The complexity of constraint satisfaction problems and symmetric Datalog /
Bibliographic record
Abstract
Constraint satisfaction problems (CSPs) provide a unified framework for studying a wide variety of computational problems naturally arising in combinatorics, artificial intelligence and database theory. To any finite domain D and any constraint language Γ (a finite set of relations over D), we associate the constraint satisfaction problem CSP(Γ): an instance of CSP(Γ) consists of a list of variables x1, x2,..., x n and a list of constraints of the form "(x 7, x2,..., x5) ∈ R" for some relation R in Γ. The goal is to determine whether the variables can be assigned values in D such that all constraints are simultaneously satisfied. The computational complexity of CSP(Γ) is entirely determined by the structure of the constraint language Γ and, thus, one wishes to identify classes of Γ such that CSP(Γ) belongs to a particular complexity class. In recent years, logical and algebraic perspectives have been particularly successful in classifying CSPs. A major weapon in the arsenal of the logical perspective is the database-theory-inspired logic programming language called Datalog. A Datalog program can be used to solve a restricted class of CSPs by either accepting or rejecting a (suitably encoded) set of input constraints. Inspired by Dalmau's work on linear Datalog and Reingold's breakthrough that undirected graph connectivity is in logarithmic space, we use a new restriction of Datalog called symmetric Datalog to identify a class of CSPs solvable in logarithmic space. We establish that expressibility in symmetric Datalog is equivalent to expressibility in a specific restriction of second order logic called Symmetric Restricted Krom Monotone SNP that has already received attention for its close relationship with logarithmic space. We also give a combinatorial description of a large class of CSPs lying in L by showing that they are definable in symmetric Datalog. The main result of this thesis is that directed st-connectivity and a closely related CSP cannot be defined in symmetric Datalog. Because undirected st-connectivity can be defined in symmetric Datalog, this result also sheds new light on the computational differences between the undirected and directed st-connectivity problems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.005 | 0.013 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".