{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T14:33:10Z","timestamp":1787495590775,"version":"build-2736575974"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:p>\n                    To capture the informal concept of linear time computability, we propose and discuss the class TIME(n\n                    <jats:sup>1+<\/jats:sup>\n                    ), consisting of all functions which are computable by a Successor RAM with exponent at most one; the exponent of a function is the infimum of all rational numbers r such that the function is computable in time O(n\n                    <jats:sup>r<\/jats:sup>\n                    ). This class properly contains the class NLT (\u201cNearly Linear Time\u201d)\u2014proposed by Gurevich and Shelah\u2014which contains all functions computable by a Successor RAM in time O(n(log n)\n                    <jats:sup>k<\/jats:sup>\n                    ) for some k\u2208N. Both classes are very robust under changes of the underlying machine model: using the same time bounds they can be defined by Random Access Computers, Storage Modification Machines, Kolmogorov algorithms, Random Access Turing machines etc.; this distinguishes them from similar classes defined by ordinary Turing machines. However, we show that TIME(n\n                    <jats:sup>1+<\/jats:sup>\n                    ) can be defined e.g. by multi-dimensional Turing machines or by Turing machines which can jump; this is probably not true for NLT. Furthermore we consider two notions of completeness for TIME(n\n                    <jats:sup>1+<\/jats:sup>\n                    ) and construct complete problems. These problems are based on restrictions of Gurevich\u2019s function logic for P.\n                  <\/jats:p>","DOI":"10.1142\/s0129054190000217","type":"journal-article","created":{"date-parts":[[2004,11,28]],"date-time":"2004-11-28T21:14:37Z","timestamp":1101676477000},"page":"295-307","source":"Crossref","is-referenced-by-count":15,"title":["ON THE NOTION OF LINEAR TIME COMPUTABILITY"],"prefix":"10.1142","volume":"01","author":[{"given":"ERICH","family":"GR\u00c4DEL","sequence":"first","affiliation":[{"name":"Mathematisches Institut, Universit\u00e4t Basel, Rheinsprung 21 CH-4051 Basel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054190000217","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:07:32Z","timestamp":1565172452000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054190000217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[1990,9]]}},"alternative-id":["10.1142\/S0129054190000217"],"URL":"https:\/\/doi.org\/10.1142\/s0129054190000217","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}