{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:35:25Z","timestamp":1759638925801},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,9]]},"abstract":"<jats:p>Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labeled with powers [Formula: see text] for binary encoded numbers [Formula: see text]. It is shown that polynomial identity testing for powerful skew arithmetic circuits belongs to [Formula: see text], which generalizes a corresponding result for (standard) skew circuits. Two applications of this result are presented: (i) Equivalence of higher-dimensional straight-line programs can be tested in [Formula: see text]; this result is even new in the one-dimensional case, where the straight-line programs produce words. (ii) The compressed word problem (or circuit evaluation problem) for certain wreath products of finitely generated abelian groups belongs to [Formula: see text]. Using the Magnus embedding, it follows that the compressed word problem for a free metabelian group belongs to [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0218196718500431","type":"journal-article","created":{"date-parts":[[2018,6,19]],"date-time":"2018-06-19T03:10:00Z","timestamp":1529377800000},"page":"979-1004","source":"Crossref","is-referenced-by-count":3,"title":["Parallel identity testing for skew circuits with big powers and applications"],"prefix":"10.1142","volume":"28","author":[{"given":"Daniel","family":"K\u00f6nig","sequence":"first","affiliation":[{"name":"Department f\u00fcr Elektrotechnik und Informatik, Universit\u00e4t Siegen, Germany"}]},{"given":"Markus","family":"Lohrey","sequence":"additional","affiliation":[{"name":"Department f\u00fcr Elektrotechnik und Informatik, Universit\u00e4t Siegen, Germany"}]}],"member":"219","published-online":{"date-parts":[[2018,9,17]]},"reference":[{"key":"S0218196718500431BIB001","doi-asserted-by":"publisher","DOI":"10.1145\/792538.792540"},{"key":"S0218196718500431BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804090"},{"key":"S0218196718500431BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793249530"},{"key":"S0218196718500431BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/0221006"},{"key":"S0218196718500431BIB005","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2002.1852"},{"key":"S0218196718500431BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(85)80041-3"},{"key":"S0218196718500431BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/0218066"},{"key":"S0218196718500431BIB009","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195085914.001.0001","volume-title":"Limits to Parallel Computation: -Completeness Theory","author":"Greenlaw R.","year":"1995"},{"key":"S0218196718500431BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(02)00025-9"},{"key":"S0218196718500431BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00064-X"},{"key":"S0218196718500431BIB012","doi-asserted-by":"publisher","DOI":"10.1145\/322358.322373"},{"key":"S0218196718500431BIB014","doi-asserted-by":"publisher","DOI":"10.1145\/2631920"},{"key":"S0218196718500431BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-004-0182-6"},{"key":"S0218196718500431BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-017-0343-z"},{"key":"S0218196718500431BIB018","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539704445950"},{"key":"S0218196718500431BIB019","doi-asserted-by":"publisher","DOI":"10.1515\/gcc-2012-0016"},{"key":"S0218196718500431BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-0748-9"},{"key":"S0218196718500431BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2014.12.014"},{"key":"S0218196718500431BIB022","doi-asserted-by":"publisher","DOI":"10.2307\/1968892"},{"key":"S0218196718500431BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/BF02522825"},{"key":"S0218196718500431BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03927-4"},{"key":"S0218196718500431BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/BF01214771"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500431","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T22:50:59Z","timestamp":1661467859000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":22,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2018,9,17]]},"published-print":{"date-parts":[[2018,9]]}},"alternative-id":["10.1142\/S0218196718500431"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500431","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}