Standard CoT transformers are limited to TC^0 for length-generalizable reasoning but can simulate Turing machines with linear-length traces if vocabulary grows, using signpost tokens and change encodings.
We ensure to generate no problem instance where all variables are initialized to the same object, so the task does not become trivial
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Barriers to Universal Reasoning With Transformers (And How to Overcome Them)
Standard CoT transformers are limited to TC^0 for length-generalizable reasoning but can simulate Turing machines with linear-length traces if vocabulary grows, using signpost tokens and change encodings.