{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T18:49:50Z","timestamp":1777056590179,"version":"3.51.4"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Lt","issue":"05n06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2004,10]]},"abstract":"<jats:p> We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We give a faithful representation in the Cuntz C<jats:sup>\u22c6<\/jats:sup>-algebra. For the finitely presented simple group V we show that the word-length and the table size satisfy an n log n relation. We show that the word problem of V belongs to the parallel complexity class AC<jats:sup>1<\/jats:sup> (a subclass of P), whereas the generalized word problem of V is undecidable. <\/jats:p><jats:p> We study the distortion functions of V and show that V contains all finite direct products of finitely generated free groups as subgroups with linear distortion. As a consequence, up to polynomial equivalence of functions, the following three sets are the same: the set of distortions of V, the set of Dehn functions of finitely presented groups, and the set of time complexity functions of nondeterministic Turing machines. <\/jats:p>","DOI":"10.1142\/s0218196704001980","type":"journal-article","created":{"date-parts":[[2004,12,17]],"date-time":"2004-12-17T11:17:03Z","timestamp":1103282223000},"page":"569-626","source":"Crossref","is-referenced-by-count":47,"title":["THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY"],"prefix":"10.1142","volume":"14","author":[{"given":"JEAN-CAMILLE","family":"BIRGET","sequence":"first","affiliation":[{"name":"Department of Computer Science, Rutgers University at Camden, Camden, NJ 08102, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Theory of Codes","author":"Berstel J.","year":"1985"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000132"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.2307\/3597196"},{"key":"rf4","first-page":"215","volume":"42","author":"Cannon J. 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