{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:10:59Z","timestamp":1750219859315,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"PLDI","license":[{"start":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T00:00:00Z","timestamp":1686009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Proc. ACM Program. Lang."],"published-print":{"date-parts":[[2023,6,6]]},"abstract":"<jats:p>The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division protocols for the most standard setting, where the agents want to split a single item, however, the protocols are highly intricate and the proofs of envy-freeness involve tedious case analysis.<\/jats:p>\n          <jats:p>We propose Slice, a domain specific language for fair-division. Programs in our language can be converted to logical formulas encoding envy-freeness and other target properties. Then, the constraints can be dispatched to automated solvers. We prove that our constraint generation procedure is sound and complete. We also report on a prototype implementation of Slice, which we have used to automatically check envy-freeness for several protocols from the fair division literature.<\/jats:p>","DOI":"10.1145\/3591293","type":"journal-article","created":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T20:06:24Z","timestamp":1686081984000},"page":"1779-1800","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Cutting the Cake: A Language for Fair Division"],"prefix":"10.1145","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9842-7624","authenticated-orcid":false,"given":"Noah","family":"Bertram","sequence":"first","affiliation":[{"name":"Cornell University, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-4722-024X","authenticated-orcid":false,"given":"Alex","family":"Levinson","sequence":"additional","affiliation":[{"name":"Cornell University, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8953-7060","authenticated-orcid":false,"given":"Justin","family":"Hsu","sequence":"additional","affiliation":[{"name":"Cornell University, USA"}]}],"member":"320","published-online":{"date-parts":[[2023,6,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6423(99)00007-6"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2016.52"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897518.2897522"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.6092\/issn.1972-5787\/7235"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-07602-7_4"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v28i1.8802"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-99524-9_24"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2676726.2677000"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-54110-4_20"},{"key":"e_1_2_1_10_1","unstructured":"Noah Bertram Alex Levinson and Justin Hsu. 2023. Cutting the Cake: A Language for Fair Division. arxiv:2304.04642. \t\t\t\t  Noah Bertram Alex Levinson and Justin Hsu. 2023. Cutting the Cake: A Language for Fair Division. arxiv:2304.04642."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.7814374"},{"key":"e_1_2_1_12_1","first-page":"1314","article-title":"Better Ways to Cut a Cake","volume":"53","author":"Brams Steven J","year":"2006","unstructured":"Steven J Brams , Michael A Jones , and Christian Klamler . 2006 . Better Ways to Cut a Cake . Notices of the AMS , 53 , 11 (2006), 1314 \u2013 1321 . Steven J Brams, Michael A Jones, and Christian Klamler. 2006. Better Ways to Cut a Cake. Notices of the AMS, 53, 11 (2006), 1314\u20131321.","journal-title":"Notices of the AMS"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v30i1.10042"},{"key":"#cr-split#-e_1_2_1_14_1.1","unstructured":"Simina Br\u00e2nzei and Noam Nisan. 2017. The Query Complexity of Cake Cutting. https:\/\/doi.org\/10.48550\/ARXIV.1705.02946 10.48550\/ARXIV.1705.02946"},{"key":"#cr-split#-e_1_2_1_14_1.2","unstructured":"Simina Br\u00e2nzei and Noam Nisan. 2017. The Query Complexity of Cake Cutting. https:\/\/doi.org\/10.48550\/ARXIV.1705.02946"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2764468.2764511"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78800-3_24"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17511-4_20"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-89884-1_20"},{"key":"e_1_2_1_20_1","doi-asserted-by":"crossref","unstructured":"Jack Robertson and William Webb. 1998. Cake-cutting algorithms: Be fair if you can. AK Peters\/CRC Press. \t\t\t\t  Jack Robertson and William Webb. 1998. 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