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Space-Bounded OTMs and REG$^{\infty}$

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Merlin Carl

Logic · Submitted 17 Jul 2017

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

The authors' main claim Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA.

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arXiv ID1707.05297 (version 3)
Pith IDT2G77LJW, Pith's permanent record of this paper and its review
CitationMerlin Carl. "Space-Bounded OTMs and REG$^{\infty}$." arXiv:1707.05297 (2017). https://pith.science/paper/T2G77LJW
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,259 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.69 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

An important theorem in classical complexity theory is that LOGLOGSPACE=REG, i.e. that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs), show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA.

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 An important theorem in classical complexity theory is that LOGLOGSPACE=REG, i.e. that languages decidable with double-logarithmic space bound are regular. background 1.00 0.03 0.04 asserted 1.00
s1 We consider a transfinite analogue of this theorem. contribution 0.82 0.54 0.03 unclear 0.61
s2 To this end, we introduce deterministic ordinal automata (DOAs), show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. contribution 0.81 0.94 0.06 asserted 1.00
s3 We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. contribution 0.72 0.59 0.04 unclear 0.61
s4 Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA. result 0.99 0.91 0.83 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • full text
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  • P abstract
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  • 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

An important theorem in classical complexity theory is that LOGLOGSPACE=REG, i.e. that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs), show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA.

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