rnn-turing-completeness-siegelmann-sontag

IN premise — entries/2026/06/21/wiki-Neural_network_28machine_learning29-chunk-9.md

Created 2026-06-21T09:55:51+00:00

Siegelmann & Sontag (1994) proved that recurrent neural networks with rational weights are Turing-complete, and with real-valued weights they are super-Turing.

Dependents

These beliefs depend on this one:

• IN rnn-theoretical-power-exceeded-practical-utility — RNNs possess strong theoretical computational power — Turing-completeness with rational weights (Siegelmann & Sontag 1994) and context-sensitive language recognition via LSTM that surpasses what HMM-based models achieve — while their sequential hidden-state processing, which updates state at each time step, represents an inherent constraint on parallelism.
• IN rnn-turing-completeness-purest-case-of-theoretical-irrelevance — RNNs' proven Turing-completeness (Siegelmann & Sontag 1994) — the strongest computational-theoretic result for any neural architecture family — is the purest demonstration that theoretical computational power is irrelevant to paradigm survival, as Transformers displaced RNNs solely through superior hardware utilization despite possessing strictly less formal computational power.