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Record W4249399534 · doi:10.1109/lics.2004.1319634

A second-order theory for NL

2004· article· en· W4249399534 on OpenAlexaff
Simon Cook, Antonina Kolokolova

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldComputer Science
TopicLogic, Reasoning, and Knowledge
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsNondeterministic algorithmOrder (exchange)Discrete mathematicsHorn clauseBounded functionSet theoryQuantifier (linguistics)PolynomialSet (abstract data type)CombinatoricsAlgebra over a fieldPure mathematicsComputer scienceArtificial intelligence

Abstract

fetched live from OpenAlex

We introduce a second-order theory V-Krom of bounded arithmetic for nondeterministic log space. This system is based on Gradel's characterization of NL by second-order Krom formulae with only universal first-order quantifiers, which in turn is motivated by the result that the decision problem for 2-CNF satisfiability is complete for coNL (and hence for NL). This theory has the style of the authors' theory Vi-Horn [APAL 124 (2003)] for polynomial time. Both theories use Zambella's elegant second-order syntax, and are axiomatized by a set 2-BASIC of simple formulae, together with a comprehension scheme for either second-order Horn formulae (in the case of V/sub 1/-Horn), or second-order Krom (2CNF) formulae (in the case of V-Krom). Our main result for V-Krom is a formalization of the Immerman-Szelepcsenyi theorem that NL is closed under complementation. This formalization is necessary to show that the NL functions are /spl Sigma//sub 1//sup B/-definable in V-Krom. The only other theory for NL in the literature relies on the Immerman-Szelepcsenyi's result rather than proving it.

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.

How this classification was reachedexpand

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)0.000
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 score0.780
Threshold uncertainty score0.291

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.014
GPT teacher head0.243
Teacher spread0.229 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreMethods

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations5
Published2004
Admission routes1
Has abstractyes

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