{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T18:29:29Z","timestamp":1725560969200},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540206804"},{"type":"electronic","value":"9783540245971"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/978-3-540-24597-1_14","type":"book-chapter","created":{"date-parts":[[2010,7,29]],"date-time":"2010-07-29T03:39:20Z","timestamp":1280374760000},"page":"156-167","source":"Crossref","is-referenced-by-count":4,"title":["Word Equations over Graph Products"],"prefix":"10.1007","author":[{"given":"Volker","family":"Diekert","sequence":"first","affiliation":[]},{"given":"Markus","family":"Lohrey","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"14_CR1","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0304-3975(80)90037-7","volume":"11","author":"L. Berman","year":"1980","unstructured":"Berman, L.: The complexity of logical theories. Theo. Comp. Sci.\u00a011, 71\u201377 (1980)","journal-title":"Theo. Comp. Sci."},{"key":"14_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-663-09367-1","volume-title":"Transductions and context\u2013free languages","author":"J. Berstel","year":"1979","unstructured":"Berstel, J.: Transductions and context\u2013free languages. Teubner, Stuttgart (1979)"},{"key":"14_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/3-540-44693-1_15","volume-title":"STACS 2001","author":"V. Diekert","year":"2001","unstructured":"Diekert, V., Guti\u00e9rrez, C., Hagenah, C.: The existential theory of equations with rational constraints in free groups is PSPACE-complete. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol.\u00a02010, pp. 170\u2013182. Springer, Heidelberg (2001)"},{"issue":"1 & 2","key":"14_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0218196702000870","volume":"12","author":"V. Diekert","year":"2002","unstructured":"Diekert, V., Lohrey, M.: A note on the existential theory of equations in plain groups. Int. J. Algebra Comput.\u00a012(1 & 2), 1\u20137 (2002)","journal-title":"Int. J. Algebra Comput."},{"key":"14_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/3-540-45841-7_41","volume-title":"STACS 2002","author":"V. Diekert","year":"2002","unstructured":"Diekert, V., Lohrey, M.: Existential and positive theories of equations in graph products. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol.\u00a02285, pp. 501\u2013512. Springer, Heidelberg (2002)"},{"key":"14_CR6","doi-asserted-by":"crossref","unstructured":"Diekert, V., Lohrey, M.: Word equations over graph products. Manuscript available from the authors (2003)","DOI":"10.1007\/978-3-540-24597-1_14"},{"issue":"1-2","key":"14_CR7","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0304-3975(98)00313-2","volume":"224","author":"V. Diekert","year":"1999","unstructured":"Diekert, V., Matiyasevich, Y., Muscholl, A.: Solving word equations modulo partial commutations. Theo. Comp. Sci.\u00a0224(1-2), 215\u2013235 (1999)","journal-title":"Theo. Comp. Sci."},{"key":"14_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/3-540-48224-5_45","volume-title":"Automata, Languages and Programming","author":"V. Diekert","year":"2001","unstructured":"Diekert, V., Muscholl, A.: Solvability of equations in free partially commutative groups is decidable. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol.\u00a02076, pp. 543\u2013554. Springer, Heidelberg (2001)"},{"volume-title":"The Book of Traces","year":"1995","key":"14_CR9","unstructured":"Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)"},{"issue":"5","key":"14_CR10","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1007\/BF02112533","volume":"36","author":"V.G. Durnev","year":"1995","unstructured":"Durnev, V.G.: Undecidability of the positive \u2200\u2009\u22033-theory of a free semi-group. Sib. Math. J.\u00a036(5), 1067\u20131080 (1995)","journal-title":"Sib. Math. J."},{"key":"14_CR11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.4064\/fm-47-1-57-103","volume":"47","author":"S. Feferman","year":"1959","unstructured":"Feferman, S., Vaught, R.L.: The first order properties of products of algebraic systems. Fund. Mat.\u00a047, 57\u2013103 (1959)","journal-title":"Fund. Mat."},{"key":"14_CR12","unstructured":"Green, E.R.: Graph Products of Groups. PhD thesis, University of Leeds (1990)"},{"key":"14_CR13","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1006\/jabr.1995.1010","volume":"171","author":"S. Hermiller","year":"1995","unstructured":"Hermiller, S., Meier, J.: Algorithms and geometry for graph products of groups. J. Algebra\u00a0171, 230\u2013257 (1995)","journal-title":"J. Algebra"},{"key":"14_CR14","first-page":"147","volume":"103","author":"G.S. Makanin","year":"1977","unstructured":"Makanin, G.S.: The problem of solvability of equations in a free semigroup. Math. Sbornik\u00a0103, 147\u2013236 (1977)","journal-title":"Math. Sbornik"},{"key":"14_CR15","first-page":"735","volume":"48","author":"G.S. Makanin","year":"1984","unstructured":"Makanin, G.S.: Decidability of the universal and positive theories of a free group. Izv. Akad. Nauk SSSR, Ser. Mat.\u00a048, 735\u2013749 (1984)","journal-title":"Izv. Akad. Nauk SSSR, Ser. Mat."},{"key":"14_CR16","unstructured":"Muscholl, A.: Decision and Complexity Issues on Concurrent Systems. Habilitation thesis, Universit\u00e4t Stuttgart (1999)"},{"key":"14_CR17","first-page":"495","volume-title":"Proc. FOCS 1999","author":"W. Plandowski","year":"1999","unstructured":"Plandowski, W.: Satisfiability of word equations with constants is in PSPACE. In: Proc. FOCS 1999, pp. 495\u2013500. IEEE Computer Society Press, Los Alamitos (1999)"},{"key":"14_CR18","unstructured":"Presburger, M.: \u00dcber die Vollst\u00e4ndigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In: C. R. Congr\u00e8s Math. Pays slaves, pp. 92\u2013101 (1929)"},{"key":"14_CR19","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/BF01241140","volume":"120","author":"E. Rips","year":"1995","unstructured":"Rips, E., Sela, Z.: Canonical representatives and equations in hyperbolic groups. Invent. Math.\u00a0120, 489\u2013512 (1995)","journal-title":"Invent. Math."},{"key":"14_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/3-540-55124-7_4","volume-title":"Word Equations and Related Topics","author":"K.U. Schulz","year":"1992","unstructured":"Schulz, K.U.: Makanin\u2019s algorithm for word equations \u2014 Two improvements and a generalization. In: Schulz, K.U. (ed.) IWWERT 1990. LNCS, vol.\u00a0572, pp. 85\u2013150. Springer, Heidelberg (1992)"},{"key":"14_CR21","unstructured":"Sela, Z.: Diophantine geometry over groups VIII: The elementary theory of a hyperbolic group (2002), Available via http:\/\/www.ma.huji.ac.il\/zlil\/"}],"container-title":["Lecture Notes in Computer Science","FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-24597-1_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T19:42:39Z","timestamp":1559331759000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-24597-1_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540206804","9783540245971"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-24597-1_14","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2003]]}}}