{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:09:22Z","timestamp":1767236962802},"reference-count":36,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a restricted variant of the simultaneous compressed conjugacy problem is polynomial time Turing-reducible to the same problem for the vertex groups. A direct corollary of this result is that the word problem for the outer automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Finally, it is shown that the compressed variant of the ordinary conjugacy problem can be solved in polynomial time for right-angled Artin groups. <\/jats:p>","DOI":"10.1142\/s0218196712400073","type":"journal-article","created":{"date-parts":[[2012,9,28]],"date-time":"2012-09-28T00:00:35Z","timestamp":1348790435000},"page":"1240007","source":"Crossref","is-referenced-by-count":5,"title":["COMPRESSED DECISION PROBLEMS FOR GRAPH PRODUCTS AND APPLICATIONS TO (OUTER) AUTOMORPHISM GROUPS"],"prefix":"10.1142","volume":"22","author":[{"given":"NIKO","family":"HAUBOLD","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Informatik, Universit\u00e4t Leipzig, Germany"}]},{"given":"MARKUS","family":"LOHREY","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Informatik, Universit\u00e4t Leipzig, Germany"}]},{"given":"CHRISTIAN","family":"MATHISSEN","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Informatik, Universit\u00e4t Leipzig, Germany"}]}],"member":"219","published-online":{"date-parts":[[2013,1,4]]},"reference":[{"key":"rf1","volume-title":"Algorithmic Number Theory, Vol. 1: Efficient Algorithms","author":"Bach E.","year":"1996"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9771-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2307\/1970103"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-007-9148-6"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2007.11.2227"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdn108"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1993.1052"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196711006698"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1112\/jtopol\/jtp018"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2009.13.817"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-53031-2"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196708004548"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/2563"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-02-06774-6"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-007-9054-1"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-003-0430-y"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-010-9295-2"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1010"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00167-4"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9964-6"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003001"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/52.2.318"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1145\/322017.322031"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(90)90010-F"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539704445950"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671000542X"},{"key":"rf38","volume-title":"Group-Based Cryptography","author":"Myasnikov A.","year":"2008"},{"key":"rf39","first-page":"1","volume":"9","author":"Novikov P. 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