{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:14:05Z","timestamp":1767237245303,"version":"3.40.3"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319155784"},{"type":"electronic","value":"9783319155791"}],"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\/978-3-319-15579-1_5","type":"book-chapter","created":{"date-parts":[[2015,2,23]],"date-time":"2015-02-23T08:36:13Z","timestamp":1424680573000},"page":"70-81","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Shuffle Product: New Research Directions"],"prefix":"10.1007","author":[{"given":"Antonio","family":"Restivo","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,2,24]]},"reference":[{"key":"5_CR1","doi-asserted-by":"crossref","unstructured":"Baeten, J., Weijland, W.: Process Algebra. Cambridge University Press (1990)","DOI":"10.1017\/CBO9780511624193"},{"issue":"13","key":"5_CR2","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.tcs.2005.04.007","volume":"341","author":"MH ter Beek","year":"2005","unstructured":"ter Beek, M.H., Martn-Vide, C., Mitrana, V.: Synchronized shuffles. Theoretical Computer Science 341(13), 263\u2013275 (2005)","journal-title":"Theoretical Computer Science"},{"issue":"11","key":"5_CR3","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1016\/j.ic.2010.06.002","volume":"208","author":"J Berstel","year":"2010","unstructured":"Berstel, J., Boasson, L., Carton, O., Pin, J.\u00c9., Restivo, A.: The expressive power of the shuffle product. Inf. Comput. 208(11), 1258\u20131272 (2010)","journal-title":"Inf. Comput."},{"issue":"4","key":"5_CR4","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1016\/j.jcss.2013.11.002","volume":"80","author":"S Buss","year":"2014","unstructured":"Buss, S., Soltys, M.: Unshuffling a square is np-hard. J. Comput. Syst. Sci. 80(4), 766\u2013776 (2014)","journal-title":"J. Comput. Syst. Sci."},{"key":"5_CR5","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.ic.2013.07.003","volume":"230","author":"A Cano","year":"2013","unstructured":"Cano, A., Guaiana, G., Pin, J.\u00c9.: Regular languages and partial commutations. Information and Computation 230, 76\u201396 (2013)","journal-title":"Information and Computation"},{"issue":"1\u20134","key":"5_CR6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.3233\/FI-2012-666","volume":"116","author":"G Castiglione","year":"2012","unstructured":"Castiglione, G., Restivo, A.: On the shuffle of star-free languages. Fundam. Inform. 116(1\u20134), 35\u201344 (2012)","journal-title":"Fundam. Inform."},{"key":"5_CR7","unstructured":"Currie, J.: Shuffle squares are avoidable. Manuscript"},{"key":"5_CR8","doi-asserted-by":"crossref","unstructured":"Currie, J.D., Saari, K.: Square-free words with square-free self-shuffles. Electr. J. Comb., 1\u20139 (2014)","DOI":"10.37236\/3605"},{"key":"5_CR9","doi-asserted-by":"publisher","DOI":"10.1142\/9789814261456","volume-title":"The Book of Traces","author":"V Diekert","year":"1995","unstructured":"Diekert, V., Rozenberg, G.: The Book of Traces. World Scientific, River Edge (1995)"},{"key":"5_CR10","volume-title":"Automata, Languages, and Machines","author":"S Eilenberg","year":"1976","unstructured":"Eilenberg, S.: Automata, Languages, and Machines. Academic Press Inc., Orlando (1976)"},{"issue":"3","key":"5_CR11","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1145\/321281.321294","volume":"12","author":"S Ginsburg","year":"1965","unstructured":"Ginsburg, S., Spanier, E.H.: Mappings of languages by two-tape devices. J. ACM 12(3), 423\u2013434 (1965)","journal-title":"J. ACM"},{"issue":"23","key":"5_CR12","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1016\/j.tcs.2003.10.034","volume":"312","author":"AC G\u00f3mez","year":"2004","unstructured":"G\u00f3mez, A.C., Pin, J.\u00c9.: Shuffle on positive varieties of languages. Theoretical Computer Science 312(23), 433\u2013461 (2004)","journal-title":"Theoretical Computer Science"},{"key":"5_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/978-3-540-85238-4_3","volume-title":"Mathematical Foundations of Computer Science 2008","author":"AC G\u00f3mez","year":"2008","unstructured":"G\u00f3mez, A.C., Pin, J.\u00c9.: A robust class of regular languages. In: Ochma\u0144ski, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 36\u201351. Springer, Heidelberg (2008)"},{"key":"5_CR14","unstructured":"Gon\u00e7alves, D., Montassier, M., Pinlou, A.: Entropy compression method applied to graph colorings. CoRR abs\/1406.4380 (2014). http:\/\/arxiv.org\/abs\/1406.4380"},{"issue":"2","key":"5_CR15","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/0304-3975(92)90080-Y","volume":"97","author":"G Guaiana","year":"1992","unstructured":"Guaiana, G., Restivo, A., Salemi, S.: Star-free trace languages. Theor. Comput. Sci. 97(2), 301\u2013311 (1992)","journal-title":"Theor. Comput. Sci."},{"key":"5_CR16","unstructured":"Guegan, G., Ochem, P.: Avoiding shuffle squares using entropy compression. 15e Journ\u00e9es Montoises d\u2019Informatique Th\u00e9orique (2014)"},{"key":"5_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/978-3-642-40579-2_17","volume-title":"Combinatorics on Words","author":"T Harju","year":"2013","unstructured":"Harju, T.: A note on square-free shuffles of words. In: Karhum\u00e4ki, J., Lepist\u00f6, A., Zamboni, L. (eds.) WORDS 2013. LNCS, vol. 8079, pp. 154\u2013160. Springer, Heidelberg (2013)"},{"key":"5_CR18","unstructured":"Harju, T., M\u00fcller, M.: Square-free shuffles of words. CoRR abs\/1309.2137 (2013). http:\/\/arxiv.org\/abs\/1309.2137"},{"key":"5_CR19","first-page":"131","volume":"107","author":"D Henshall","year":"2012","unstructured":"Henshall, D., Rampersad, N., Shallit, J.: Shuffling and unshuffling. Bulletin of the EATCS 107, 131\u2013142 (2012)","journal-title":"Bulletin of the EATCS"},{"key":"5_CR20","unstructured":"Aoki, H., Uehara, R., Yamazaki, K.: Expected length of longest common subsequences of two biased random strings and its application. In: LA Symposium (2001)"},{"issue":"13","key":"5_CR21","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/S0166-218X(98)00074-2","volume":"88","author":"J Kececioglu","year":"1998","unstructured":"Kececioglu, J., Gusfield, D.: Reconstructing a history of recombinations from a set of sequences. Discrete Applied Mathematics 88(13), 239\u2013260 (1998). computational Molecular Biology DAM - CMB Series","journal-title":"Discrete Applied Mathematics"},{"key":"5_CR22","doi-asserted-by":"crossref","unstructured":"Kimura, T.: An algebraic system for process structuring and interprocess communication. In: STOC 1976, pp. 92\u2013100 (1976)","DOI":"10.1145\/800113.803636"},{"issue":"1","key":"5_CR23","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/0020-0190(82)90138-7","volume":"14","author":"J van Leeuwen","year":"1982","unstructured":"van Leeuwen, J., Nivat, M.: Efficient recognition of rational relations. Information Processing Letters 14(1), 34\u201338 (1982)","journal-title":"Information Processing Letters"},{"key":"5_CR24","doi-asserted-by":"crossref","unstructured":"Lothaire, M.: Algebraic Combinatorics on Words. Cambridge University Press (2002)","DOI":"10.1017\/CBO9781107326019"},{"issue":"4","key":"5_CR25","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1307\/mmj\/1028998766","volume":"9","author":"RC Lyndon","year":"1962","unstructured":"Lyndon, R.C., Sch\u00fctzenberger, M.P.: The equation $$a^m=b^nc^p$$ in a free group. Michigan Math. J. 9(4), 289\u2013298 (1962)","journal-title":"Michigan Math. J."},{"issue":"3","key":"5_CR26","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/0166-218X(82)90039-7","volume":"4","author":"A Mansfield","year":"1982","unstructured":"Mansfield, A.: An algorithm for a merge recognition problem. Discrete Applied Mathematics 4(3), 193\u2013197 (1982)","journal-title":"Discrete Applied Mathematics"},{"issue":"1","key":"5_CR27","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/0166-218X(83)90021-5","volume":"5","author":"A Mansfield","year":"1983","unstructured":"Mansfield, A.: On the computational complexity of a merge recognition problem. Discrete Applied Mathematics 5(1), 119\u2013122 (1983)","journal-title":"Discrete Applied Mathematics"},{"key":"5_CR28","volume-title":"Counter-Free Automata","author":"R McNaughton","year":"1971","unstructured":"McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)"},{"key":"5_CR29","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0304-3975(78)90049-X","volume":"7","author":"JF Perrot","year":"1978","unstructured":"Perrot, J.F.: Varietes de langages et operations. Theor. Comput. Sci. 7, 197\u2013210 (1978)","journal-title":"Theor. Comput. Sci."},{"key":"5_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-2215-3","volume-title":"Varieties of formal languages","author":"J\u00c9 Pin","year":"1986","unstructured":"Pin, J.\u00c9.: Varieties of formal languages. North Oxford, London and Plenum (1986). (Traduction de Vari\u00e9t\u00e9s de langages formels)"},{"key":"5_CR31","doi-asserted-by":"crossref","unstructured":"Pin, J.-\u00c9.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, chap. 10, vol. 1, pp. 679\u2013746. Springer (1997)","DOI":"10.1007\/978-3-642-59136-5_10"},{"key":"5_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/978-3-642-21493-6_3","volume-title":"Algebraic Informatics","author":"J\u00c9 Pin","year":"2011","unstructured":"Pin, J.\u00c9.: Theme and variations on the concatenation product. In: Winkler, F. (ed.) CAI 2011. LNCS, vol. 6742, pp. 44\u201364. Springer, Heidelberg (2011)"},{"key":"5_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-642-38536-0_21","volume-title":"Computer Science \u2013 Theory and Applications","author":"R Rizzi","year":"2013","unstructured":"Rizzi, R., Vialette, S.: On recognizing words that are squares for the shuffle product. In: Bulatov, A.A., Shur, A.M. (eds.) CSR 2013. LNCS, vol. 7913, pp. 235\u2013245. Springer, Heidelberg (2013)"},{"issue":"3","key":"5_CR34","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1109\/TSE.1978.231501","volume":"SE\u20134","author":"A Shaw","year":"1978","unstructured":"Shaw, A.: Software descriptions with flow expressions. IEEE Transactions on Software Engineering SE\u20134(3), 242\u2013254 (1978)","journal-title":"IEEE Transactions on Software Engineering"},{"issue":"4","key":"5_CR35","first-page":"535","volume":"20","author":"HJ Shyr","year":"1994","unstructured":"Shyr, H.J., Yu, S.S.: Non-primitive words in the language $$p^+q^+$$. Soochow J. Math. 20(4), 535\u2013546 (1994)","journal-title":"Soochow J. Math."},{"key":"5_CR36","doi-asserted-by":"crossref","unstructured":"Tesson, P., Therien, D.: Diamonds are forever: The variety da. In: Semigroups, Algorithms, Automata and Languages, Coimbra (Portugal) 2001, pp. 475\u2013500. World Scientific (2002)","DOI":"10.1142\/9789812776884_0021"},{"issue":"3","key":"5_CR37","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/0022-0000(84)90018-7","volume":"28","author":"MK Warmuth","year":"1984","unstructured":"Warmuth, M.K., Haussler, D.: On the complexity of iterated shuffle. Journal of Computer and System Sciences 28(3), 345\u2013358 (1984)","journal-title":"Journal of Computer and System Sciences"}],"container-title":["Lecture Notes in Computer Science","Language and Automata Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-15579-1_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T10:27:38Z","timestamp":1674556058000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-15579-1_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319155784","9783319155791"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-15579-1_5","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":"24 February 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}