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- W4386880015 abstract "In this paper, we show that the constant-dimensional Weisfeiler–Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) can be fruitfully used to improve parallel complexity upper bounds on isomorphism testing for several families of groups. In particular, we show: We finally consider the count-free Weisfeiler–Leman algorithm, where we show that count-free WL is unable to even distinguish Abelian groups in polynomial-time. Nonetheless, we use count-free WL in tandem with bounded non-determinism and limited counting to obtain a new upper bound of $$beta _{1}textsf {MAC}^{0}(textsf {FOLL})$$ for isomorphism testing of Abelian groups. This improves upon the previous $$textsf {TC}^{0}(textsf {FOLL})$$ upper bound due to Chattopadhyay, Torán, & Wagner (ACM Trans. Comput. Theory, 2013)." @default.
- W4386880015 created "2023-09-21" @default.
- W4386880015 creator A5061484797 @default.
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- W4386880015 date "2023-01-01" @default.
- W4386880015 modified "2023-09-27" @default.
- W4386880015 title "On the Parallel Complexity of Group Isomorphism via Weisfeiler–Leman" @default.
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- W4386880015 doi "https://doi.org/10.1007/978-3-031-43587-4_17" @default.
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