{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:29:40Z","timestamp":1759638580964},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540432838"},{"type":"electronic","value":"9783540458418"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002]]},"DOI":"10.1007\/3-540-45841-7_39","type":"book-chapter","created":{"date-parts":[[2007,8,12]],"date-time":"2007-08-12T08:11:17Z","timestamp":1186906277000},"page":"477-488","source":"Crossref","is-referenced-by-count":3,"title":["On the Average Parallelism in Trace Monoids"],"prefix":"10.1007","author":[{"given":"Daniel","family":"Krob","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean","family":"Mairesse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis","family":"Michos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2002,2,21]]},"reference":[{"key":"39_CR1","doi-asserted-by":"crossref","unstructured":"J. Berstel and C. Reutenauer. Rational Series and their Languages. Springer Verlag, 1988.","DOI":"10.1007\/978-3-642-73235-5"},{"issue":"9","key":"39_CR2","doi-asserted-by":"publisher","first-page":"1762","DOI":"10.1109\/9.880644","volume":"45","author":"V. Blondel","year":"2000","unstructured":"V. Blondel, S. Gaubert, and J. Tsitsiklis. Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard. IEEE Trans. Autom. Control, 45(9):1762\u20131765, 2000.","journal-title":"IEEE Trans. Autom. Control"},{"key":"39_CR3","unstructured":"M. Brilman. Evaluation de Performances d\u2019une Classe de Syst\u00e8mes de Ressources Partag\u00e9es. PhD thesis, Univ. Joseph Fourier-Grenoble I, 1996."},{"issue":"2","key":"39_CR4","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1287\/moor.23.2.305","volume":"23","author":"M. Brilman","year":"1998","unstructured":"M. Brilman and J.M. Vincent. On the estimation of the throughput for a class of stochastic resources sharing systems. Mathematics of Operations Research, 23(2):305\u2013321, 1998.","journal-title":"Mathematics of Operations Research"},{"key":"39_CR5","doi-asserted-by":"crossref","unstructured":"P. Cartier and D. Foata. Probl\u00e8mes combinatoires de commutation et r\u00e9arrangements. Number 85 in Lecture Notes in Mathematics. Springer Verlag, 1969.","DOI":"10.1007\/BFb0079468"},{"key":"39_CR6","doi-asserted-by":"crossref","unstructured":"C. C\u00e9rin and A. Petit. Speedup of recognizable trace languages. In Proc. MFCS 93, number 711 in Lect. Notes Comput. Sci., pages 332\u2013341. Springer, 1993.","DOI":"10.1007\/3-540-57182-5_25"},{"key":"39_CR7","volume-title":"Pure and Applied Mathematics","author":"D. Cvetkovi\u0107","year":"1980","unstructured":"D. Cvetkovi\u0107, M. Doob, and H. Sachs. Spectra of Graphs. Theory and Application, volume 87 of Pure and Applied Mathematics. Academic Press, Paris, 1980."},{"key":"39_CR8","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/978-3-642-59126-6_8","volume":"3","author":"V. Diekert","year":"1997","unstructured":"V. Diekert and Y. M\u00e9tivier. Partial commutation and traces. In Handbook of formal languages, volume 3, pages 457\u2013533. Springer, 1997.","journal-title":"Handbook of formal languages"},{"key":"39_CR9","doi-asserted-by":"crossref","unstructured":"V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapour, 1995.","DOI":"10.1142\/2563"},{"key":"39_CR10","doi-asserted-by":"crossref","unstructured":"S. Gaubert and J. Mairesse. Task resource models and (max,+) automata. In J. Gunawardena, editor, Idempotency, volume 11, pages 133\u2013144. Cambridge University Press, 1998.","DOI":"10.1017\/CBO9780511662508.009"},{"key":"39_CR11","unstructured":"S. Gaubert and J. Mairesse. Performance evaluation of timed Petri nets using heaps of pieces. In P. Bucholz and M. Silva, editors, Petri Nets and Performance Models (PNPM\u201999), pages 158\u2013169. IEEE Computer Society, 1999."},{"issue":"3","key":"39_CR12","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0020-0190(00)00086-7","volume":"75","author":"M. Goldwurm","year":"2000","unstructured":"M. Goldwurm and M. Santini. Clique polynomials have a unique root of smallest modulus. Information Processing Letters, 75(3):127\u2013132, 2000.","journal-title":"Information Processing Letters"},{"key":"39_CR13","doi-asserted-by":"publisher","first-page":"L213","DOI":"10.1088\/0305-4470\/16\/7\/003","volume":"16","author":"V. Hakim","year":"1983","unstructured":"V. Hakim and J.-P. Nadal. Exact results for 2d directed animals on a strip of finite width. J. Phys. A: Math. Gen., 16:L213\u2013L218, 1983.","journal-title":"J. Phys. A: Math. Gen."},{"key":"39_CR14","unstructured":"A. Jean-Marie. Ers: A tool set for performance evaluation of discrete event systems. http:\/\/www-sop.inria.fr\/mistral\/soft\/ers.html ."},{"key":"39_CR15","doi-asserted-by":"crossref","unstructured":"D. Krob, J. Mairesse, and I. Michos. On the average Cartier-Foata height of traces. In Proceedings of Comb\u201901: Combinatorics, Graph Theory and Applications, Electronic Notes in Discrete Mathematics, 2001.","DOI":"10.1016\/S1571-0653(04)00386-5"},{"key":"39_CR16","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/0166-218X(92)90287-K","volume":"24","author":"N. Saheb","year":"1989","unstructured":"N. Saheb. Concurrency measure in commutation monoids. Discrete Applied Mathematics,24:223\u2013236, 1989.","journal-title":"Discrete Applied Mathematics"},{"key":"39_CR17","doi-asserted-by":"crossref","unstructured":"E. Seneta. Non-negative Matrices and Markov Chains. Springer series in statistics. Springer Verlag, Berlin, 1981.","DOI":"10.1007\/0-387-32792-4"},{"key":"39_CR18","doi-asserted-by":"crossref","unstructured":"R. Stanley. Enumerative Combinatorics, Volume I. Wadsworth & Brooks\/Cole, Monterey, 1986.","DOI":"10.1007\/978-1-4615-9763-6"},{"key":"39_CR19","doi-asserted-by":"crossref","unstructured":"G.X. Viennot. Heaps of pieces, I: Basic definitions and combinatorial lemmas. In Labelle and Leroux, editors, Combinatoire \u00c9num\u00e9rative, number 1234 in Lect. Notes in Math., pages 321\u2013350. Springer, 1986.","DOI":"10.1007\/BFb0072524"},{"key":"39_CR20","unstructured":"H. Wilf. Generatingfunctionology. Academic Press, 1990."}],"container-title":["Lecture Notes in Computer Science","STACS 2002"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45841-7_39","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T00:00:17Z","timestamp":1556755217000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45841-7_39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002]]},"ISBN":["9783540432838","9783540458418"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/3-540-45841-7_39","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2002]]}}}