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Context-Dependent Functions: Narrowing the Realm of Turing's Halting Problem

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Nicholas J. Macias

Logic in Computer Science · Submitted 13 Jan 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The conclusion of the proof of HP's undecidability is thus shown to be overly strong, as it doesn't show that no solution to HP exists, but rather that a solution must be a CDF.

how it is stated · asserted 1.00 read the record →

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arXiv ID1501.03018 (version 1)
Pith IDWWZOZALK, Pith's permanent record of this paper and its review
CitationNicholas J. Macias. "Context-Dependent Functions: Narrowing the Realm of Turing's Halting Problem." arXiv:1501.03018 (2015). https://pith.science/paper/WWZOZALK
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,284 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.22 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.74 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This paper describes Turing's Halting Problem (HP), and reviews the classic proof that no function exists that can solve HP. The concept of a "Context-Dependent Function" (CDF), whose behavior varies based on seemingly irrelevant changes to a program calling that function, is introduced, and the proof of HP's undecidability is re-examined in light of CDFs. The existence of CDFs is established via a pair of examples of such functions. The conclusion of the proof of HP's undecidability is thus shown to be overly strong, as it doesn't show that no solution to HP exists, but rather that a solution must be a CDF. A higher-level analysis of this work is given, followed by conclusions and comments on future work.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper describes Turing's Halting Problem (HP), and reviews the classic proof that no function exists that can solve HP. background 1.00 0.37 0.02 asserted 0.97
s1 The concept of a "Context-Dependent Function" (CDF), whose behavior varies based on seemingly irrelevant changes to a program calling that function, is introduced, and the proof of HP's undecidability is re-examined in light of CDFs. contribution 0.99 0.84 0.08 asserted 0.97
s2 The existence of CDFs is established via a pair of examples of such functions. result 0.49 0.89 0.04 asserted 1.00
s3 The conclusion of the proof of HP's undecidability is thus shown to be overly strong, as it doesn't show that no solution to HP exists, but rather that a solution must be a CDF. interpretation 0.64 0.89 0.91 asserted 1.00
s4 A higher-level analysis of this work is given, followed by conclusions and comments on future work. future work 0.62 0.69 0.03 asserted 0.61

What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper describes Turing's Halting Problem (HP), and reviews the classic proof that no function exists that can solve HP. The concept of a "Context-Dependent Function" (CDF), whose behavior varies based on seemingly irrelevant changes to a program calling that function, is introduced, and the proof of HP's undecidability is re-examined in light of CDFs. The existence of CDFs is established via a pair of examples of such functions. The conclusion of the proof of HP's undecidability is thus shown to be overly strong, as it doesn't show that no solution to HP exists, but rather that a solution must be a CDF. A higher-level analysis of this work is given, followed by conclusions and comments on future work.

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