The Illusion of Computation: Why LLMs Are Not Universal Turing Machines
This working paper argues that LLMs fail at algorithmic tasks such as arithmetic and recursion not because of scale or token-limit constraints, but because they cannot maintain deterministic state across reasoning steps. The authors conclude that LLMs are powerful statistical pattern recognizers but not universal Turing machines, and that closing this gap requires new architectures rather than further scaling.
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