{"publication":"SIAM Journal on Computing","issue":"4","month":"07","date_created":"2023-09-24T22:01:11Z","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics","external_id":{"isi":["001082972300004"],"arxiv":["1811.01421"]},"status":"public","article_type":"original","_id":"14364","acknowledgement":"We would like to thank Valerie King, Toniann Pitassi, and Michael Saks for helpful discussions and Shi Hao Liu for his useful feedback.\r\nThis research was supported by the Natural Science and Engineering Research Council of Canada under grants RGPIN-2015-05080 and RGPIN-2020-04178, a postgraduate scholarship, and a postdoctoral fellowship; a University of Toronto postdoctoral fellowship; the National Science Foundation under grants CCF-1217921, CCF-1301926, CCF-1637385, CCF-1650596, and IIS-1447786; the U.S. Department of Energy under grant ER26116/DE-SC0008923; the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement 805223 ScaleML; and the Oracle and Intel corporations. Some of the work on this paper was done while Faith Ellen was visiting IST Austria.","ec_funded":1,"oa_version":"Preprint","department":[{"_id":"DaAl"}],"doi":"10.1137/20M1375851","project":[{"call_identifier":"H2020","grant_number":"805223","name":"Elastic Coordination for Scalable Machine Learning","_id":"268A44D6-B435-11E9-9278-68D0E5697425"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-12-13T12:28:29Z","type":"journal_article","day":"25","language":[{"iso":"eng"}],"author":[{"full_name":"Alistarh, Dan-Adrian","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","first_name":"Dan-Adrian","last_name":"Alistarh","orcid":"0000-0003-3650-940X"},{"first_name":"James","last_name":"Aspnes","full_name":"Aspnes, James"},{"full_name":"Ellen, Faith","last_name":"Ellen","first_name":"Faith"},{"first_name":"Rati","last_name":"Gelashvili","full_name":"Gelashvili, Rati"},{"first_name":"Leqi","last_name":"Zhu","full_name":"Zhu, Leqi","id":"a2117c59-cee4-11ed-b9d0-874ecf0f8ac5"}],"page":"913-944","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.01421"}],"isi":1,"oa":1,"abstract":[{"lang":"eng","text":"We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve -set agreement among  processes or approximate agreement on a cycle of length 4 among  processes in a wait-free manner in asynchronous models where processes communicate using objects that can be constructed from shared registers. However, it was unknown whether proofs based on simpler techniques were possible. We show that these impossibility results cannot be obtained by extension-based proofs in the iterated snapshot model and, hence, extension-based proofs are limited in power."}],"year":"2023","quality_controlled":"1","volume":52,"date_published":"2023-07-25T00:00:00Z","scopus_import":"1","article_processing_charge":"No","citation":{"mla":"Alistarh, Dan-Adrian, et al. “Why Extension-Based Proofs Fail.” <i>SIAM Journal on Computing</i>, vol. 52, no. 4, Society for Industrial and Applied Mathematics, 2023, pp. 913–44, doi:<a href=\"https://doi.org/10.1137/20M1375851\">10.1137/20M1375851</a>.","ista":"Alistarh D-A, Aspnes J, Ellen F, Gelashvili R, Zhu L. 2023. Why extension-based proofs fail. SIAM Journal on Computing. 52(4), 913–944.","ieee":"D.-A. Alistarh, J. Aspnes, F. Ellen, R. Gelashvili, and L. Zhu, “Why extension-based proofs fail,” <i>SIAM Journal on Computing</i>, vol. 52, no. 4. Society for Industrial and Applied Mathematics, pp. 913–944, 2023.","apa":"Alistarh, D.-A., Aspnes, J., Ellen, F., Gelashvili, R., &#38; Zhu, L. (2023). Why extension-based proofs fail. <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/20M1375851\">https://doi.org/10.1137/20M1375851</a>","chicago":"Alistarh, Dan-Adrian, James Aspnes, Faith Ellen, Rati Gelashvili, and Leqi Zhu. “Why Extension-Based Proofs Fail.” <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/20M1375851\">https://doi.org/10.1137/20M1375851</a>.","ama":"Alistarh D-A, Aspnes J, Ellen F, Gelashvili R, Zhu L. Why extension-based proofs fail. <i>SIAM Journal on Computing</i>. 2023;52(4):913-944. doi:<a href=\"https://doi.org/10.1137/20M1375851\">10.1137/20M1375851</a>","short":"D.-A. Alistarh, J. Aspnes, F. Ellen, R. Gelashvili, L. Zhu, SIAM Journal on Computing 52 (2023) 913–944."},"title":"Why extension-based proofs fail","intvolume":"        52","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"6676"}]},"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]}}