Maximal Kolmogorov Complexity in a Hamming Ball
研究了在给定Hamming距离r内字符串的最大Kolmogorov复杂度g_x(r)的可能取值及函数形式，通过界定g_x(r)的上下限，并探讨了其性质。
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Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument
This paper investigates necessary and sufficient conditions for the Weisfeiler–Leman (WL) graph isomorphism test to distinguish two graphs $G_1$ and $G_2$. Building on graph homomorphism counting theory, we prove that $G_1$ and $G_2$ are distinguished by the $k$-dimensional WL test if and only if there exists a tree $T$ such that the number of homomorphisms from $T$ to $G_1$ differs from that to $G_2$. To provide a concise proof of the Dvořák–Dell–Grohe–Rattan theorem, we introduce a novel asymptotic analysis framework that avoids intricate logical encodings and high-dimensional linear algebra. Instead, our approach leverages the asymptotic behavior and combinatorial structure of WL label sequences. This method significantly enhances interpretability and generality, successfully reproducing and simplifying the core argument of the original theorem. The result yields a more intuitive, lightweight algebraic–combinatorial perspective on WL tests, advancing both theoretical understanding and practical graph isomorphism discrimination.
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Maximal Kolmogorov Complexity in a Hamming Ball
研究了在给定Hamming距离r内字符串的最大Kolmogorov复杂度g_x(r)的可能取值及函数形式，通过界定g_x(r)的上下限，并探讨了其性质。
0 citationsRead paper
Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument
This paper investigates necessary and sufficient conditions for the Weisfeiler–Leman (WL) graph isomorphism test to distinguish two graphs $G_1$ and $G_2$. Building on graph homomorphism counting theory, we prove that $G_1$ and $G_2$ are distinguished by the $k$-dimensional WL test if and only if there exists a tree $T$ such that the number of homomorphisms from $T$ to $G_1$ differs from that to $G_2$. To provide a concise proof of the Dvořák–Dell–Grohe–Rattan theorem, we introduce a novel asymptotic analysis framework that avoids intricate logical encodings and high-dimensional linear algebra. Instead, our approach leverages the asymptotic behavior and combinatorial structure of WL label sequences. This method significantly enhances interpretability and generality, successfully reproducing and simplifying the core argument of the original theorem. The result yields a more intuitive, lightweight algebraic–combinatorial perspective on WL tests, advancing both theoretical understanding and practical graph isomorphism discrimination.
0 citationsRead paper