Denote by HH the Halting problem. Let RU:={x∣CU(x)≥∣x∣}RU:={x∣CU(x)≥∣x∣}, where CU(x)CU(x) is the plain Kolmogorov complexity of xx under a universal decompressor UU. We prove that there exists a universal UU such that H∈PRUH∈PRU, solving the problem posted by Eric Allender.
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