A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds

M. Skórski, in:, G. Jäger, S. Steila (Eds.), Springer, 2017, pp. 586–599.


Conference Paper | Published | English
Editor
;
Department
Series Title
LNCS
Abstract
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.
Publishing Year
Date Published
2017-01-01
Volume
10185
Page
586 - 599
Conference
TAMC: Theory and Applications of Models of Computation
Conference Location
Bern, Switzerland
Conference Date
2017-04-20 – 2017-04-22
ISSN
IST-REx-ID

Cite this

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:10.1007/978-3-319-55911-7_42
Skórski, M. (2017). A cryptographic view of regularity lemmas: Simpler unified proofs and refined bounds. In G. Jäger & S. Steila (Eds.) (Vol. 10185, pp. 586–599). Presented at the TAMC: Theory and Applications of Models of Computation, Bern, Switzerland: Springer. https://doi.org/10.1007/978-3-319-55911-7_42
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. https://doi.org/10.1007/978-3-319-55911-7_42.
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.
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.
Skórski, Maciej. A Cryptographic View of Regularity Lemmas: Simpler Unified Proofs and Refined Bounds. Edited by Gerhard Jäger and Silvia Steila, vol. 10185, Springer, 2017, pp. 586–99, doi:10.1007/978-3-319-55911-7_42.

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