Encoding Turing machine tapes in Peano Arithmetic via Gödel's beta function
jessi_cata · x · 2026-10-18
A technical exchange on simulating a Turing machine within Peano Arithmetic: encode the tape's left and right halves as numbers in a base given by the number of tape symbols, then represent lists using Gödel's beta function, which relies on the Chinese remainder theorem, capturing the full machine state arithmetically.
Related event: Addition and Multiplication Alone Suffice to Simulate Turing Machines(4 posts)→
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