Finite-state tools add only log|M| bits to finite-precision recurrent controllers, while a single tape tool yields Turing completeness with O(log|Q|+log|Γ|) bits, realized exactly by one-layer selective SSMs.
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When Does Tool Use Increase the Expressive Power of Finite-Precision Recurrent Models?
Finite-state tools add only log|M| bits to finite-precision recurrent controllers, while a single tape tool yields Turing completeness with O(log|Q|+log|Γ|) bits, realized exactly by one-layer selective SSMs.