Root / CYBERNETICS AND PHYSICS / Volume 15, 2026, Number 2 / An engineering reading of the bounded halting problem and observable properties of a universal machine

An engineering reading of the bounded halting problem and observable properties of a universal machine

Sergey Salishev

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.
CYBERNETICS AND PHYSICS, VOL. 15, NO. 2, 2026, 234–242
https://doi.org/10.35470/2226-4116-2026-15-2-234-242

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