Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1602.01366

Semantic Acyclicity Under Constraints

Pablo Barcelo·Georg Gottlob·Andreas Pieris
View original source ↗Read source document ↗Export metadata ↓

Abstract

A conjunctive query (CQ) is semantically acyclic if it is equivalent to an acyclic one. Semantic acyclicity has been studied in the constraint-free case, and deciding whether a query enjoys this property is NP-complete. However, in case the database is subject to constraints such as tuple-generating dependencies (tgds) that can express, e.g., inclusion dependencies, or equality-generating dependencies (egds) that capture, e.g., functional dependencies, a CQ may turn out to be semantically acyclic under the constraints while not semantically acyclic in general. This opens avenues to new query optimization techniques. In this paper we initiate and develop the theory of semantic acyclicity under constraints. More precisely, we study the following natural problem: Given a CQ and a set of constraints, is the query semantically acyclic under the constraints, or, in other words, is the query equivalent to an acyclic one over all those databases that satisfy the set of constraints? We show that, contrary to what one might expect, decidability of CQ containment is a necessary but not sufficient condition for the decidability of semantic acyclicity. In particular, we show that semantic acyclicity is undecidable in the presence of full tgds (i.e., Datalog rules). In view of this fact, we focus on the main classes of tgds for which CQ containment is decidable, and do not capture the class of full tgds, namely guarded, non-recursive and sticky tgds. For these classes we show that semantic acyclicity is decidable, and its complexity coincides with the complexity of CQ containment. In the case of egds, we show that for keys over unary and binary predicates semantic acyclicity is decidable (NP-complete). We finally consider the problem of evaluating a semantically acyclic query over a database that satisfies a set of constraints; for guarded tgds and functional dependencies this problem is tractable.

Explore related subjects

cs.DBcs.LO

Keep this discovery

BibTeXRIS

Pablo Barcelo, Georg Gottlob, Andreas Pieris. 2016-02-03. Semantic Acyclicity Under Constraints. https://arxiv.org/abs/1602.01366

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

OmniTable: A Unified Wide-Table System for Petabyte-Scale LLM Data Curation and Exploration

Data curation is a critical bottleneck in industrial-grade LLM development, where petabyte-scale unstructured corpora are scattered across hundreds of physical tables, feature engineering relies on manual, table-centric pipeline orchestration, and data lineage is largely absent. We present OmniTable as an architecture blueprint for a unified wide-table layer built on Logical Unification, Physical Separation, targeting petabyte-scale LLM data curation and exploration. OmniTable makes four contributions: (1) a unified wide-table abstraction that consolidates multi-source heterogeneous data and thousands of derived features under a single logical schema via logical-physical mapping; (2) declarative feature lifecycle management that automates dependency resolution, execution planning, operator fusion, and lineage tracking, replacing manual pipeline orchestration with a "declare-and-execute" paradigm; (3) an adaptive execution engine with autonomous governance that achieves stable PB-scale feature backfill through heterogeneous compute routing (CPU/GPU), adaptive tuning, UDF-level fault tolerance, and automated storage layout optimization; and (4) hybrid-accelerated data exploration combining a global ID index, transparent OLAP offloading, and background materialized views to deliver second-level point lookups and filtered exports exceeding 20 TB/hour. In production, OmniTable manages over 35 PB of training data across web, code, PDF, and SFT domains, reducing the human-in-the-loop curation cycle from approximately 14 days to approximately 2.5 days (5.6x over the pre-OmniTable production workflow), with consistent feature versioning, auditable lineage, and minimal manual intervention.

cs.DB↗
arXiv2026

When Does Low-Bit Quantization Preserve the Decisions of Vector Search?

Low-bit quantization can achieve high recall on some vector representations and fail sharply on others, while average distortion and global rank correlation do not explain the difference. We study quantized vector search at the level of the comparisons consumed by ranking and graph-pruning algorithms. Our first result is a distribution-free decomposition: the probability that a comparison flips is bounded by the probability mass of exact margins near zero plus the tail probability of the calibrated residual. We then account for dependence between residuals that share a query or graph node, and derive covariance-aware second-moment identities and tail bounds under a joint MGF proxy. For a frozen candidate permutation, we prove a deterministic coupling theorem for Vamana neighbour selection: the approximate replay returns the exact neighbour list exactly when all candidate-level pruning actions agree on the frozen exact states. We connect these results to representation geometry through an exact Gaussian oracle, establish a strict correlation gain from a deterministic magnitude bit in an aligned bilinear model, and give a rare-contamination construction showing why marginal Gaussian diagnostics do not imply the required residual tails. When analytical assumptions are unavailable, a held-out block certificate bounds the selective failure risk of a frozen quantized rule. Across learned, classical, and synthetic embeddings, standardized exact margins predict held-out ranking and pruning flip rates substantially better than global rank correlation. The framework applies to coordinate binary codes, RaBitQ, Lucene BBQ, and product quantizers through a common decision interface.

cs.DB↗
arXiv2026

Contextual Utility of Quantization Moves in Extreme Low-Bit LLMs

Post-training quantizers select finite code changes using reconstruction proxies or local loss approximations, but the utility of a quantization move depends on the state through which it is executed. We identify two sources of this contextual dependence. First, the displacement of the move matters: evaluating the gradient at the move midpoint captures curvature accumulated along the move that a current-state linearization omits. Across frozen two-bit moves from Llama-3.2 models, midpoint evaluation predicts the direction of exact endpoint loss changes substantially more accurately than current-state gradients. Second, moves interact: exhaustive lattices of legal quantized states are well approximated by quadratic pseudo-Boolean functions, yet their small pairwise components can determine Pareto fronts and cause different evaluation functionals to prefer opposite directions. These effects explain failures of reconstruction-optimal code re-selection and additive composition. Reading each move at its own midpoint repairs the local selection step and improves downstream accuracy and held-out perplexity, while larger supports require evaluating exact endpoints from the state actually reached. Exact-endpoint beam search finds sparse changes that dominate much larger one-shot updates, and repricing the same moves after intervening changes produces widespread sign reversals. These results show that quantization utility is contextual at the granularity of a few moves: reliable construction must evaluate finite changes along their own paths and compose them from the evolving quantized state.

cs.DB↗