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Universal Construction and Exact Self-Reproduction in Ternary McCulloch-Pitts Networks — arXiv:2610.12251

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.12251
License (as archived): CC0-1.0
Archived: 2026-10-09T06:35:35.986Z
SHA-256 of the archived text: 3d935e13b5321bc641ef233f9fc72d01a82d1d399e86e28620ac5f0f321fe8c9
Stable URL of this page: https://metraipolis.com/documento/dc_eea89989be79

How to cite

Universal Construction and Exact Self-Reproduction in Ternary McCulloch-Pitts Networks — arXiv:2610.12251 — arXiv (en), https://arxiv.org/abs/2610.12251 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eea89989be79 (Metraipolis archive dc_eea89989be79, sha256 3d935e13b5321bc641ef233f9fc72d01a82d1d399e86e28620ac5f0f321fe8c9)

BibTeX

@misc{dceea89989be79,
  title = {Universal Construction and Exact Self-Reproduction in Ternary McCulloch-Pitts Networks — arXiv:2610.12251},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.12251},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eea89989be79; sha256 3d935e13b5321bc641ef233f9fc72d01a82d1d399e86e28620ac5f0f321fe8c9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.12251. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A fixed network of McCulloch-Pitts threshold units with weights in {-1,0,1} can hold other threshold networks in its state and run them: the state is a ring of banks of records, each record a unit of a stored network, and each step evaluates one record. We use such a network to carry out von Neumann's universal construction and self-reproduction exactly. As a cellular automaton keeps its rule, the fixed network keeps its weights, and what reproduces is a stored network. A constructor of 143 records reads the description of a network from its tape, builds that network in the next bank, copies the description onto the next tape and hands control to what it built; started on its own description, it rebuilds itself, weights included, in every generation. The scheme scales to a universal computer. A SUBLEQ computer of 17,598 ternary units, stored as 36,080 records and running a program of 27 instructions, builds any network that fits a bank and reproduces itself in the same way, at every word width from eight bits on; run directly, it emits the serialization of its own weights, memory and tape. Integer pre-activations give every orbit a margin of 1/2, and replicating each unit r times multiplies it by r. That suffices against noise of any size on the pre-activations, but against von Neumann's output flips only below a threshold inversely proportional to the fan-in. These results are proved in Rocq.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.NE, nuovi lavori del giorno).
Categorie arXiv: Logic in Computer Science (cs.LO) ; Neural and Evolutionary Computing (cs.NE).
Pagina del lavoro: https://arxiv.org/abs/2610.12251 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:55:51.420Z dalla pagina https://arxiv.org/list/cs.NE/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).