"issue":"7","key":"9_CR11","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.ipl.2013.01.004","volume":"113","author":"T Chen","year":"2013","unstructured":"Chen, T., Han, T., Kwiatkowska, M.: On the complexity of model checking interval-valued discrete time Markov chains. Inf. Process. Lett. 113(7), 210\u2013216 (2013)","journal-title":"Inf. Process. Lett."},{"key":"9_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044450813-3\/50026-6","volume-title":"Model Checking","author":"EM Clarke","year":"2001","unstructured":"Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2001)"},{"issue":"2","key":"9_CR13","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1109\/TASE.2016.2530623","volume":"13","author":"L Feng","year":"2016","unstructured":"Feng, L., Wiltsche, C., Humphrey, L.R., Topcu, U.: Synthesis of human-in-the-loop control protocols for autonomous systems. IEEE Trans. Autom. Sci. Eng. 13(2), 450\u2013462 (2016)","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"9_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/978-3-642-21455-4_3","volume-title":"Formal Methods for Eternal Networked Software Systems","author":"V Forejt","year":"2011","unstructured":"Forejt, V., Kwiatkowska, M., Norman, G., Parker, D.: Automated verification techniques for probabilistic systems. In: Bernardo, M., Issarny, V. (eds.) SFM 2011. LNCS, vol. 6659, pp. 53\u2013113. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-21455-4_3"},{"issue":"1\u20132","key":"9_CR15","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/S0004-3702(00)00047-3","volume":"122","author":"R Givan","year":"2000","unstructured":"Givan, R., Leach, S.M., Dean, T.L.: Bounded-parameter Markov decision processes. Artif. Intell. 122(1\u20132), 71\u2013109 (2000)","journal-title":"Artif. Intell."},{"key":"9_CR16","unstructured":"Gregersen, H., Jensen, H.E.: Formal design of reliable real time systems. Master\u2019s thesis, Department of Mathematics and Computer Science, Aalborg University (1995)"},{"key":"9_CR17","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.tcs.2016.12.003","volume":"735","author":"S Haddad","year":"2018","unstructured":"Haddad, S., Monmege, B.: Interval iteration algorithm for MDPs and IMDPs. Theor. Comput. Sci. 735, 111\u2013131 (2018)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR18","unstructured":"Hahn, E.M.: Model checking stochastic hybrid systems. Ph.D., thesis, Universit\u00e4t des Saarlandes (2013)"},{"key":"9_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/978-3-642-20398-5_12","volume-title":"NASA Formal Methods","author":"EM Hahn","year":"2011","unstructured":"Hahn, E.M., Han, T., Zhang, L.: Synthesis for PCTL in parametric Markov decision processes. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 146\u2013161. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-20398-5_12"},{"key":"9_CR20","doi-asserted-by":"crossref","unstructured":"Hashemi, V., Hatefi, H., Krc\u00e1l, J.: Probabilistic bisimulations for PCTL model checking of interval MDPs. In: Andr\u00e9, \u00c9., Frehse, G., (eds.) Proceedings of SynCoP 2014 EPTCS, vol. 145, pp. 19\u201333 (2014)","DOI":"10.4204\/EPTCS.145.4"},{"issue":"1","key":"9_CR21","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1006\/jcss.1998.1581","volume":"57","author":"TA Henzinger","year":"1998","unstructured":"Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What\u2019s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94\u2013124 (1998)","journal-title":"J. Comput. Syst. Sci."},{"key":"9_CR22","unstructured":"Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Proceedings of LICS 1991, pp. 266\u2013277. IEEE Computer Society (1991)"},{"issue":"3","key":"9_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2168\/LMCS-4(3:12)2008","volume":"4","author":"M Jurdzi\u0144ski","year":"2008","unstructured":"Jurdzi\u0144ski, M., Laroussinie, F., Sproston, J.: Model checking probabilistic timed automata with one or two clocks. Log. Methods Comput. Sci. 4(3), 1\u201328 (2008)","journal-title":"Log. Methods Comput. Sci."},{"issue":"2","key":"9_CR24","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1023\/A:1014745904458","volume":"8","author":"IO Kozine","year":"2002","unstructured":"Kozine, I.O., Utkin, L.V.: Interval-valued finite Markov chains. Reliab. Comput. 8(2), 97\u2013113 (2002)","journal-title":"Reliab. Comput."},{"key":"9_CR25","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/S0304-3975(01)00046-9","volume":"286","author":"M Kwiatkowska","year":"2002","unstructured":"Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 286, 101\u2013150 (2002)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/978-3-540-28644-8_25","volume-title":"CONCUR 2004 - Concurrency Theory","author":"F Laroussinie","year":"2004","unstructured":"Laroussinie, F., Markey, N., Schnoebelen, P.: Model checking timed automata with one or two clocks. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 387\u2013401. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-28644-8_25"},{"issue":"5","key":"9_CR27","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1287\/opre.1050.0216","volume":"53","author":"A Nilim","year":"2005","unstructured":"Nilim, A., El Ghaoui, L.: Robust control of Markov decision processes with uncertain transition matrices. Oper. Res. 53(5), 780\u2013798 (2005)","journal-title":"Oper. Res."},{"issue":"2","key":"9_CR28","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1007\/s10703-012-0177-x","volume":"43","author":"G Norman","year":"2013","unstructured":"Norman, G., Parker, D., Sproston, J.: Model checking for probabilistic timed automata. Form. Methods Syst. Des. 43(2), 164\u2013190 (2013)","journal-title":"Form. Methods Syst. Des."},{"issue":"3","key":"9_CR29","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1287\/moor.12.3.441","volume":"12","author":"CH Papadimitriou","year":"1987","unstructured":"Papadimitriou, C.H., Tsitsiklis, J.N.: The complexity of Markov decision processes. Math. Oper. Res. 12(3), 441\u2013450 (1987)","journal-title":"Math. Oper. Res."},{"key":"9_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/978-3-642-39799-8_35","volume-title":"Computer Aided Verification","author":"A Puggelli","year":"2013","unstructured":"Puggelli, A., Li, W., Sangiovanni-Vincentelli, A.L., Seshia, S.A.: Polynomial-time verification of PCTL properties of MDPs with convex uncertainties. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 527\u2013542. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39799-8_35"},{"key":"9_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1007\/11691372_26","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"K Sen","year":"2006","unstructured":"Sen, K., Viswanathan, M., Agha, G.: Model-checking markov chains in the presence of uncertainties. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 394\u2013410. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11691372_26"},{"key":"9_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1007\/978-3-319-67089-8_11","volume-title":"Reachability Problems","author":"J Sproston","year":"2017","unstructured":"Sproston, J.: Probabilistic timed automata with clock-dependent probabilities. In: Hague, M., Potapov, I. (eds.) RP 2017. LNCS, vol. 10506, pp. 144\u2013159. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-67089-8_11"},{"key":"9_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/978-3-030-00250-3_11","volume-title":"Reachability Problems","author":"J Sproston","year":"2018","unstructured":"Sproston, J.: Qualitative reachability for open interval Markov chains. In: Potapov, I., Reynier, P.-A. (eds.) RP 2018. LNCS, vol. 11123, pp. 146\u2013160. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-00250-3_11"},{"key":"9_CR34","doi-asserted-by":"crossref","unstructured":"Sproston, J.: Probabilistic timed automata with one clock and initialised clock-dependent probabilities. CoRR (2020)","DOI":"10.46298\/lmcs-17(4:6)2021"},{"key":"9_CR35","unstructured":"Winkler, T., Junges, S., P\u00e9rez, G.A., Katoen, J.: On the complexity of reachability in parametric Markov decision processes. In: Fokkink, W., van Glabbeek, R. (eds.) Proceedings of CONCUR 2019 LIPIcs, vol. 140, pp. 14:1\u201314:17. Leibniz-Zentrum f\u00fcr Informatik (2019)"},{"issue":"8\u20139","key":"9_CR36","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1016\/j.artint.2007.12.002","volume":"172","author":"D Wu","year":"2008","unstructured":"Wu, D., Koutsoukos, X.D.: Reachability analysis of uncertain systems using bounded-parameter Markov decision processes. Artif. Intell. 172(8\u20139), 945\u2013954 (2008)","journal-title":"Artif. Intell."}],"container-title":["Lecture Notes in Computer Science","Formal Techniques for Distributed Objects, Components, and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-50086-3_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T23:02:14Z","timestamp":1717887734000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-50086-3_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030500856","9783030500863"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-50086-3_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"8 June 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FORTE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Formal Techniques for Distributed Objects, Components, and Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Valletta","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Malta","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 June 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 June 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"40","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"forte2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.discotec.org\/2020\/forte","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"25","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"10","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"40% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held virtually due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}