An Engineering Reading of the Bounded Halting Problem and Observable Properties of a Universal Machine
Abstract
The halting problem asks whether a program eventually halts, with unrestricted resources. Engineering systems instead certify bounded halting: given a program, an input, and a step budget T, decide whether the program halts within T steps. This paper studies two of its uses. First, it defines an exact finite-budget problem, placing the simulated program and the checker on the same unit-cost timescale, so the checker can be embedded in an adversarial program. A diagonal argument with explicit additive overhead shows that no fixed deterministic checker decides every instance within any fixed fraction of T below one, for large T. In the nondeterministic case, T bounds the branch depth allowed for a stable observable decision. Second, bounded-halting instances give adversarial tests for finitary universality, since a universal model must support arbitrary finite computations as T grows. The tests check resource growth with T, the absence of a fixed deliberation bound, and later access to intermediate data. They separate a fixed model with extendable external resources, a model family that grows with T, and a larger system built around a fixed component. For machine-learning systems, this identifies the resource growth a universality claim assumes and whether it fails for deployed models.
Versions
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BibTeX
@misc{salishev2026engineering,
title = {{An Engineering Reading of the Bounded Halting Problem and Observable Properties of a Universal Machine}},
author = {Sergey Salishev},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06303},
eprint = {2611.06303},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06303},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - An Engineering Reading of the Bounded Halting Problem and Observable Properties of a Universal Machine
AU - Sergey Salishev
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06303
UR - https://arxiv.org/abs/2611.06303
AB - The halting problem asks whether a program eventually halts, with unrestricted resources. Engineering systems instead certify bounded halting: given a program, an input, and a step budget T, decide whether the program halts within T steps. This paper studies two of its uses. First, it defines an exact finite-budget problem, placing the simulated program and the checker on the same unit-cost timescale, so the checker can be embedded in an adversarial program. A diagonal argument with explicit additive overhead shows that no fixed deterministic checker decides every instance within any fixed fraction of T below one, for large T. In the nondeterministic case, T bounds the branch depth allowed for a stable observable decision. Second, bounded-halting instances give adversarial tests for finitary universality, since a universal model must support arbitrary finite computations as T grows. The tests check resource growth with T, the absence of a fixed deliberation bound, and later access to intermediate data. They separate a fixed model with extendable external resources, a model family that grows with T, and a larger system built around a fixed component. For machine-learning systems, this identifies the resource growth a universality claim assumes and whether it fails for deployed models.
ER -