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Abstract computation over first-order structures. Extras: From programs to decision trees I — arXiv:2608.20424

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.20424
License (as archived): CC0-1.0
Archived: 2026-10-18T10:57:33.603Z
SHA-256 of the archived text: d8955d86ca34949e293668b80b2e9e5a31d4ccc06f869b4438c67e6da2c3c8f6
Stable URL of this page: https://metraipolis.com/documento/dc_3aebde30ea49

How to cite

Abstract computation over first-order structures. Extras: From programs to decision trees I — arXiv:2608.20424 — arXiv (en), https://arxiv.org/abs/2608.20424 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3aebde30ea49 (Metraipolis archive dc_3aebde30ea49, sha256 d8955d86ca34949e293668b80b2e9e5a31d4ccc06f869b4438c67e6da2c3c8f6)

BibTeX

@misc{dc3aebde30ea49,
  title = {Abstract computation over first-order structures. Extras: From programs to decision trees I — arXiv:2608.20424},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.20424},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3aebde30ea49; sha256 d8955d86ca34949e293668b80b2e9e5a31d4ccc06f869b4438c67e6da2c3c8f6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.20424. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Decisions and their consequences can be described and analyzed by means of decision trees. The decisions themselves depend on questions that, whenever possible, should be answered with yes or no. The original BSS machines over the real numbers are graphs with computation nodes and branching nodes for decisions. The evaluation of BSS machines and algebraic decision trees in computer-aided geometry which have been introduced for various types of numbers generally involves the evaluation of systems of literals of first-order logic. Flowchart-like representations and decision trees are also helpful for analyzing decisions made by BSS RAMs over first-order structures. All algorithms defined by machine-oriented programs of BSS RAMs can be illustrated using flowcharts, walks, and paths in program trees. The basic structures of these tools are graphs and their visual representations can help to characterize the behavior of individual BSS RAMs and other first-order machines. We offer a theoretical framework for linking various models. Here, we introduce program paths and transition systems for transforming partial configurations which are defined syntactically and can be extended and refined later. Finally, we define standard orders for program paths and present algorithms for enumerating finite program paths.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-24 in cs.LO).
Categorie arXiv: Logic (math.LO) ; Logic in Computer Science (cs.LO).
Pagina del lavoro: https://arxiv.org/abs/2608.20424 — 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 2026-10-18T10:57:28.213Z dalla pagina https://arxiv.org/catchup/cs.LO/2026-08-24?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).