{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T19:34:01Z","timestamp":1725824041392},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662476659"},{"type":"electronic","value":"9783662476666"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"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":[[2015]]},"DOI":"10.1007\/978-3-662-47666-6_15","type":"book-chapter","created":{"date-parts":[[2015,6,19]],"date-time":"2015-06-19T03:46:47Z","timestamp":1434685607000},"page":"184-196","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Greatest Fixed Points of Probabilistic Min\/Max Polynomial Equations, and Reachability for Branching Markov Decision Processes"],"prefix":"10.1007","author":[{"given":"Kousha","family":"Etessami","sequence":"first","affiliation":[]},{"given":"Alistair","family":"Stewart","sequence":"additional","affiliation":[]},{"given":"Mihalis","family":"Yannakakis","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,20]]},"reference":[{"key":"15_CR1","doi-asserted-by":"publisher","first-page":"e00747","DOI":"10.7554\/eLife.00747","volume":"2","author":"I Bozic","year":"2013","unstructured":"Bozic, I., et al.: Evolutionary dynamics of cancer in response to targeted combination therapy. Elife 2, e00747 (2013)","journal-title":"Elife"},{"key":"15_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-642-54830-7_3","volume-title":"Foundations of Software Science and Computation Structures","author":"R Bonnet","year":"2014","unstructured":"Bonnet, R., Kiefer, S., Lin, A.W.: Analysis of probabilistic basic parallel processes. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 43\u201357. Springer, Heidelberg (2014)"},{"issue":"8","key":"15_CR3","doi-asserted-by":"publisher","first-page":"1160","DOI":"10.1016\/j.ic.2011.02.002","volume":"209","author":"T Br\u00e1zdil","year":"2011","unstructured":"Br\u00e1zdil, T., Brozek, V., Kucera, A., Obdrz\u00e1lek, J.: Qualitative reachability in stochastic BPA games. Inf. Comput. 209(8), 1160\u20131183 (2011)","journal-title":"Inf. Comput."},{"issue":"5","key":"15_CR4","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1016\/j.ic.2007.09.002","volume":"206","author":"T Br\u00e1zdil","year":"2008","unstructured":"Br\u00e1zdil, T., Brozek, V., Forejt, V., Kucera, A.: Reachability in recursive Markov decision processes. Inf. Comput. 206(5), 520\u2013537 (2008)","journal-title":"Inf. Comput."},{"key":"15_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/978-3-642-32589-2_26","volume-title":"Mathematical Foundations of Computer Science 2012","author":"T Chen","year":"2012","unstructured":"Chen, T., Dr\u00e4ger, K., Kiefer, S.: Model checking stochastic branching processes. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 271\u2013282. Springer, Heidelberg (2012)"},{"key":"15_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1007\/978-3-540-70575-8_57","volume-title":"Automata, Languages and Programming","author":"J Esparza","year":"2008","unstructured":"Esparza, J., Gawlitza, T., Kiefer, S., Seidl, H.: Approximative methods for monotone systems of min-max-polynomial equations. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 698\u2013710. Springer, Heidelberg (2008)"},{"issue":"1","key":"15_CR7","first-page":"1","volume":"2","author":"J Esparza","year":"2006","unstructured":"Esparza, J., Ku\u010dera, A., Mayr, R.: Model checking probabilistic pushdown automata. Logical Methods in Computer Science 2(1), 1\u201331 (2006)","journal-title":"Logical Methods in Computer Science"},{"doi-asserted-by":"crossref","unstructured":"Etessami, K., Stewart, A., Yannakakis, M.: Polynomial-time algorithms for multi-type branching processes and stochastic context-free grammars. In: Proc. 44th ACM Symposium on Theory of Computing (STOC) (2012)","key":"15_CR8","DOI":"10.1145\/2213977.2214030"},{"key":"15_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1007\/978-3-642-31594-7_27","volume-title":"Automata, Languages, and Programming","author":"K Etessami","year":"2012","unstructured":"Etessami, K., Stewart, A., Yannakakis, M.: Polynomial time algorithms for branching markov decision processes and probabilistic min(max) polynomial bellman equations. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 314\u2013326. Springer, Heidelberg (2012)"},{"unstructured":"Full preprint of this paper (2015). arXiv:1502.05533","key":"15_CR10"},{"key":"15_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1007\/978-3-540-70575-8_58","volume-title":"Automata, Languages and Programming","author":"K Etessami","year":"2008","unstructured":"Etessami, K., Wojtczak, D., Yannakakis, M.: Recursive stochastic games with positive rewards. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 711\u2013723. Springer, Heidelberg (2008)"},{"doi-asserted-by":"crossref","unstructured":"Etessami, K., Yannakakis, M.: Recursive Markov decision processes and recursive stochastic games. Journal of the ACM (2015)","key":"15_CR12","DOI":"10.1145\/2699431"},{"doi-asserted-by":"crossref","unstructured":"Etessami, K., Yannakakis, M.: Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations. Journal of the ACM 56(1) (2009)","key":"15_CR13","DOI":"10.1145\/1462153.1462154"},{"doi-asserted-by":"crossref","unstructured":"Pliska, S.: Optimization of multitype branching processes. Management Sci., 23(2), 117\u2013124 (1976\/1977)","key":"15_CR14","DOI":"10.1287\/mnsc.23.2.117"},{"key":"15_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/978-3-642-39799-8_6","volume-title":"Computer Aided Verification","author":"JG Reiter","year":"2013","unstructured":"Reiter, J.G., Bozic, I., Chatterjee, K., Nowak, M.A.: TTP: tool for tumor progression. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 101\u2013106. Springer, Heidelberg (2013)"},{"issue":"4","key":"15_CR16","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1287\/moor.7.4.582","volume":"7","author":"U Rothblum","year":"1982","unstructured":"Rothblum, U., Whittle, P.: Growth optimality for branching Markov decision chains. Math. Oper. Res. 7(4), 582\u2013601 (1982)","journal-title":"Math. Oper. Res."}],"container-title":["Lecture Notes in Computer Science","Automata, Languages, and Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-47666-6_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T13:28:04Z","timestamp":1674221284000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-662-47666-6_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783662476659","9783662476666"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-47666-6_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"20 June 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}