{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:16:49Z","timestamp":1750306609868,"version":"3.41.0"},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2015,3,21]],"date-time":"2015-03-21T00:00:00Z","timestamp":1426896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Polish National Science Centre","doi-asserted-by":"crossref","award":["DEC 2012\/07\/D\/ST6\/02435"],"award-info":[{"award-number":["DEC 2012\/07\/D\/ST6\/02435"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"crossref"}]},{"name":"FWO Pegasus Marie Curie fellowship"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2015,3,21]]},"abstract":"<jats:p>\n            The\n            <jats:italic>spectrum<\/jats:italic>\n            of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models. In this article, we study the hierarchy of first-order spectra based on the number of variables. It has been conjectured that it collapses to three variables. We show the opposite: it forms an infinite hierarchy. However, despite the fact that more variables can express more spectra, we show that to establish whether the class of first-order spectra is closed under complement, it is sufficient to consider sentences using only three variables and binary relations.\n          <\/jats:p>","DOI":"10.1145\/2733376","type":"journal-article","created":{"date-parts":[[2015,4,3]],"date-time":"2015-04-03T20:29:44Z","timestamp":1428092984000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Variable Hierarchy of First-Order Spectra"],"prefix":"10.1145","volume":"16","author":[{"given":"Eryk","family":"Kopczy\u0144ski","sequence":"first","affiliation":[{"name":"University of Warsaw"}]},{"given":"Tony","family":"Tan","sequence":"additional","affiliation":[{"name":"Hasselt University and Transnational University of Limburg"}]}],"member":"320","published-online":{"date-parts":[[2015,4,2]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804090"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19550010403"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1007352.1007391"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2006.04.007"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(73)80028-5"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.2178\/bsl.1804020"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of SIAM-AMS Complexity of Computation. 27--41","author":"Fagin R.","year":"1974","unstructured":"R. Fagin . 1974 . Generalized first-order spectra and polynomial-time recognizable sets . In Proceedings of SIAM-AMS Complexity of Computation. 27--41 . R. Fagin. 1974. Generalized first-order spectra and polynomial-time recognizable sets. In Proceedings of SIAM-AMS Complexity of Computation. 27--41."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19750210117"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(93)90218-I"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/0213025"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01699468"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(90)90009-A"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.09.002"},{"key":"e_1_2_1_15_1","doi-asserted-by":"crossref","unstructured":"N. Immerman. 1999. Descriptive Complexity. Springer.  N. Immerman. 1999. Descriptive Complexity. Springer.","DOI":"10.1007\/978-1-4612-0539-5"},{"volume-title":"Proceedings of the IEEE Conference on Computational Complexity.","author":"Impagliazzo R.","key":"e_1_2_1_16_1","unstructured":"R. Impagliazzo and R. Paturi . 1999. Complexity of k-SAT . In Proceedings of the IEEE Conference on Computational Complexity. R. Impagliazzo and R. Paturi. 1999. Complexity of k-SAT. In Proceedings of the IEEE Conference on Computational Complexity."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2272354"},{"key":"e_1_2_1_18_1","doi-asserted-by":"crossref","unstructured":"E. Kopczy\u0144ski and T. Tan. 2015. Regular graphs and the spectra of two-variable logic with counting. To appear in SIAM Journal on Computing.  E. Kopczy\u0144ski and T. Tan. 2015. Regular graphs and the spectra of two-variable logic with counting. To appear in SIAM Journal on Computing.","DOI":"10.1137\/130943625"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01786976"},{"volume-title":"Computational Complexity","author":"Papadimitriou C. H.","key":"e_1_2_1_20_1","unstructured":"C. H. Papadimitriou . 1994. Computational Complexity . Addison-Wesley . C. H. Papadimitriou. 1994. Computational Complexity. Addison-Wesley."},{"key":"e_1_2_1_21_1","first-page":"395","article-title":"The observational predicate calculus and complexity of computations","volume":"16","author":"Pudl\u00e1k P.","year":"1975","unstructured":"P. Pudl\u00e1k . 1975 . The observational predicate calculus and complexity of computations . Commentationes Mathematicae Universitatis Carolinae 16 , 395 -- 398 . P. Pudl\u00e1k. 1975. The observational predicate calculus and complexity of computations. Commentationes Mathematicae Universitatis Carolinae 16, 395--398.","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200100076"}],"container-title":["ACM Transactions on Computational Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2733376","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2733376","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:17:02Z","timestamp":1750227422000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2733376"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,21]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,3,21]]}},"alternative-id":["10.1145\/2733376"],"URL":"https:\/\/doi.org\/10.1145\/2733376","relation":{},"ISSN":["1529-3785","1557-945X"],"issn-type":[{"type":"print","value":"1529-3785"},{"type":"electronic","value":"1557-945X"}],"subject":[],"published":{"date-parts":[[2015,3,21]]},"assertion":[{"value":"2014-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-04-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}