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Record W39832950

An Exponential Time/Space Speedup For Resolution

2007· article· en· W39832950 on OpenAlexaff
Philipp Hertel, Toniann Pitassi

Bibliographic record

VenueElectronic colloquium on computational complexity · 2007
Typearticle
Languageen
FieldComputer Science
TopicLogic, Reasoning, and Knowledge
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsResolution (logic)DPLL algorithmSatisfiabilitySpeedupHeuristicsBottleneckPSPACEMathematical proofHeuristicProof complexitySpace (punctuation)Computer scienceMathematicsAlgorithmConjunctive normal formAutomated theorem provingExponential functionDiscrete mathematicsComputational complexity theoryMathematical optimizationParallel computingArtificial intelligence
DOInot available

Abstract

fetched live from OpenAlex

Satisfiability algorithms have become one of the most practi cal and successful approaches for solving a variety of real-world problems, including hardware verifi cation, experimental design, planning and diagnosis problems. The main reason for the success is due to highly optimized algorithms for SAT based on resolution. The most successful of these is clause learning, a DPLL scheme based on caching intermediate clauses that are “learned” throughout the backtrack search procedure. The main bottleneck to this approach is space, and thus there has been a tremendous amount of research aimed at identifying good heuristics for deciding what information to cache. Haken first suggested a formal approach to this issue, and Ben-Sasson [3] posed the question of whether there is a time/space tradeoff for resolution. Our main result is an optimal time/space tradeoff for resolution. Namely, we present an infinite family of propositional formulas whose minimal space proofs all have exponential time, but if just three extra units of storage are allowed, then the formulas can be proved in linear time. We also prove another related theorem. Given an unsatisfiabl e formula F and an integer k, the resolution space problem is to determine if F has a resolution proof which can be verified using space k. We prove that this problem is PSPACE complete.

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 machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.004
metaresearch head score (Gemma)0.016
Version: metacan-v3-hybrid-931329e0061cValidation 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: Methods
Teacher disagreement score0.030
Threshold uncertainty score0.099

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0040.016
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0010.003
Bibliometrics0.0010.002
Science and technology studies0.0010.002
Scholarly communication0.0040.014
Open science0.0030.003
Research integrity0.0030.006
Insufficient payload (model declined to judge)0.0300.006

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 head0.026
GPT teacher head0.298
Teacher spread0.272 · 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 source (direct Gemma or distilled Codex), 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

Citations10
Published2007
Admission routes1
Has abstractyes

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