{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:01:01Z","timestamp":1773244861343,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":19,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662445211","type":"print"},{"value":"9783662445228","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-662-44522-8_20","type":"book-chapter","created":{"date-parts":[[2014,8,12]],"date-time":"2014-08-12T06:12:23Z","timestamp":1407823943000},"page":"232-243","source":"Crossref","is-referenced-by-count":5,"title":["Information Rate of Some Classes of Non-regular Languages: An Automata-Theoretic Approach"],"prefix":"10.1007","author":[{"given":"Cewei","family":"Cui","sequence":"first","affiliation":[]},{"given":"Zhe","family":"Dang","sequence":"additional","affiliation":[]},{"given":"Thomas R.","family":"Fischer","sequence":"additional","affiliation":[]},{"given":"Oscar H.","family":"Ibarra","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"2","key":"20_CR1","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. Theoretical Computer Science\u00a0126(2), 183\u2013235 (1994)","journal-title":"Theoretical Computer Science"},{"key":"20_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/978-3-642-04081-8_6","volume-title":"CONCUR 2009 - Concurrency Theory","author":"E. Asarin","year":"2009","unstructured":"Asarin, E., Degorre, A.: Volume and entropy of regular timed languages: Discretization approach. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol.\u00a05710, pp. 69\u201383. Springer, Heidelberg (2009)"},{"issue":"3","key":"20_CR3","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/S0022-0000(74)80027-9","volume":"8","author":"B.S. Baker","year":"1974","unstructured":"Baker, B.S., Book, R.V.: Reversal-bounded multipushdown machines. J. Comput. Syst. Sci.\u00a08(3), 315\u2013332 (1974)","journal-title":"J. Comput. Syst. Sci."},{"key":"20_CR4","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/S0019-9958(58)90082-2","volume":"1","author":"N. Chomsky","year":"1958","unstructured":"Chomsky, N., Miller, G.A.: Finite state languages. Information and Control\u00a01, 91\u2013112 (1958)","journal-title":"Information and Control"},{"key":"20_CR5","doi-asserted-by":"crossref","unstructured":"Dang, Z.: Pushdown timed automata: A binary reachability characterization and safety verification. Theor. Comput. Sci.\u00a01-3(302), 93\u2013121 (2003)","DOI":"10.1016\/S0304-3975(02)00743-0"},{"key":"20_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/10722167_9","volume-title":"Computer Aided Verification","author":"Z. Dang","year":"2000","unstructured":"Dang, Z., Ibarra, O.H., Bultan, T., Kemmerer, R.A., Su, J.: Binary reachability analysis of discrete pushdown timed automata. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol.\u00a01855, pp. 69\u201384. Springer, Heidelberg (2000)"},{"key":"20_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/3-540-55210-3_209","volume-title":"STACS 92","author":"G. Hansel","year":"1992","unstructured":"Hansel, G., Perrin, D., Simon, I.: Compression and Entropy. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol.\u00a0577, pp. 513\u2013528. Springer, Heidelberg (1992)"},{"issue":"1","key":"20_CR8","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1145\/322047.322058","volume":"25","author":"O.H. Ibarra","year":"1978","unstructured":"Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. Journal of the ACM\u00a025(1), 116\u2013133 (1978)","journal-title":"Journal of the ACM"},{"key":"20_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1007\/978-3-540-45138-9_42","volume-title":"Mathematical Foundations of Computer Science 2003","author":"O.H. Ibarra","year":"2003","unstructured":"Ibarra, O.H., Dang, Z., Egecioglu, O., Saxena, G.: Characterizations of Catalytic Membrane Computing Systems. In: Rovan, B., Vojt\u00e1\u0161, P. (eds.) MFCS 2003. LNCS, vol.\u00a02747, pp. 480\u2013489. Springer, Heidelberg (2003)"},{"issue":"2","key":"20_CR10","first-page":"175","volume":"17","author":"F.P. Kaminger","year":"1970","unstructured":"Kaminger, F.P.: The noncomputability of the channel capacity of context-senstitive languages. Inf. Comput.\u00a017(2), 175\u2013182 (1970)","journal-title":"Inf. Comput."},{"issue":"2","key":"20_CR11","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/S0019-9958(70)90105-1","volume":"16","author":"W. Kuich","year":"1970","unstructured":"Kuich, W.: On the entropy of context-free languages. Information and Control\u00a016(2), 173\u2013200 (1970)","journal-title":"Information and Control"},{"issue":"3","key":"20_CR12","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0019-9958(71)90075-1","volume":"19","author":"W. Kuich","year":"1971","unstructured":"Kuich, W., Maurer, H.: The structure generating function and entropy of tuple languages. Information and Control\u00a019(3), 195\u2013203 (1971)","journal-title":"Information and Control"},{"issue":"4","key":"20_CR13","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1145\/321356.321364","volume":"13","author":"R.J. Parikh","year":"1966","unstructured":"Parikh, R.J.: On Context-Free Languages. J. ACM\u00a013(4), 570\u2013581 (1966)","journal-title":"J. ACM"},{"key":"20_CR14","doi-asserted-by":"crossref","unstructured":"Paun, G.: Membrane Computing, An Introduction. Springer (2002)","DOI":"10.1007\/978-3-642-56196-2"},{"key":"20_CR15","unstructured":"Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press (1949)"},{"key":"20_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/3-540-46011-X_12","volume-title":"Developments in Language Theory","author":"L. Staiger","year":"2002","unstructured":"Staiger, L.: The entropy of Lukasiewicz-languages. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol.\u00a02295, pp. 155\u2013165. Springer, Heidelberg (2002)"},{"key":"20_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1007\/3-540-45061-0_53","volume-title":"Automata, Languages and Programming","author":"G. Xie","year":"2003","unstructured":"Xie, G., Dang, Z., Ibarra, O.H.: A solvable class of quadratic Diophantine equations with applications to verification of infinite state systems. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol.\u00a02719, pp. 668\u2013680. Springer, Heidelberg (2003)"},{"key":"20_CR18","unstructured":"Yang, L., Cui, C., Dang, Z., Fischer, T.R.: An information-theoretic complexity metric for labeled graphs (2011) (in review)"},{"issue":"4","key":"20_CR19","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/s00165-011-0175-6","volume":"23","author":"L. Yang","year":"2011","unstructured":"Yang, L., Dang, Z., Fischer, T.R.: Information gain of black-box testing. Form. Asp. Comput.\u00a023(4), 513\u2013539 (2011)","journal-title":"Form. Asp. Comput."}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2014"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-44522-8_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T11:01:37Z","timestamp":1558954897000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-44522-8_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783662445211","9783662445228"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-44522-8_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}