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This problem is solvable (by the recursive doubling technique) on {\\bf circuits} of depth $O(\\log k)$ and size $O(kn^3)$. In contrast, we show that solving this problem on {\\bf formulas} of depth $\\log n/(\\log\\log n)^{O(1)}$ requires size $n^{\\Omega(\\log k)}$ for all $k(n) \\leq \\log\\log n$. 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Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are connected by a path of length at most $k(n)$. This problem is solvable (by the recursive doubling technique) on {\\bf circuits} of depth $O(\\log k)$ and size $O(kn^3)$. In contrast, we show that solving this problem on {\\bf formulas} of depth $\\log n/(\\log\\log n)^{O(1)}$ requires size $n^{\\Omega(\\log k)}$ for all $k(n) \\leq \\log\\log n$. 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