{"oa":1,"_id":"650","scopus_import":1,"publication_status":"published","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:47:42Z","abstract":[{"text":"In this work we present a short and unified proof for the Strong and Weak Regularity Lemma, based on the cryptographic tech-nique called low-complexity approximations. In short, both problems reduce to a task of finding constructively an approximation for a certain target function under a class of distinguishers (test functions), where dis-tinguishers are combinations of simple rectangle-indicators. In our case these approximations can be learned by a simple iterative procedure, which yields a unified and simple proof, achieving for any graph with density d and any approximation parameter the partition size. The novelty in our proof is: (a) a simple approach which yields both strong and weaker variant, and (b) improvements when d = o(1). At an abstract level, our proof can be seen a refinement and simplification of the “analytic” proof given by Lovasz and Szegedy.","lang":"eng"}],"volume":10185,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","day":"01","department":[{"_id":"KrPi"}],"doi":"10.1007/978-3-319-55911-7_42","type":"conference","page":"586 - 599","status":"public","author":[{"first_name":"Maciej","last_name":"Skórski","full_name":"Skórski, Maciej","id":"EC09FA6A-02D0-11E9-8223-86B7C91467DD"}],"conference":{"location":"Bern, Switzerland","start_date":"2017-04-20","end_date":"2017-04-22","name":"TAMC: Theory and Applications of Models of Computation"},"oa_version":"Submitted Version","alternative_title":["LNCS"],"publist_id":"7119","date_updated":"2021-01-12T08:07:46Z","month":"01","year":"2017","publication_identifier":{"issn":["03029743"]},"editor":[{"first_name":"Gerhard","last_name":"Jäger","full_name":"Jäger, Gerhard"},{"full_name":"Steila, Silvia","first_name":"Silvia","last_name":"Steila"}],"title":"A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds","quality_controlled":"1","main_file_link":[{"url":"https://eprint.iacr.org/2016/965.pdf","open_access":"1"}],"intvolume":"     10185","citation":{"mla":"Skórski, Maciej. <i>A Cryptographic View of Regularity Lemmas: Simpler Unified Proofs and Refined Bounds</i>. Edited by Gerhard Jäger and Silvia Steila, vol. 10185, Springer, 2017, pp. 586–99, doi:<a href=\"https://doi.org/10.1007/978-3-319-55911-7_42\">10.1007/978-3-319-55911-7_42</a>.","short":"M. Skórski, in:, G. Jäger, S. Steila (Eds.), Springer, 2017, pp. 586–599.","ieee":"M. Skórski, “A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds,” presented at the TAMC: Theory and Applications of Models of Computation, Bern, Switzerland, 2017, vol. 10185, pp. 586–599.","ama":"Skórski M. A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds. In: Jäger G, Steila S, eds. Vol 10185. Springer; 2017:586-599. doi:<a href=\"https://doi.org/10.1007/978-3-319-55911-7_42\">10.1007/978-3-319-55911-7_42</a>","chicago":"Skórski, Maciej. “A Cryptographic View of Regularity Lemmas: Simpler Unified Proofs and Refined Bounds.” edited by Gerhard Jäger and Silvia Steila, 10185:586–99. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-55911-7_42\">https://doi.org/10.1007/978-3-319-55911-7_42</a>.","apa":"Skórski, M. (2017). A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds. In G. Jäger &#38; S. Steila (Eds.) (Vol. 10185, pp. 586–599). Presented at the TAMC: Theory and Applications of Models of Computation, Bern, Switzerland: Springer. <a href=\"https://doi.org/10.1007/978-3-319-55911-7_42\">https://doi.org/10.1007/978-3-319-55911-7_42</a>","ista":"Skórski M. 2017. A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds. TAMC: Theory and Applications of Models of Computation, LNCS, vol. 10185, 586–599."},"date_published":"2017-01-01T00:00:00Z"}