{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:32:47Z","timestamp":1777645967120,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-4","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p>This paper introduces and studies two notions of easy sets without hard subsets: i) \ud835\udc9e-hollow sets are defined to be sets in P that have no \ud835\udc9e \u2013 P subsets for (presumably) superclasses \ud835\udc9e of P such as NP, PSPACE, E, NE, RE, etc.; and ii) \ud835\udc9e-scant sets are defined to be sets in P that have no many-one \ud835\udc9e-complete subsets. These sets complement well-studied objects in complexity such as P-printable sets, immune sets and complexity cores. First, characterizations of \ud835\udc9e-hollow sets and \ud835\udc9e-scant sets are obtained in terms of universally easy sets, introduced and studied in [7] as an automatic method for generating easy instances of intractable problems. Second, the following results regarding existence of \ud835\udc9e-hollow sets are obtained: infinite NP-hollow tally (equivalently, P-printable) sets exist iff some nondeterministic time complexity class equals its deterministic counterpart; in contrast, infinite E\/NE\/RE-hollow sets do not exist. Finally, it is shown that P-printable-immune sets in P are \ud835\udc9e-scant for E and NE.<\/jats:p>","DOI":"10.3233\/fi-2011-546","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T23:45:38Z","timestamp":1575330338000},"page":"321-328","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Characterizations and Existence of Easy Sets without Hard Subsets"],"prefix":"10.1177","volume":"110","author":[{"given":"Nicholas","family":"Tran","sequence":"first","affiliation":[{"name":"Department of Mathematics & Computer Science, Santa Clara University, Santa Clara, CA 95053-0290, USA. ntran@math.scu.edu"}]}],"member":"179","published-online":{"date-parts":[[2011,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-546","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-546","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:33:56Z","timestamp":1777444436000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2011-546"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,1]]},"references-count":0,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2011,6]]}},"alternative-id":["10.3233\/FI-2011-546"],"URL":"https:\/\/doi.org\/10.3233\/fi-2011-546","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,1]]}}}