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Record W4378713939 · doi:10.7561/sacs.2023.1.53

Maximal Existential and Universal Width

2023· article· en· W4378713939 on OpenAlex
Casey Keeler, Kai Salomaa

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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueScientific Annals of Computer Science · 2023
Typearticle
Languageen
FieldComputer Science
Topicsemigroups and automata theory
Canadian institutionsQueen's University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsDecidabilityMathematicsComputationExponential functionAutomatonFinite-state machinePolynomialTree (set theory)Discrete mathematicsExistentialismCombinatoricsAlgorithmMathematical analysisComputer science

Abstract

fetched live from OpenAlex

The tree width of an alternating finite automaton (AFA) measures the parallelism in all computations of the AFA on a given input. The maximal existential (respectively, universal) width of an AFA A on string w measures the maximal number of existential choices (respectively, of parallel universal branches) in one computation of A on w. We give polynomial time algorithms deciding finiteness of an AFA’s tree width and maximal universal width. Also we give a polynomial time algorithm that for an AFA A with finite maximal universal width decides whether or not the maximal existential width of A is finite. Finiteness of maximal existential width is decidable in the general case but the algorithm uses exponential time. Additionally, we establish necessary and sufficient conditions for an AFA to have exponential tree width growth rate, as well as sufficient conditions for an AFA to have exponential maximal existential width or exponential maximal universal width.

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)0.003
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: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.888
Threshold uncertainty score0.879

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.004
Science and technology studies0.0010.002
Scholarly communication0.0010.002
Open science0.0020.002
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 head0.044
GPT teacher head0.283
Teacher spread0.240 · 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