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Record W2007316622 · doi:10.1145/1714450.1714452

Formula Caching in DPLL

2010· article· en· W2007316622 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

VenueACM Transactions on Computation Theory · 2010
Typearticle
Languageen
FieldComputer Science
TopicFormal Methods in Verification
Canadian institutionsUniversity of Toronto
FundersDivision of Mathematical SciencesNational Science Foundation
KeywordsDPLL algorithmSatisfiabilityMathematical proofResolution (logic)Computer scienceTree (set theory)Simple (philosophy)AlgorithmMathematicsConjunctive normal formBoolean satisfiability problemDiscrete mathematicsTheoretical computer scienceCombinatorics

Abstract

fetched live from OpenAlex

We consider extensions of the DPLL approach to satisfiability testing that add a version of memoization , in which formulas that the algorithm has previously shown to be unsatisfiable are remembered for later use. Such formula caching algorithms have been suggested for satisfiability and stochastic satisfiability by several authors. We formalize these methods by developing extensions of the fruitful connection that has previously been developed between DPLL algorithms for satisfiability and tree-like resolution proofs of unsatisfiability. We analyze a number of variants of these formula caching methods and characterize their strength in terms of proof systems. These proof systems are new and simple, and have a rich structure. We compare them to several studied proof systems: tree-like resolution, regular resolution, general resolution, Res(k), and Frege systems and present both simulation and separations. One of our most interesting results is the introduction of a natural and implementable form of DPLL with caching, FCW reason . This system is surprisingly powerful: we prove that it can polynomially simulate regular resolution, and furthermore, it can produce short proofs of some formulas that require exponential-size resolution proofs.

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: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.632
Threshold uncertainty score0.484

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 head0.020
GPT teacher head0.308
Teacher spread0.288 · 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