{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T20:52:10Z","timestamp":1715806330840},"reference-count":42,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding \u010cern\u00fd conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns. We formulate the primitivity process in the setting of a two-player probabilistic game and we make use of convex optimization techniques to describe its behavior. We develop a tool for approximating and upper bounding the exponent of any primitive set and supported by numerical results we state a conjecture that, if true, would imply a quadratic upper bound on the reset threshold of a new class of automata. <\/jats:p>","DOI":"10.1142\/s0129054120410051","type":"journal-article","created":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T15:24:03Z","timestamp":1602516243000},"page":"777-803","source":"Crossref","is-referenced-by-count":1,"title":["The Synchronizing Probability Function for Primitive Sets of Matrices"],"prefix":"10.1142","volume":"31","author":[{"given":"Costanza","family":"Catalano","sequence":"first","affiliation":[{"name":"Department of Economics, Statistics and Research, Banca d\u2019Italia (Central Bank of Italy), Largo Guido Carli, 1, 00044 Frascati (Roma), Italy"}]},{"given":"Rapha\u00ebl M.","family":"Jungers","sequence":"additional","affiliation":[{"name":"ICTEAM Institute, UCLouvain, Avenue Georges Lema\u00eetres 4-6, 1340, Louvain-la-Neuve, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2020,10,10]]},"reference":[{"issue":"5","key":"S0129054120410051BIB001","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1007\/s10958-015-2390-9","volume":"207","author":"Al\u2019pin Y. A.","year":"2015","journal-title":"J. Math. Sci."},{"issue":"3","key":"S0129054120410051BIB002","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10958-013-1392-8","volume":"192","author":"Ananichev D. S.","year":"2013","journal-title":"J. Math. Sci."},{"key":"S0129054120410051BIB003","volume-title":"Introduction to Linear Optimization","author":"Bertsimas D.","year":"1997","edition":"1"},{"key":"S0129054120410051BIB004","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.automatica.2015.07.026","volume":"61","author":"Blondel V. D.","year":"2015","journal-title":"Automatica"},{"key":"S0129054120410051BIB005","first-page":"48:1","author":"Catalano C.","year":"2018","journal-title":"Mathematical Foundationas of Computer Science"},{"key":"S0129054120410051BIB006","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1007\/978-3-319-98654-8_16","author":"Catalano C.","year":"2018","journal-title":"Developments in Language Theory"},{"key":"S0129054120410051BIB007","first-page":"185","volume":"24","author":"Catalano C.","year":"2019","journal-title":"Journal of Automata, Languages and Combinatorics"},{"issue":"5","key":"S0129054120410051BIB008","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/BF01192046","volume":"14","author":"Chen Y. B.","year":"1995","journal-title":"Algorithmica"},{"key":"S0129054120410051BIB009","first-page":"4139","volume-title":"IEEE Conference in Decision and Control","author":"Chevalier P. Y.","year":"2015"},{"key":"S0129054120410051BIB010","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1007\/978-3-319-62809-7_8","author":"de Bondt M.","year":"2017","journal-title":"Developments in Language Theory"},{"key":"S0129054120410051BIB011","first-page":"40:1","volume":"83","author":"Dzyga M.","year":"2017","journal-title":"Math. Foundations of Comp. Scien."},{"issue":"3","key":"S0129054120410051BIB012","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1137\/0219033","volume":"19","author":"Eppstein D.","year":"1990","journal-title":"SIAM J. Computing"},{"issue":"3","key":"S0129054120410051BIB013","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1134\/S1990478918030067","volume":"12","author":"Fomichev V. M.","year":"2018","journal-title":"J. of App. and Industrial Math."},{"issue":"3","key":"S0129054120410051BIB014","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0195-6698(82)80025-5","volume":"3","author":"Frankl P.","year":"1982","journal-title":"European J. Combinatorics"},{"key":"S0129054120410051BIB015","first-page":"243","volume-title":"Mathematical Foundations of Computer Science","author":"Gawrychowski P.","year":"2015"},{"issue":"1","key":"S0129054120410051BIB016","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1137\/16M1094099","volume":"39","author":"Gerencs\u00e9r B.","year":"2018","journal-title":"Siam J. on Matrix An. and Appl."},{"key":"S0129054120410051BIB017","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-3-319-62809-7_13","author":"Gonze F.","year":"2017","journal-title":"Developments in Language Theory"},{"key":"S0129054120410051BIB018","first-page":"212","author":"Gonze F.","year":"2015","journal-title":"Language and Automata Theory and Appl."},{"key":"S0129054120410051BIB019","volume-title":"Nonhomogeneous matrix products","author":"Hartfiel D. J.","year":"2002"},{"issue":"10","key":"S0129054120410051BIB020","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1214\/aop\/1023481103","volume":"25","author":"Hennion H.","year":"1997","journal-title":"The Annals of Probability"},{"issue":"1","key":"S0129054120410051BIB021","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1137\/100816109","volume":"26","author":"Jungers R. M.","year":"2012","journal-title":"SIAM J. on Discrete Math."},{"issue":"1","key":"S0129054120410051BIB022","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/S0304-3975(02)00405-X","volume":"295","author":"Kari J.","year":"2003","journal-title":"Theoretical Computer Science"},{"key":"S0129054120410051BIB023","first-page":"331","author":"Kisielewicz A.","year":"2015","journal-title":"Math. Foundations of Comp. Scien."},{"key":"S0129054120410051BIB024","first-page":"134","author":"Mateescu A.","year":"1999","journal-title":"EATCS Bulletin"},{"key":"S0129054120410051BIB025","first-page":"132","volume-title":"SFCS","author":"Natarajan B. K.","year":"1986"},{"issue":"1","key":"S0129054120410051BIB026","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1002\/sapm1970491105","volume":"49","author":"Paterson M. S.","year":"1996","journal-title":"Studies in Applied Mathematics"},{"key":"S0129054120410051BIB027","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/S0304-0208(08)73432-7","volume":"75","author":"Pin J. E.","year":"1983","journal-title":"International Colloquium on Graph Theory and Combinatorics"},{"key":"S0129054120410051BIB028","first-page":"170","volume-title":"ACM-SIAM Symposium on Discrete Algorithms","author":"Potapov I.","year":"2017"},{"issue":"1","key":"S0129054120410051BIB029","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1070\/SM2011v202n01ABEH004139","volume":"202","author":"Protasov V. Y.","year":"2011","journal-title":"Sbornik: Mathematics"},{"key":"S0129054120410051BIB030","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/j.laa.2012.02.029","volume":"437","author":"Protasov V. Y.","year":"2012","journal-title":"Linear Algebra and its Applications"},{"issue":"1","key":"S0129054120410051BIB031","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0304-3975(96)00136-3","volume":"172","author":"Rystsov I. K.","year":"1997","journal-title":"Theoretical Computer Science"},{"issue":"3","key":"S0129054120410051BIB032","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF02732984","volume":"36","author":"Rystsov I. K.","year":"2000","journal-title":"Cybernetics and Systems Analysis"},{"issue":"1","key":"S0129054120410051BIB033","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0019-9958(64)90232-3","volume":"7","author":"Sch\u00fctzenberger M. P.","year":"1964","journal-title":"Information and Control"},{"key":"S0129054120410051BIB034","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-32792-4","volume-title":"Non-negative Matrices and Markov Chains","author":"Seneta E.","year":"1981","edition":"2"},{"key":"S0129054120410051BIB035","first-page":"367","volume":"24","author":"Shitov Y.","year":"2019","journal-title":"Journal of Automata, Languages and Combinatorics"},{"issue":"3","key":"S0129054120410051BIB036","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1145\/990308.990310","volume":"51","author":"Spielman D. A.","year":"2004","journal-title":"J. of the ACM"},{"key":"S0129054120410051BIB037","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/978-3-642-14455-4_38","author":"Steinberg B.","year":"2010","journal-title":"Developments in Language Theory"},{"key":"S0129054120410051BIB038","first-page":"56:1","volume-title":"Symposium on Theoretical Aspects of Computer Science","volume":"96","author":"Szyku\u0142a M.","year":"2018"},{"key":"S0129054120410051BIB039","first-page":"789","author":"Trahtman A. N.","year":"2006","journal-title":"Math. Foundations of Comp. Scien."},{"issue":"14","key":"S0129054120410051BIB040","first-page":"208","volume":"14","author":"\u010cern\u00fd J.","year":"1964","journal-title":"Matematicko-fysikalny Casopis SAV"},{"key":"S0129054120410051BIB041","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/978-3-540-76336-9_5","volume-title":"Int. Conf. on Implementation and Application of Automata","author":"Volkov M. V.","year":"2007"},{"key":"S0129054120410051BIB042","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/978-3-540-88282-4_4","author":"Volkov M. V.","year":"2008","journal-title":"Language and Automata Theory and Applications"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054120410051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T08:58:02Z","timestamp":1605257882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054120410051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":42,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1142\/S0129054120410051"],"URL":"https:\/\/doi.org\/10.1142\/s0129054120410051","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}