{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T04:06:38Z","timestamp":1746158798216,"version":"3.40.4"},"publisher-location":"Berlin, Heidelberg","reference-count":39,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642540127"},{"type":"electronic","value":"9783642540134"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-642-54013-4_6","type":"book-chapter","created":{"date-parts":[[2014,1,3]],"date-time":"2014-01-03T01:08:09Z","timestamp":1388711289000},"page":"98-117","source":"Crossref","is-referenced-by-count":4,"title":["Bisimulations and Logical Characterizations on Continuous-Time Markov Decision Processes"],"prefix":"10.1007","author":[{"given":"Lei","family":"Song","sequence":"first","affiliation":[]},{"given":"Lijun","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Jens Chr.","family":"Godskesen","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"1","key":"6_CR1","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1145\/174644.174651","volume":"41","author":"R. Alur","year":"1994","unstructured":"Alur, R., Henzinger, T.A.: A really temporal logic. J. ACM\u00a041(1), 181\u2013203 (1994)","journal-title":"J. ACM"},{"key":"6_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/3-540-61474-5_75","volume-title":"Computer Aided Verification","author":"A. Aziz","year":"1996","unstructured":"Aziz, A., Sanwal, K., Singhal, V., Brayton, R.K.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol.\u00a01102, pp. 269\u2013276. Springer, Heidelberg (1996)"},{"key":"6_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/3-540-60045-0_48","volume-title":"Computer Aided Verification","author":"A. Aziz","year":"1995","unstructured":"Aziz, A., Singhal, V., Balarin, F., Brayton, R.K., Sangiovanni-Vincentelli, A.L.: It usually works: The temporal logic of stochastic systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol.\u00a0939, pp. 155\u2013165. Springer, Heidelberg (1995)"},{"issue":"6","key":"6_CR4","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1109\/TSE.2003.1205180","volume":"29","author":"C. Baier","year":"2003","unstructured":"Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng.\u00a029(6), 524\u2013541 (2003)","journal-title":"IEEE Trans. Softw. Eng."},{"issue":"1","key":"6_CR5","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.tcs.2005.07.022","volume":"345","author":"C. Baier","year":"2005","unstructured":"Baier, C., Hermanns, H., Katoen, J.-P., Haverkort, B.R.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time Markov decision processes. Theor. Comput. Sci.\u00a0345(1), 2\u201326 (2005)","journal-title":"Theor. Comput. Sci."},{"issue":"2","key":"6_CR6","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.ic.2005.03.001","volume":"200","author":"C. Baier","year":"2005","unstructured":"Baier, C., Katoen, J.-P., Hermanns, H., Wolf, V.: Comparative branching-time semantics for Markov chains. Inf. Comput.\u00a0200(2), 149\u2013214 (2005)","journal-title":"Inf. Comput."},{"key":"6_CR7","doi-asserted-by":"crossref","unstructured":"B\u00f6de, E., Herbstritt, M., Hermanns, H., Johr, S., Peikenkamp, T., Pulungan, R., Wimmer, R., Becker, B.: Compositional performability evaluation for STATEMATE. In: QEST, pp. 167\u2013178. IEEE (2006)","DOI":"10.1109\/QEST.2006.10"},{"key":"6_CR8","doi-asserted-by":"crossref","unstructured":"Bouyer, P., Markey, N., Ouaknine, J., Worrell, J.: The cost of punctuality. In: LICS, pp. 109\u2013120. IEEE (2007)","DOI":"10.1109\/LICS.2007.49"},{"issue":"1-2","key":"6_CR9","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/0304-3975(88)90098-9","volume":"59","author":"M.C. Browne","year":"1988","unstructured":"Browne, M.C., Clarke, E.M., Gr\u00fcmberg, O.: Characterizing finite Kripke structures in propositional temporal logic. Theor. Comput. Sci.\u00a059(1-2), 115\u2013131 (1988)","journal-title":"Theor. Comput. Sci."},{"issue":"1","key":"6_CR10","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1145\/322234.322242","volume":"28","author":"J. Bruno","year":"1981","unstructured":"Bruno, J., Downey, P., Frederickson, G.N.: Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J. ACM\u00a028(1), 100\u2013113 (1981)","journal-title":"J. ACM"},{"key":"6_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/978-3-642-22110-1_19","volume-title":"Computer Aided Verification","author":"P. Buchholz","year":"2011","unstructured":"Buchholz, P., Hahn, E.M., Hermanns, H., Zhang, L.: Model checking algorithms for CTMDPs. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol.\u00a06806, pp. 225\u2013242. Springer, Heidelberg (2011)"},{"issue":"3","key":"6_CR12","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/j.cor.2010.08.011","volume":"38","author":"P. Buchholz","year":"2011","unstructured":"Buchholz, P., Schulz, I.: Numerical analysis of continuous time Markov decision processes over finite horizons. Computers & Operations Research\u00a038(3), 651\u2013659 (2011)","journal-title":"Computers & Operations Research"},{"key":"6_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1007\/978-3-642-24310-3_4","volume-title":"Formal Modeling and Analysis of Timed Systems","author":"T. Chen","year":"2011","unstructured":"Chen, T., Diciolla, M., Kwiatkowska, M., Mereacre, A.: Time-bounded verification of CTMCs against real-time specifications. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol.\u00a06919, pp. 26\u201342. Springer, Heidelberg (2011)"},{"key":"6_CR14","doi-asserted-by":"crossref","unstructured":"D\u2019Argenio, P.R., Wolovick, N., Terraf, P.S., Celayes, P.: Nondeterministic labeled Markov processes: Bisimulations and logical characterization. In: QEST, pp. 11\u201320. IEEE (2009)","DOI":"10.1109\/QEST.2009.17"},{"issue":"3","key":"6_CR15","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.tcs.2003.09.013","volume":"318","author":"J. Desharnais","year":"2004","unstructured":"Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov processes. Theor. Comput. Sci.\u00a0318(3), 323\u2013354 (2004)","journal-title":"Theor. Comput. Sci."},{"issue":"2","key":"6_CR16","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.ic.2009.11.002","volume":"208","author":"J. Desharnais","year":"2010","unstructured":"Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Weak bisimulation is sound and complete for pCTL*. Inf. Comput.\u00a0208(2), 203\u2013219 (2010)","journal-title":"Inf. Comput."},{"issue":"1-2","key":"6_CR17","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/S1567-8326(02)00068-1","volume":"56","author":"J. Desharnais","year":"2003","unstructured":"Desharnais, J., Panangaden, P.: Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes. J. Log. Algebr. Program.\u00a056(1-2), 99\u2013115 (2003)","journal-title":"J. Log. Algebr. Program."},{"issue":"5","key":"6_CR18","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1007\/BF01211866","volume":"6","author":"H. Hansson","year":"1994","unstructured":"Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing\u00a06(5), 512\u2013535 (1994)","journal-title":"Formal Aspects of Computing"},{"key":"6_CR19","doi-asserted-by":"crossref","unstructured":"Haverkort, B.R., Hermanns, H., Katoen, J.-P.: On the use of model checking techniques for dependability evaluation. In: SRDS, pp. 228\u2013237 (2000)","DOI":"10.1109\/RELDI.2000.885410"},{"issue":"2","key":"6_CR20","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.ic.2010.11.024","volume":"209","author":"H. Hermanns","year":"2011","unstructured":"Hermanns, H., Parma, A., Segala, R., Wachter, B., Zhang, L.: Probabilistic logical characterization. Inf. Comput.\u00a0209(2), 154\u2013172 (2011)","journal-title":"Inf. Comput."},{"key":"6_CR21","doi-asserted-by":"crossref","unstructured":"Jenkins, M., Ouaknine, J., Rabinovich, A., Worrell, J.: Alternating timed automata over bounded time. In: LICS, pp. 60\u201369. IEEE (2010)","DOI":"10.1109\/LICS.2010.45"},{"key":"6_CR22","doi-asserted-by":"crossref","unstructured":"Jonsson, B., Larsen, K., Wang, Y.: Probabilistic extensions of process algebras. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 685\u2013710. Elsevier (2001)","DOI":"10.1016\/B978-044482830-9\/50029-1"},{"key":"6_CR23","doi-asserted-by":"crossref","unstructured":"Katoen, J.-P., Zapreev, I.S., Hahn, E.M., Hermanns, H., Jansen, D.N.: The ins and outs of the probabilistic model checker MRMC. In: QEST, pp. 167\u2013176 (2009)","DOI":"10.1109\/QEST.2009.11"},{"issue":"4","key":"6_CR24","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/BF01995674","volume":"2","author":"R. Koymans","year":"1990","unstructured":"Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst.\u00a02(4), 255\u2013299 (1990)","journal-title":"Real-Time Syst."},{"key":"6_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1007\/978-3-642-22110-1_47","volume-title":"Computer Aided Verification","author":"M. Kwiatkowska","year":"2011","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol.\u00a06806, pp. 585\u2013591. Springer, Heidelberg (2011)"},{"key":"6_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1007\/978-3-540-74407-8_28","volume-title":"CONCUR 2007 \u2013 Concurrency Theory","author":"M.R. Neuh\u00e4u\u00dfer","year":"2007","unstructured":"Neuh\u00e4u\u00dfer, M.R., Katoen, J.-P.: Bisimulation and logical preservation for continuous-time Markov decision processes. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol.\u00a04703, pp. 412\u2013427. Springer, Heidelberg (2007)"},{"key":"6_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1007\/978-3-642-00596-1_26","volume-title":"Foundations of Software Science and Computational Structures","author":"M.R. Neuh\u00e4u\u00dfer","year":"2009","unstructured":"Neuh\u00e4u\u00dfer, M.R., Stoelinga, M., Katoen, J.-P.: Delayed nondeterminism in continuous-time Markov decision processes. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol.\u00a05504, pp. 364\u2013379. Springer, Heidelberg (2009)"},{"key":"6_CR28","doi-asserted-by":"crossref","unstructured":"Ouaknine, J., Worrell, J.: On the decidability of metric temporal logic. In: LICS, pp. 188\u2013197. IEEE (2005)","DOI":"10.1109\/LICS.2005.33"},{"key":"6_CR29","doi-asserted-by":"crossref","unstructured":"Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46\u201357. IEEE (1977)","DOI":"10.1109\/SFCS.1977.32"},{"issue":"5-6","key":"6_CR30","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s00236-011-0140-0","volume":"48","author":"M.N. Rabe","year":"2011","unstructured":"Rabe, M.N., Schewe, S.: Finite optimal control for time-bounded reachability in CTMDPs and continuous-time Markov games. Acta. Inf.\u00a048(5-6), 291\u2013315 (2011)","journal-title":"Acta. Inf."},{"issue":"2","key":"6_CR31","first-page":"250","volume":"2","author":"R. Segala","year":"1995","unstructured":"Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nord. J. Comput.\u00a02(2), 250\u2013273 (1995)","journal-title":"Nord. J. Comput."},{"key":"6_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1007\/978-3-642-29709-0_28","volume-title":"Perspectives of Systems Informatics","author":"A. Sharma","year":"2012","unstructured":"Sharma, A., Katoen, J.-P.: Weighted lumpability on Markov chains. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol.\u00a07162, pp. 322\u2013339. Springer, Heidelberg (2012)"},{"key":"6_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/978-3-642-23217-6_8","volume-title":"CONCUR 2011 \u2013 Concurrency Theory","author":"L. Song","year":"2011","unstructured":"Song, L., Zhang, L., Godskesen, J.C.: Bisimulations meet PCTL equivalences for probabilistic automata. In: Katoen, J.-P., K\u00f6nig, B. (eds.) CONCUR 2011. LNCS, vol.\u00a06901, pp. 108\u2013123. Springer, Heidelberg (2011)"},{"key":"6_CR34","unstructured":"Song, L., Zhang, L., Godskesen, J.C.: The branching time spectrum for continuous-time mdps. CoRR, abs\/1204.1848 (2012)"},{"key":"6_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/3-540-57208-2_6","volume-title":"CONCUR\u201993","author":"R.J. Glabbeek van","year":"1993","unstructured":"van Glabbeek, R.J.: The linear time - branching time spectrum ii. In: Best, E. (ed.) CONCUR 1993. LNCS, vol.\u00a0715, pp. 66\u201381. Springer, Heidelberg (1993)"},{"key":"6_CR36","unstructured":"van Glabbeek, R.J.: The linear time - branching time spectrum i. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 3\u201399. Elsevier (2001)"},{"key":"6_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1007\/11867340_25","volume-title":"Formal Modeling and Analysis of Timed Systems","author":"N. Wolovick","year":"2006","unstructured":"Wolovick, N., Johr, S.: A characterization of meaningful schedulers for continuous-time Markov decision processes. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol.\u00a04202, pp. 352\u2013367. Springer, Heidelberg (2006)"},{"key":"6_CR38","doi-asserted-by":"crossref","unstructured":"Zhang, L., Hermanns, H., Eisenbrand, F., Jansen, D.N.: Flow faster: Efficient decision algorithms for probabilistic simulations. Logical Methods in Computer Science\u00a04(4) (2008)","DOI":"10.2168\/LMCS-4(4:6)2008"},{"key":"6_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/978-3-642-12002-2_5","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"L. Zhang","year":"2010","unstructured":"Zhang, L., Neuh\u00e4u\u00dfer, M.R.: Model Checking Interactive Markov Chains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol.\u00a06015, pp. 53\u201368. Springer, Heidelberg (2010)"}],"container-title":["Lecture Notes in Computer Science","Verification, Model Checking, and Abstract Interpretation"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-54013-4_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T10:40:06Z","timestamp":1746096006000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-54013-4_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783642540127","9783642540134"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-54013-4_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}