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Record W2145436131 · doi:10.1080/00207160.2012.704994

Undecidability of state complexity

2012· article· en· W2145436131 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueInternational Journal of Computer Mathematics · 2012
Typearticle
Languageen
FieldComputer Science
Topicsemigroups and automata theory
Canadian institutionsWestern UniversityQueen's University
Fundersnot available
KeywordsUndecidable problemAlphabetMathematicsState (computer science)Regular languageComputational complexity theoryDiscrete mathematicsAlgebra over a fieldAutomatonAlgorithmTheoretical computer sciencePure mathematicsComputer scienceDecidabilityLinguistics

Abstract

fetched live from OpenAlex

We consider the state complexity of compositions of regularity-preserving language operations. As our main result, we establish that determining the state complexity of an operation composed just from intersections and marked concatenations is undecidable. The proof relies on the undecidability of Hilbert's Tenth Problem. The languages used in the construction are over a fixed alphabet with at most 50 letters. We also consider some implications and generalizations, as well as discuss open problems.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.413
Threshold uncertainty score0.319

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.038
GPT teacher head0.296
Teacher spread0.258 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it