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BB(3, 4) > Ack(14)
Pavel has found a 3-state 4-symbol TM which can compute an “Ackermann-level” function and halts with exactly
His code was not able to specify a human-readable bound on the TM score and it was simply specified as Halt(SuperPowers(13)) indicating 13 layers of inductive rules needed to prove it. H_n \\ & = & B(k+1, 0, g_{k+1}^{n+1}(m)) \\ \end{array}\] Through what appears to be a remarkable series of coincidences, there is a relatively simple closed form evaluation of \(g_k\) using only Knuth up-arrows and arithmetic: The goal of this project is to develop a standardized certificate format for “inductive proofs” (an umbrella term for all the sort of forward-reasoning, rule-based analyses that are ubiquitous on this blog).
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