{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T08:38:05Z","timestamp":1726043885791},"publisher-location":"Cham","reference-count":17,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030308056"},{"type":"electronic","value":"9783030308063"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-30806-3_2","type":"book-chapter","created":{"date-parts":[[2019,9,6]],"date-time":"2019-09-06T09:08:36Z","timestamp":1567760916000},"page":"13-21","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Primitivity and Synchronizing Automata: A Functional Analytic Approach"],"prefix":"10.1007","author":[{"given":"Vladimir Yu.","family":"Protasov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,9,6]]},"reference":[{"key":"2_CR1","unstructured":"Alpin, Yu.A., Alpina, V.S.: Combinatorial properties of irreducible semigroups of nonnegative matrices. J. Math. Sci. (N. Y.) 191(1), 4\u20139 (2013)"},{"key":"2_CR2","doi-asserted-by":"crossref","unstructured":"Alpin, Yu.A., Alpina, V.S.: A new proof of the Protasov-Voynov theorem on semigroups of nonnegative matrices. Math. Notes 105, 805\u2013811 (2019)","DOI":"10.1134\/S0001434619050183"},{"key":"2_CR3","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1016\/j.ins.2016.07.049","volume":"369","author":"MV Berlinkov","year":"2016","unstructured":"Berlinkov, M.V., Szykula, M.: Algebraic synchronization criterion and computing reset words. Inf. Sci. 369, 718\u2013730 (2016)","journal-title":"Inf. Sci."},{"key":"2_CR4","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.automatica.2015.07.026","volume":"61","author":"VD Blondel","year":"2015","unstructured":"Blondel, V.D., Jungers, R.M., Olshevsky, A.: On primitivity of sets of matrices. Automatica 61, 80\u201388 (2015)","journal-title":"Automatica"},{"key":"2_CR5","doi-asserted-by":"crossref","unstructured":"Cabrelli, C.A., Heil, C., Molter, U.M.: Self-similarity and Multiwavelets in Higher Dimensions, vol. 170, no. 807. Memoirs of the American Mathematical Society (2004)","DOI":"10.1090\/memo\/0807"},{"key":"2_CR6","doi-asserted-by":"crossref","unstructured":"Cavaretta, A.S., Dahmen, W., Micchelli, C.A.: Stationary Subdivision, vol. 93, no. 453. Memoirs of the American Mathematical Society (1991)","DOI":"10.1090\/memo\/0453"},{"key":"2_CR7","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0024-3795(90)90224-Z","volume":"140","author":"E Fornasini","year":"1990","unstructured":"Fornasini, E.: 2D Markov chains. Linear Algebra Appl. 140, 101\u2013127 (1990)","journal-title":"Linear Algebra Appl."},{"key":"2_CR8","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/S0024-3795(96)00540-X","volume":"263","author":"E Fornasini","year":"1997","unstructured":"Fornasini, E., Valcher, M.: Directed graphs, 2D state models and characteristic polynomials of irreducible matrix pairs. Linear Alg. Appl. 263, 275\u2013310 (1997)","journal-title":"Linear Alg. Appl."},{"issue":"2\u20133","key":"2_CR9","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1016\/j.laa.2005.11.006","volume":"413","author":"E Fornasini","year":"2006","unstructured":"Fornasini, E., Valcher, M.: A polynomial matrix approach to the structural properties of 2D positive systems. Linear Algebra Appl. 413(2\u20133), 458\u2013473 (2006)","journal-title":"Linear Algebra Appl."},{"issue":"5\u20136","key":"2_CR10","doi-asserted-by":"publisher","first-page":"1550","DOI":"10.1016\/j.laa.2008.03.011","volume":"430","author":"Y Gao","year":"2009","unstructured":"Gao, Y., Shao, Y.: Generalized exponents of primitive two-colored digraphs. Linear Algebra Appl. 430(5\u20136), 1550\u20131565 (2009)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"2_CR11","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1137\/16M1094099","volume":"39","author":"B Gerencs\u00e9r","year":"2018","unstructured":"Gerencs\u00e9r, B., Gusev, V.V., Jungers, R.M.: Primitive sets of nonnegative matrices and synchronizing automata. SIAM J. Matr. Anal. 39(1), 83\u201398 (2018)","journal-title":"SIAM J. Matr. Anal."},{"issue":"1\u20133","key":"2_CR12","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/S0024-3795(02)00365-8","volume":"356","author":"DD Olesky","year":"2002","unstructured":"Olesky, D.D., Shader, B., van den Driessche, P.: Exponents of tuples of nonnegative matrices. Linear Algebra Appl. 356(1\u20133), 123\u2013134 (2002)","journal-title":"Linear Algebra Appl."},{"key":"2_CR13","unstructured":"Protasov, V.Yu.: Extremal \n                    \n                      \n                    \n                    $$L_p$$\n                    \n                      \n                        \n                          L\n                          p\n                        \n                      \n                    \n                  -norms of linear operators and self-similar functions. Linear Alg. Appl. 428(10), 2339\u20132356 (2008)"},{"issue":"6","key":"2_CR14","doi-asserted-by":"publisher","first-page":"1186","DOI":"10.1070\/RM2010v065n06ABEH004722","volume":"65","author":"Vladimir Yu Protasov","year":"2010","unstructured":"Protasov, V.Yu.: Semigroups of non-negative matrices. Russian Math. Surv. 65(6), 1186\u20131188 (2010)","journal-title":"Russian Mathematical Surveys"},{"key":"2_CR15","doi-asserted-by":"crossref","unstructured":"Protasov, V.Yu.: Classification of \n                    \n                      \n                    \n                    $$k$$\n                    \n                      \n                        k\n                      \n                    \n                  -primitive sets of matrices. SIAM J. Matrix Anal. 34(3), 1174\u20131188 (2013)","DOI":"10.1137\/120883414"},{"issue":"3","key":"2_CR16","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1016\/j.laa.2012.02.029","volume":"437","author":"V.Yu. Protasov","year":"2012","unstructured":"Protasov, V.Yu., Voynov, A.S.: Sets of nonnegative matrices without positive products. Linear Alg. Appl. 437(3), 749\u2013765 (2012)","journal-title":"Linear Algebra and its Applications"},{"issue":"7","key":"2_CR17","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1070\/SM2015v206n07ABEH004483","volume":"206","author":"A S Voynov","year":"2015","unstructured":"Voynov, A.S., Protasov, V.Yu.: Compact noncontraction semigroups of affine operators. Sb. Math. 206(7), 921\u2013940 (2015)","journal-title":"Sbornik: Mathematics"}],"container-title":["Lecture Notes in Computer Science","Reachability Problems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-30806-3_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,6]],"date-time":"2019-09-06T09:10:23Z","timestamp":1567761023000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-30806-3_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030308056","9783030308063"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-30806-3_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"6 September 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"RP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Reachability Problems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Brussels","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Belgium","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 September 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 September 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"rp2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sites.uclouvain.be\/rp2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}