{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T22:08:47Z","timestamp":1725746927997},"publisher-location":"Cham","reference-count":31,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319024431"},{"type":"electronic","value":"9783319024448"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-319-02444-8_9","type":"book-chapter","created":{"date-parts":[[2013,8,29]],"date-time":"2013-08-29T01:11:21Z","timestamp":1377738681000},"page":"102-117","source":"Crossref","is-referenced-by-count":5,"title":["Kleene Algebras and Semimodules for Energy Problems"],"prefix":"10.1007","author":[{"given":"Zolt\u00e1n","family":"\u00c9sik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Uli","family":"Fahrenberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Axel","family":"Legay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karin","family":"Quaas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"1","key":"9_CR1","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1093\/logcom\/exm062","volume":"18","author":"P.A. Abdulla","year":"2008","unstructured":"Abdulla, P.A., Bouajjani, A., d\u2019Orso, J.: Monotonic and downward closed games. J. Log. Comput.\u00a018(1), 153\u2013169 (2008)","journal-title":"J. Log. Comput."},{"issue":"1-2","key":"9_CR2","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1006\/inco.1999.2843","volume":"160","author":"P.A. Abdulla","year":"2000","unstructured":"Abdulla, P.A., \u010cer\u0101ns, K., Jonsson, B., Tsay, Y.-K.: Algorithmic analysis of programs with well quasi-ordered domains. Inf. Comput.\u00a0160(1-2), 109\u2013127 (2000)","journal-title":"Inf. Comput."},{"issue":"2","key":"9_CR3","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.\u00a0126(2), 183\u2013235 (1994)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/3-540-45351-2_8","volume-title":"Hybrid Systems: Computation and Control","author":"R. Alur","year":"2001","unstructured":"Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol.\u00a02034, pp. 49\u201362. Springer, Heidelberg (2001)"},{"key":"9_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/3-540-45351-2_15","volume-title":"Hybrid Systems: Computation and Control","author":"G. Behrmann","year":"2001","unstructured":"Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.W.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol.\u00a02034, pp. 147\u2013161. Springer, Heidelberg (2001)"},{"key":"9_CR6","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/978-3-642-78034-9_6","volume-title":"Iteration Theories","author":"Stephen L. Bloom","year":"1993","unstructured":"Bloom, S.L., \u00c9sik, Z.: Iteration Theories: The Equational Logic of Iterative Processes. EATCS monographs on theoretical computer science. Springer (1993)"},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed automata with observers under energy constraints. In: HSCC, pp. 61\u201370 (2010)","DOI":"10.1145\/1755952.1755963"},{"key":"9_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-3-540-85778-5_4","volume-title":"Formal Modeling and Analysis of Timed Systems","author":"P. Bouyer","year":"2008","unstructured":"Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol.\u00a05215, pp. 33\u201347. Springer, Heidelberg (2008)"},{"key":"9_CR9","doi-asserted-by":"crossref","unstructured":"Bouyer, P., Larsen, K.G., Markey, N.: Lower-bound constrained runs in weighted timed automata. In: QEST, pp. 128\u2013137 (2012)","DOI":"10.1109\/QEST.2012.28"},{"key":"9_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1007\/978-3-642-14162-1_40","volume-title":"Automata, Languages and Programming","author":"T. Br\u00e1zdil","year":"2010","unstructured":"Br\u00e1zdil, T., Jan\u010dar, P., Ku\u010dera, A.: Reachability games on extended vector addition systems with states. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol.\u00a06199, pp. 478\u2013489. Springer, Heidelberg (2010)"},{"key":"9_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/978-3-642-15349-5_7","volume-title":"Reachability Problems","author":"J. Chaloupka","year":"2010","unstructured":"Chaloupka, J.: Z-reachability problem for games on 2-dimensional vector addition systems with states is in P. In: Ku\u010dera, A., Potapov, I. (eds.) RP 2010. LNCS, vol.\u00a06227, pp. 104\u2013119. Springer, Heidelberg (2010)"},{"issue":"6","key":"9_CR12","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0020-0190(88)90184-6","volume":"26","author":"T.-H. Chan","year":"1988","unstructured":"Chan, T.-H.: The boundedness problem for three-dimensional vector addition systems with states. Inf. Proc. Letters\u00a026(6), 287\u2013289 (1988)","journal-title":"Inf. Proc. Letters"},{"key":"9_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1007\/978-3-642-14162-1_50","volume-title":"Automata, Languages and Programming","author":"K. Chatterjee","year":"2010","unstructured":"Chatterjee, K., Doyen, L.: Energy parity games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol.\u00a06199, pp. 599\u2013610. Springer, Heidelberg (2010)"},{"key":"9_CR14","unstructured":"Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Generalized mean-payoff and energy games. In: FSTTCS, pp. 505\u2013516 (2010)"},{"key":"9_CR15","unstructured":"Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall (1971)"},{"key":"9_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/978-3-642-15205-4_22","volume-title":"Computer Science Logic","author":"A. Degorre","year":"2010","unstructured":"Degorre, A., Doyen, L., Gentilini, R., Raskin, J.-F., Toru\u0144czyk, S.: Energy and mean-payoff games with imperfect information. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol.\u00a06247, pp. 260\u2013274. Springer, Heidelberg (2010)"},{"key":"9_CR17","doi-asserted-by":"crossref","unstructured":"Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. Springer (2009)","DOI":"10.1007\/978-3-642-01492-5"},{"key":"9_CR18","unstructured":"\u00c9sik, Z., Fahrenberg, U., Legay, A., Quaas, K.: Kleene algebras and semimodules for energy problems. CoRR, abs\/1307.0635 (2013), \n                    \n                      http:\/\/arxiv.org\/abs\/1307.0635"},{"key":"9_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1007\/978-3-540-28629-5_50","volume-title":"Mathematical Foundations of Computer Science 2004","author":"Z. \u00c9sik","year":"2004","unstructured":"\u00c9sik, Z., Kuich, W.: An algebraic generalization of \u03c9-regular languages. In: Fiala, J., Koubek, V., Kratochv\u00edl, J. (eds.) MFCS 2004. LNCS, vol.\u00a03153, pp. 648\u2013659. Springer, Heidelberg (2004)"},{"key":"9_CR20","first-page":"203","volume":"10","author":"Z. \u00c9sik","year":"2005","unstructured":"\u00c9sik, Z., Kuich, W.: A semiring-semimodule generalization of \u03c9-regular languages, Parts 1 and 2. J. Aut. Lang. Comb.\u00a010, 203\u2013264 (2005)","journal-title":"J. Aut. Lang. Comb."},{"key":"9_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-3-642-23283-1_9","volume-title":"Theoretical Aspects of Computing \u2013 ICTAC 2011","author":"U. Fahrenberg","year":"2011","unstructured":"Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J.: Energy games in multiweighted automata. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol.\u00a06916, pp. 95\u2013115. Springer, Heidelberg (2011)"},{"key":"9_CR22","unstructured":"Fahrenberg, U., Legay, A., Thrane, C.: The quantitative linear-time\u2013branching-time spectrum. In: FSTTCS, pp. 103\u2013114 (2011)"},{"issue":"1-2","key":"9_CR23","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/S0304-3975(00)00102-X","volume":"256","author":"A. Finkel","year":"2001","unstructured":"Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci.\u00a0256(1-2), 63\u201392 (2001)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1007\/BFb0029594","volume-title":"Mathematical Foundations of Computer Science 1990","author":"D. Kozen","year":"1990","unstructured":"Kozen, D.: On Kleene algebras and closed semirings. In: Rovan, B. (ed.) MFCS 1990. LNCS, vol.\u00a0452, pp. 26\u201347. Springer, Heidelberg (1990)"},{"issue":"2","key":"9_CR25","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1006\/inco.1994.1037","volume":"110","author":"D. Kozen","year":"1994","unstructured":"Kozen, D.: A completeness theorem for kleene algebras and the algebra of regular events. Inf. Comput.\u00a0110(2), 366\u2013390 (1994)","journal-title":"Inf. Comput."},{"key":"9_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1007\/11734673_15","volume-title":"Relational Methods in Computer Science","author":"V. Mathieu","year":"2006","unstructured":"Mathieu, V., Desharnais, J.: Verification of pushdown systems using omega algebra with domain. In: MacCaull, W., Winter, M., D\u00fcntsch, I. (eds.) RelMiCS 2005. LNCS, vol.\u00a03929, pp. 188\u2013199. Springer, Heidelberg (2006)"},{"key":"9_CR27","unstructured":"Perrin, D., Pin, J.-E.: Infinite Words: Automata, Semigroups, Logic and Games. Academic Press (2004)"},{"key":"9_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1007\/978-3-642-21254-3_36","volume-title":"Language and Automata Theory and Applications","author":"K. Quaas","year":"2011","unstructured":"Quaas, K.: On the interval-bound problem for weighted timed automata. In: Dediu, A.-H., Inenaga, S., Mart\u00edn-Vide, C. (eds.) LATA 2011. LNCS, vol.\u00a06638, pp. 452\u2013464. Springer, Heidelberg (2011)"},{"issue":"6","key":"9_CR29","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.entcs.2005.04.005","volume":"128","author":"J.-F. Raskin","year":"2005","unstructured":"Raskin, J.-F., Samuelides, M., Begin, L.V.: Games for counting abstractions. Electr. Notes Theor. Comput. Sci.\u00a0128(6), 69\u201385 (2005)","journal-title":"Electr. Notes Theor. Comput. Sci."},{"key":"9_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/978-3-642-15349-5_4","volume-title":"Reachability Problems","author":"P. Schnoebelen","year":"2010","unstructured":"Schnoebelen, P.: Lossy counter machines decidability cheat sheet. In: Ku\u010dera, A., Potapov, I. (eds.) RP 2010. LNCS, vol.\u00a06227, pp. 51\u201375. Springer, Heidelberg (2010)"},{"key":"9_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"588","DOI":"10.1007\/3-540-54233-7_166","volume-title":"Automata, Languages and Programming","author":"T. Wilke","year":"1991","unstructured":"Wilke, T.: An Eilenberg theorem for infinity-languages. In: Leach Albert, J., Monien, B., Rodr\u00edguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol.\u00a0510, pp. 588\u2013599. Springer, Heidelberg (1991)"}],"container-title":["Lecture Notes in Computer Science","Automated Technology for Verification and Analysis"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-02444-8_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T20:25:55Z","timestamp":1558038355000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-02444-8_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783319024431","9783319024448"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-02444-8_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}