{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:13:01Z","timestamp":1750306381785,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2016,9,10]],"date-time":"2016-09-10T00:00:00Z","timestamp":1473465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Limits of Theorem Proving"},{"DOI":"10.13039\/100000925","name":"John Templeton Foundation","doi-asserted-by":"crossref","award":["20517"],"award-info":[{"award-number":["20517"]}],"id":[{"id":"10.13039\/100000925","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2016,11,15]]},"abstract":"<jats:p>\n            We study the proof complexity of Paris-Harrington\u2019s Large Ramsey Theorem for bi-colorings of graphs and of off-diagonal Ramsey\u2019s Theorem. For Paris-Harrington, we prove a non-trivial conditional lower bound in Resolution and a non-trivial upper bound in bounded-depth Frege. The lower bound is conditional on a (very reasonable) hardness assumption for a weak (quasi-polynomial) Pigeonhole principle in R\n            <jats:sc>es<\/jats:sc>\n            (2). We show that under such an assumption, there is no refutation of the Paris-Harrington formulas of size quasi-polynomial in the number of propositional variables. The proof technique for the lower bound extends the idea of using a combinatorial principle to blow up a counterexample for another combinatorial principle beyond the threshold of inconsistency. A strong link with the proof complexity of an unbalanced off-diagonal Ramsey principle is established. This is obtained by adapting some constructions due to Erd\u0151s and Mills. We prove a non-trivial Resolution lower bound for a family of such off-diagonal Ramsey principles.\n          <\/jats:p>","DOI":"10.1145\/2946801","type":"journal-article","created":{"date-parts":[[2016,9,12]],"date-time":"2016-09-12T13:33:37Z","timestamp":1473687217000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Proof Complexity of Paris-Harrington and Off-Diagonal Ramsey Tautologies"],"prefix":"10.1145","volume":"17","author":[{"given":"Lorenzo","family":"Carlucci","sequence":"first","affiliation":[{"name":"University of Rome I, Roma"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola","family":"Galesi","sequence":"additional","affiliation":[{"name":"University of Rome I, Roma"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Massimo","family":"Lauria","sequence":"additional","affiliation":[{"name":"Universitat Polit\u00e8cnica de Catalunya, Catalonia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,9,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(80)90030-8"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.05.001"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/0221068"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1995.1126"},{"volume-title":"Dubhashi and Alessandro Panconesi","year":"2009","author":"Devdatt","key":"e_1_2_1_5_1"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1961-029-9"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(81)90040-6"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(68)80038-9"},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"Leo Harrington and Jeff Paris. 1977. A mathematical incompleteness in Peano arithmetic. In Handbook of Mathematical Logic John Barwise (Ed.). North-Holland 1133--1142.  Leo Harrington and Jeff Paris. 1977. A mathematical incompleteness in Peano arithmetic. In Handbook of Mathematical Logic John Barwise (Ed.). North-Holland 1133--1142.","DOI":"10.1016\/S0049-237X(08)71130-3"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/12130.12132"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/2006985"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240070302"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275250"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm170-1-8"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-010-0212-9"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/800076.802454"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1992-1095225-4"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2002.1830"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(85)90018-4"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200028061"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.5555\/647840.736235"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2012.05.004"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.5555\/647860.736303"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539703428555"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90044-9"}],"container-title":["ACM Transactions on Computational Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2946801","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2946801","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:07:02Z","timestamp":1750223222000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2946801"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,10]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,11,15]]}},"alternative-id":["10.1145\/2946801"],"URL":"https:\/\/doi.org\/10.1145\/2946801","relation":{},"ISSN":["1529-3785","1557-945X"],"issn-type":[{"type":"print","value":"1529-3785"},{"type":"electronic","value":"1557-945X"}],"subject":[],"published":{"date-parts":[[2016,9,10]]},"assertion":[{"value":"2015-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-09-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}