database developers

Abstract: The rise of Large Language Models (LLMs) has significantly advanced text-to-SQL capabilities, but generated queries may have errors. Test datasets are important for catching errors, but having only one or a few test datasets leaves many bugs undetected. Effective testing requires multiple test datasets that can expose subtle semantic bugs and edge cases. Recent work on test data generation and equivalence checking has focused on using constraint solvers. However, constraint-based approaches are slow and not scalable. In this paper, we introduce LASSO, a framework inspired by XData, but designed to minimize the use of constraint solvers, instead prioritizing use of data generation strategies based on fast heuristics. LASSO deploys a number of "attack strategies", each targeting a specific class of semantic errors. LASSO code was built using LLM-based agentic coding. We used carefully designed workflows and rules to support effective code generation and to avoid common code generation issues. A large number of internal test cases are included in LASSO to catch errors in generated code, and more are added when we extend LASSO, to avoid subsequent regressions. Our empirical evaluation across multiple benchmarks demonstrates that LASSO outperforms the state of the art, including XData, SpotIT, ParSEval, and Polygon.

Abstract: A property-based test (PBT) checks a property of a program on many generated inputs, but writing one takes a property, a generator of valid inputs, and an oracle. LLM-based PBT writers produce all three, yet they have been evaluated only on Python libraries. We study how two of them, Proptest-AI and Agentic-PBT, generalize to ten programs in five domains: deep learning libraries, databases, system software, compilers, and LLM serving engines. Most of these programs take text in their own language, such as queries, configurations, and programs. Agentic-PBT covers more branches than Proptest-AI on seven of the ten programs with Opus 5 and on all ten with GLM-5.3-Flash. Domain-specific fuzzers cover more of the compilers and of PostgreSQL and less of PyTorch than Agentic-PBT. We filed 180 bug reports, 44 of which duplicate reports that others filed after the models' knowledge cutoffs; maintainers have confirmed 65 of the others, in all five domains, and fixed 23. We draw lessons for building and evaluating such writers: low observability hurts them, and mature fuzzers paired with LLM-written properties could check that each feature behaves as documented.

Abstract: In STOC 1972, J{ü}rg Nievergelt and Edward M.~Reingold introduced the $BB[α]$-tree, also known as a \emph{weight-balanced} tree, which for any $α\in (0,\frac{1}{2}]$ is a binary search tree where every node with induced subtree size $s$ has children with induced subtree sizes at least $α(s+1)-1$. A new rotation-based binary search tree, the \emph{PopTree}, is introduced. The PopTree stores $n$ elements and is a $BB[\tfrac1{20}]$-tree after the execution of each search and a $BB[\tfrac1{729}]$-tree at all times, notably while rebalancing. For any constant $α$, its performance on search sequences of length $Ω(n \log n)$ is proved to be within a constant factor (which can depend on $α$) of the optimal offline rotation-based binary search tree that maintains the $BB[α]$ balance invariant.

Abstract: Teams of large language model (LLM) agents are increasingly applied to complex tasks, but their collaboration protocols are mostly designed empirically, without convergence guarantees. We formalize collaborative problem solving as block optimization: each agent improves one part of a shared solution, guided by its local objective plus a correction for how its changes affect the other parts. A coordinator checks every proposal against the global objective and merges proposals that do not interfere with each other. We prove linear convergence up to an error floor that vanishes when the corrections are exact. Interfering proposals can also be merged once their combination has been checked; the rate then depends on how well the proposals actually combine, not on worst-case interactions. With GPT-OSS-120B agents on robot routing, a three-agent team finds collision-free plans in every run, better than those of a single agent that controls all robots. On a larger routing task, a six-agent team completes its search about twice as fast as the single agent (in median). Merging the best checked combination of proposals, rather than only proposals that do not interfere, cuts the team's search time by about 30%. With constants measured on the runs, our convergence bound holds in every round and follows the observed progress. We also test the theory on query planning in SQLite and on a synthetic task.

Abstract: While retrieval-augmented language models increasingly serve as literature assistants in the physical sciences, existing benchmarks evaluate them primarily on qualitative text overlap or through model-based scoring rather than against verified experimental ground truth. In experimental materials disciplines such as perovskite photovoltaics, however, the most critical inquiries are inherently quantitative and aggregate measurements across dozens or hundreds of papers. Here, we present a quantitative question-answering benchmark where all 755 ground-truth answers are computed directly from 45,441 measured device records (40,889 human-curated records through 2021 and 4,552 records extracted from 2022-2026 literature). Benchmarking six retrieval architectures over 158,274 passages from 25,662 papers using an open 14B model on a single 24 GB GPU, standard passage retrieval tops out at 16-23% accuracy (compared to 1.6-6.5% zero-shot). In contrast, equipping the language model with read-only SQL execution over the structured device table elevates accuracy to 51.5% on historical and 50.8% on prospective literature -- a 33.01.8 percentage-point advantage over hybrid text retrieval. Aggregate queries spanning extrema, distributions, and filtered record counts prove virtually unsolvable via text retrieval alone, demonstrating that systematic table extraction is an operational prerequisite for literature-scale quantitative inquiry.

Abstract: The Jaro-Winkler measure, originally developed for U.S.\ Census record linkage, captures similarities between strings and accounts for common typographical variations. Despite its widespread use, finding all string pairs that exceed a given Jaro-Winkler threshold remains challenging as the string collection grows large. Existing algorithms for computing the Jaro-Winkler similarity between two strings are either slow for short strings or require quadratic time and fail to scale to long strings. To reduce the number of string comparisons, state-of-the-art techniques perform an index-nested-loop join on trie-based indexes; however, they have only been evaluated on small datasets and high similarity thresholds. For lower similarity thresholds that are relevant in practice, these techniques incur an excessive number of costly Jaro-Winkler computations. We present a novel approach for efficient Jaro-Winkler similarity joins on large string collections. Our solution is based on three key techniques: (1) JUMP is a fast algorithm for computing the Jaro-Winkler similarity between two strings that runs in linear time for bounded alphabets. (2) Dual-bound intersection bitmaps encode strings -- represented as character sets -- into fixed-size bitmaps, which are used to prune candidate string pairs by providing effective bounds on their character overlap; unlike prior bitmap techniques, our bitmaps are equipped with a cost model and adapt to the input data. (3) Our PUMA framework groups strings by prefix to tighten filter conditions, thereby reducing the number of similarity computations. Extensive experiments on large string collections demonstrate that our approach consistently outperforms the state of the art, achieving speedups of up to three orders of magnitude.

Abstract: Tree edit distance (TED), the analog of string edit distance (ED) for hierarchical data, is the minimum number of node insertions, deletions, and substitutions transforming one labeled rooted ordered tree into another. We narrow polynomial gaps between TED and ED in near-linear-time approximation, sublinear algorithms, and dynamic algorithms. We give an $n^{o(1)}$-approximation in $O(n)$ time and, for every $0<δ<1$, a $(\log n)^{O(1/δ)}$-approximation in $O(n^{1+δ})$ time. This improves the previous near-linear-time $O(\sqrt n)$-approximation [Boroujeni et al., STOC'19] and brings TED to parity with ED in this regime up to polylogarithmic factors. With query access to the balanced-parentheses (Euler-tour) representation of the input trees, we give the first sublinear-time TED algorithm: for every $τ\in[1,n]$, it computes a $τn^{o(1)}$-approximation of $1+\mathrm{ted}$ in $O(n/τ)$ time. For dynamic TED, we give an exact algorithm with amortized update time $\tilde{O}(k^7)$ and a $(1+\varepsilon)$-approximation with amortized update time $\tilde{O}_{\varepsilon}(k)$, where $k$ caps the distance that must be reported. The exact algorithm is the first to beat recomputation in a nontrivial parameter regime. The approximation improves prior dynamic guarantees [Das et al., FOCS'25] and cannot be significantly improved in any parameter regime without a breakthrough for static $(1+\varepsilon)$-approximation of ED. All results use dynamic programming on a new hierarchical tree decomposition, analogous to partitioning strings into blocks of geometrically decreasing sizes. It combines structural properties previously achieved only in isolation, providing a framework for transferring algorithmic ideas from ED to TED, with additional ingredients addressing the obstacles in each computational setting.

Abstract: We study fully dynamic data structures for random-walk quantities on undirected expanders and fast-mixing directed graphs. For an unweighted graph whose normalized Laplacian has spectral gap at least $γ$, we give a $(1\pm\varepsilon)$ effective-resistance data structure with expected update time $O(γ^{-4}\varepsilon^{-2}\log n\log^4(n/\varepsilon))$ and expected $O(1)$ query time. For directed graphs, somewhat surprisingly, the OMv conjecture precludes a fast data structure based on rapid mixing conditions alone. To address this, we introduce the notion of $κ$-uniform directed graphs, which requires the stationary distribution to $κ$-approximate the uniform distribution, and show that in this setting, random walk based data structures with $\text{poly}(κ, \log{n}, \varepsilon^{-1})$ update/query times are possible.

Abstract: Large Language Models (LLMs) have recently improved Text-to-SQL generation, but their computational cost can hinder deployment in resource-constrained settings. This paper evaluates the Text-to-SQL capabilities of small and medium open-source LLMs (1B-8B parameters) under a controlled inference budget, focusing on how model specialization and prompt formulation affect performance. Using the Spider benchmark, we compare multiple prompt representations and assess the accuracy of generated queries. Our results show that SQL-specialized models are consistently more reliable than general-purpose and chat-oriented models at small scales, and that performance can vary substantially depending on the prompt used. To reduce this variability without resorting to larger models, we introduce three lightweight inference workflows that automatically retry with alternative prompts and/or models when failures occur, including an optional syntax-correction step. These workflows significantly improve end-to-end success rates, with a trade-off in additional inference calls. These results demonstrate a practical path to stronger Text-to-SQL performance with small LLMs, by trading modest additional inference cost for higher reliability.

Abstract: Linearizability is a standard correctness condition for concurrent objects.It takes a correct by construction sequential specification of a concurrent data structure, and produces a composable specification under atomic interleavings of operations. However, some operations like atomic exchangers are not specifiable atomically, making it difficult to reason compositionally about their specifications. Interval linearizability is the state of the art in relaxing linearizability's constraints. Formally it is a powerful framework, but it requires an interval-sequential specification of the target data structure, which we show is challenging to correctly generate or understand, even for simple operations on a single concurrent register. We propose substep linearizability, which we show is equivalent to interval linearizability using X-CCorrectness, a relaxed concurrency framework we created to compare existing linearizability semantics. We show that substep linearizability's sequential specifications are suitable for previously infeasible specification tasks, while being comparable in complexity to linearizability's sequential specifications. For evaluation, we model an atomic exchanger, a popular non-linearizable queue structure, and snapshot isolation between database transactions.

Abstract: Conversational task disambiguation over tabular data uses dialogue to resolve missing information about a user's intended task before producing a solution over tables or databases. Existing evaluation and training lack a leakage-aware foundation. Task success mixes the agent's disambiguation and solution-generation capabilities and can also reflect oracle leakage, that is, information that a user simulator reveals beyond what a real user would. Existing datasets also lack a shared representation of ambiguities and access boundaries. We introduce the notion of an ambiguous verifiable task, which formalizes ambiguities and resolutions, decomposing the agent into an asking policy and a solution policy, and the environment into an oracle and verifier. This framework provides baselines and metrics for evaluating task disambiguation separately from solution generation, formal definitions of oracle leakage, judge-free leakage diagnostics, and a training objective for the asking policy. We instantiate the framework in text-to-SQL with AmbiTab, a benchmark suite that unifies six ambiguous datasets under a common representation specifying what the agent, oracle, and verifier may access. We evaluate clarification strategies and oracle leakage, and train an asking policy with reinforcement learning. The trained asker improves our disambiguation metrics on all six datasets and task success on five, and our leakage diagnostics measure how training affects oracle leakage.

Abstract: Logic programming is increasingly used as the symbolic component of neurosymbolic AI systems. We survey the main rule-based languages in this setting, namely Datalog, answer set, and probabilistic logic programs, along four axes: semantics, expressiveness, neural integration, and evaluation mechanism. We analyse over 50 recent systems and applications, comparing formalism usage across four research areas: databases and programming languages, machine learning, vision, and robotics. We provide a decision matrix mapping application scenarios to required features and close by outlining open problems.

Abstract: We introduce \emph{sub-connectivity logic}, denoted by $\textsf{FOscon}$, an extension of first-order logic for graphs with a specified set $Z$ of admissible edges. Its additional atom $\textsf{scon}(x,y;\bar z)$ asserts that $x$ and $y$ are connected by a path using only edges of $Z$ and avoiding the vertices in $\bar z$. Our main structural result states that, for every weakly sparse graph class $\mathscr C$, the class of all expansions of graphs in $\mathscr C$ by rooted spanning forest orders has bounded twin-width if and only if $\mathscr C$ excludes a fixed minor. When $\mathscr C$ excludes a fixed minor, we can also compute an additional linear order that preserves bounded twin-width in polynomial time. We translate $\textsf{FOscon}$ into first-order logic over an expansion by a depth-first spanning forest order of the admissible-edge graph. Combining this translation with our structural result, we obtain a model checking algorithm for $\textsf{FOscon}$ with running time $f(|φ|,h(G))\cdot |G|^c$, where $f$ is computable, $c$ is an absolute constant, and $h(G)$ is the Hadwiger number of $G$. The translation and model-checking algorithm extend to binary relational structures, with the Hadwiger number measured on the Gaifman graph. For a graph class $\mathscr C$ let $\mathscr C_Z:=\{(G,Z):G\in\mathscr C,\ Z\subseteq E(G)\}$. We show that for every weakly sparse graph class $\mathscr C$, the class $\mathscr C_Z$ is monadically dependent for $\textsf{FOscon}$ if and only if $\mathscr C$ excludes a fixed minor. For monotone classes that admit efficient minor encodings, a corresponding hardness result makes this frontier computationally tight. We give applications to combinatorial reconfiguration and solution discovery problems, and study a guarded extension of $\textsf{FOscon}$ motivated by database queries.

Abstract: SQL queries that large language models write from natural language questions can execute successfully yet produce incorrect results, so execution alone does not reveal what to fix. An error taxonomy says why the query is wrong, but not where to look or how to change it. Existing methods can guide SQL correction through feedback, error reports, or generated plans alongside an unmasked query. We introduce TEG(Taxonomy-guided Error Grounding), which turns a supplied diagnosis into a structured correction input for natural language-to-SQL (NL2SQL) correction. Type-specific rules map each error type to construct classes to reconsider and an edit operation to request. TEG masks the selected constructs in the query when applicable and states that operation in an edit instruction. TEG generates candidate corrections from this input, uses execution feedback to guide candidate selection, and repeats the process one annotation at a time for queries with several errors. On NL2SQL-BUGs, TEG reaches 47.3 single-error execution accuracy and 37.0 overall with Qwen2.5-7B-Instruct. Across the model sizes and thinking modes evaluated in the main comparison, TEG outperforms all evaluated baselines on single-error queries, even when the baselines receive the same error-type annotations. With predicted types, TEG stays above direct LLM correction and ErrorLLM on single-error queries.

Abstract: In recent years, several variants of classical hash table schemes have been developed by engineers in order to take advantage of the processor's internal parallelism using SIMD instructions, which make it possible to operate on multiple bytes simultaneously. At a small additional memory cost, this enables a significant speedup, making it a data structure that is increasingly popular in practice, when very high performance is required. In this article, we provide a detailed theoretical analysis of the dynamics of such hash tables. From a methodological standpoint, we use and adapt a technique developed by Wormald in the 1990s to study dynamic graphs. This approach, which can be adapted to many variants, enables us to accurately estimate the quantities of interest by capturing the dynamics of the data structure through systems of differential equations. Although complex, we provide an explicit description of the solutions of these systems, which can furthermore be efficiently approximated numerically. Our main results are stated with high probability, which is significantly more precise than average-case analyses, and they match experimental results remarkably well, even for hash tables of moderate size.

Abstract: In this paper, we study the number of bits required to construct a dynamic dictionary with optimal time for $\texttt{rank}/\texttt{select}$ operations. Using the standard (multiplication) Word-RAM model with $w$-bit words, we construct a data-structure for a dynamic $\texttt{rank}/\texttt{select}$ dictionary for a set $S\subseteq\{0,1,\cdots,u-1\}$ of $n$ elements that, given a parameter $1\leq k\leq \log^*w$, uses $$\operatorname{lg}\binom{u}{n}+\mathcal{O}(n\log^{(k)}w)\text{ bits}$$ taking optimal $\mathcal{O}(k+\log_w n)$ time (worst-case) for all operations. We show optimality for $n=w^{\mathcal{O}(1)}$ by extending the lower bound of Li, Liang, Yu, and Zhou [FOCS 2023] to super-polynomial universes: any dynamic dictionary for $n\leq \sqrt{u}$ elements that uses $\operatorname{lg}\binom{u}{n}+\mathcal{O}(n\log^{(k)}n)$ bits requires $Ω(k)$ time for operations. Lastly, we extend the data-structure to a dynamic fully indexable dictionary (that also supports $\texttt{rank}/\texttt{select}$ on the complement of $S$).

Abstract: We present \emph{multitable} and its Rust reference implementation: a stable hash table both materially faster at equal physical memory and more flexible than the SwissTable in its Rust's hashbrown implementation. As an arithmetic mean over 84 configurations it delivers $\mathbf{2.1\times}$ hashbrown's throughput when both hash the same raw bytes and $\mathbf{1.9\times}$ when hashbrown is keyed on native integers, its best case; on negative lookups alone, $3.2\times$ and $2.9\times$. Multitable reaches \textbf{any physical load factor} up to and \textbf{including one} ($0.9999$ demonstrated), exactly for the requested capacity, compared to hashbrown which doubles at $0.777$ for 4-byte keys and values. At $75\%$ saturation of hashbrown (assumed average case of its rigid ladder) and multitable sized to $0.97$ physical load factor, hashbrown takes $66\%$ more space. The lookup probe count has no cliff as the load factor approaches one. Bucket size, physical load factor, and failure budget are parameters, and the multitable can be grown without rehashing. We implement two variants of multitable: plain and filtered. At equal physical memory on an Apple M2 Pro the filtered multitable leads hashbrown in all $84$ insert, hit, and miss configurations. Multitable is more \textbf{memory-efficient}, at equal mixed-lookup throughput on the map of $4$-byte keys and values the filtered multitable needs up to $12\%$ fewer bytes than hashbrown, and the plain multitable is $18\%$ smaller, holding $\mathbf{22\%}$ more keys in the same memory.

Abstract: Graph databases are increasingly queried through natural language, yet every existing benchmark evaluates isolated single-turn queries rather than the multi-turn sessions through which analysts actually work. We introduce CypherTurn, the first benchmark for conversational Text-to-Cypher evaluation, comprising 721 sessions and 5,927 turns across 7 knowledge graphs and 13 conversational phenomena. We evaluate 15 models under a guided oracle protocol and a fully autonomous agentic protocol, yielding four findings. First, the best model reaches only 64.7% execution accuracy, and session-level correctness remains below 5%. Second, despite strong overall rank correlation, frontier models exhibit a consequential reordering of the top of the leaderboard under autonomous operation, a phenomenon we term the Autonomy Divergence, which reveals error-management as a partially independent capability from raw generation skill. Third, scaling action budgets from x3 to x10 fails to close the autonomy gap, as the strongest frontier models self-limit to approximately two actions per turn regardless of available budget. Fourth, single-turn Cypher fine-tuning degrades multi-turn instruction following, while architecture-appropriate specialization outperforms several frontier models. These results establish CypherTurn as an open challenge for conversational graph database reasoning. Code and data are available at https://github.com/BarryQ/CypherTurn.

Abstract: Relational in-context learning (ICL) conditions predictions on the labeled support examples and their linked tables, creating a failure mode when the support set contains target-derived features that are unavailable for the query. We formulate this problem as support-set target leakage, distinct from leakage during dataset construction, temporal splitting, or representation learning. Here, the target-derived (leaker) columns are present only in the labeled support set during relational in-context inference, while queries remain clean. We construct 14 synthetic leaker types, corresponding to 20 columns, spanning proxies with different noise levels, coverage, modalities, semantic transparency, and relational distances. We evaluate a frozen relational encoder with an ICL head on held-out RelBench databases and use Integrated Gradients (IG) to rank and remove suspicious columns. Our results show that the effect of support-set leakage varies across tasks and relational distances. Target-table leakers cause the clearest degradation, while one- and two-hop leakers are not consistently used by the model. IG ranks target-table leakers highly across datasets and partially recovers performance in settings where leakage has the largest effect.

Abstract: Relational deep learning models database rows and foreign-key links as a heterogeneous graph for prediction from record attributes and relational context. These graphs contain two distinct temporal signals: record age changes with the prediction cutoff, while intervals between observed records remain fixed. Prior work often treats time as a single signal or studies temporal representation and pretraining separately. We investigate how explicitly encoding both signals affects temporal pretraining for downstream tasks. Our framework combines Multi-scale Time Encoding, which captures record age using learnable time scales and type-specific projections, with Rotary Time Encoding, which represents signed inter-record intervals through rotary transformations during graph propagation. We pair these encodings with three self-supervised objectives: historical relation recovery, horizon-aware future relation activity prediction, and temporal subgraph contrast. All inputs respect their observation cutoffs. Pretraining proceeds in two stages: subgraph contrast first learns neighborhood representations, followed by refinement through either relation recovery or future activity prediction. We evaluate on five RelBench datasets across 11 classification and regression tasks using heterogeneous GNN and graph Transformer backbones. With both encodings, the best evaluated staged schedules improve over supervised training with the same encodings by 3.02% and 1.06% on the two backbones, respectively, and over controls without pretraining or either encoding by 3.24% and 2.37%.

Abstract: Navigable graphs for nearest-neighbor search are built either incrementally, each inserted point searching a graph that mutates as construction proceeds, or in batch over a fixed substrate, which buys determinism and parallelism at a price in build time. We measure that price and find where it comes from. Instrumenting a tuned Vamana and PiPNN and building every system repeatedly in a paired design on one 64-thread machine, we separate build time into work (distance evaluations) and cost per evaluation. Letting the batch builder's substrate mutate in $B$ synchronous blocks recovers the feedback loop of incremental construction while the graph stays a function of (data, seed, parameters, $B$): eight trees with batched feedback match thirty-two frozen trees, and the build does $0.88\times$ Vamana's distance work. Yet it takes $1.55\times$ Vamana's wall-clock, because the mutating substrate costs more per evaluation. Pushing further, we find a wall that no search-based builder crosses. Every one of them, incremental or batched, evaluates distances adaptively, one dependent random access at a time, and runs $20$-$27\times$ below a dense kernel on the same machine at $d \approx 100$, five to six times of it with the data resident in cache. The gap is not a low-dimension artifact: an adaptive evaluation costs $d^{1.04}$ and a blocked one $d^{0.63}$, so the wall grows as $d^{0.4}$ and is twice as high at $d = 960$ as at $d = 128$. PiPNN's order-of-magnitude build advantage is that kernel: it evaluates as many distances per point, but as fixed-in-advance dense blocks. We show the beam cannot be batched after the fact (the useful density of a lockstep block is 2-3%), state the wall as a two-ceiling roofline, and delimit it: it binds whenever the distance is a black box or the evaluation order is data-dependent.

Abstract: Choosing Shellsort gaps is a well-known open problem. For over sixty years, successful sequences have relied on human-designed formulas, numerical searches, or number-theoretic constructions. Although stronger general bounds exist for dense or mainly theoretical families, the worst-case upper bound for a short, sparse, and practically competitive construction has not advanced beyond $N^{4/3}$ for decades. We ask whether the sequence itself can instead be learned from execution. We present an RL-driven, self-supervised system that searches over executable gap generators. Every proposal is valid by construction, and executed candidates return exact comparison and move counts; no classical sequence is used as a target. Across five independent searches, the system discovers a common rational-geometric family. A second self-supervised stage tunes only a finite prefix, producing the practical sequence $1,3,8,20,47,116,300,585,1416,3303,\ldots$. Once frozen, it obtains the lowest equal-task average operation count among seven classical baselines on 25 large tasks with $10^7<N\leq 10^8$. We complete the learned tail without changing its practical behavior: only beyond $10^{1000}$, a zero-density set of unit companions $h_s+1$ removes the remaining congruence barriers. The resulting sparse sequence has matching polynomial upper and lower exponents, up to polylogarithmic factors: $Ω(N^{1.024296451657\ldots}) \leq T(N) \leq O(N^{1.024296451657\ldots}\operatorname{polylog} N)$. The lower bound follows from Zang's recent theorem for rational-geometric sequences; our contribution is the matching upper bound. Thus one exact sequence connects self-supervised discovery, large-scale practical performance, and a substantial step below the classical $N^{4/3}$ bound for sparse practical Shellsort sequences.

Abstract: We consider union-find with deletions, where the representation and the cost of a query must depend on the current number of live elements rather than on the number of elements ever created. For every integer parameter $k\ge 2$, we give a linear-space data structure supporting $\mathsf{MakeSet}$ in $O(1)$ worst-case time, $\mathsf{Union}$ in $O(k)$ worst-case time, $\mathsf{Delete}$ in $O(1)$ worst-case time, and $\mathsf{Find}$ in $O\left(1+\frac{\log n}{\log k}\right)$ worst-case time for a set containing $n$ live elements. A deletion is given only an element handle, not the identifier of its current set. The construction separates global rank growth from local deletion repair. A logical set is represented by fewer than $k$ disjoint ranked trees. Equal-level trees are collected without physical linking until $k$ certificates are available, at which point one base-$k$ carry is performed in $O(k)$ time. Each member tree uses a strengthened form of the full/reduced local rebuilding scheme of Ben-Amram and Yoffe. A $q$-ary value argument, with $q=3/2$, couples the local trees to the base-$k$ certificates and yields the stated current-size height bound. A small but essential rule handles high-rank stars, a state that the base-$k$ carry can create but that does not arise directly in the binary-rank construction underlying the earlier local scheme.

Abstract: Assuming the Exponential Time Hypothesis (ETH), fixed-parameter tractability and polynomial-time solvability coincide for homomorphism problems specified by classes of pattern hypergraphs of bounded incidence degeneracy or bounded primal independence number. In both cases, tractability is characterised by bounded fractional hypertree width. Grohe (JACM 2007) established the corresponding FPT-PTIME equivalence under bounded arity. Our result allows unbounded arity and covers important cases such as bounded-degree patterns and patterns whose incidence graphs exclude a fixed minor. Building on the recent fractional balanced-separator framework and rounding theorem of Korchemna et al. (FOCS 2024), we prove a near-linear bound on fractional hypertree width ($\mathsf{fhw}$) in terms of adaptive width ($\mathsf{adw}$). For every hypergraph $H$ with $\mathsf{adw}(H)\geq 2$, \[ \mathsf{fhw}(H)=O\bigl(λ(H)\mathsf{adw}(H)\log\mathsf{adw}(H)\bigr), \] where $λ(H)=\min\{μ(H),\max\{1,\logα(H)\}\}$, with $μ(H)$ denoting incidence degeneracy and $α(H)$ the independence number of the primal graph. As a further consequence, we obtain a corresponding FPT-PTIME collapse for exact homomorphism counting on every bounded-$λ$ class. More generally, for every recursively enumerable class of pattern hypergraphs, fixed-parameter tractability of the parameterised homomorphism problem implies quasipolynomial-time solvability of the corresponding unparameterised problem, assuming ETH.

Abstract: Random walks are a standard tool for search problems in which a state can be updated locally and tested for being marked. When updating the state and checking whether it is marked have different costs, two classical strategies optimize different parts of the cost: checking after every step is optimal in the number of updates, while repeatedly checking only after mixing is optimal in the number of checks. For a single marked state $m$ and a walk started from its stationary distribution $π$, Dohotaru and Høyer stated that both guarantees can be matched simultaneously, for a walk that checks after blocks of a fixed length; their argument is sketched through quantum walks, and they observe that they know of no classical proof. We give a short and self-contained classical proof of such a tradeoff, for arbitrary irreducible Markov chains. The algorithm replaces the original transition matrix $P$ by the averaged walk $ \overline P_τ= \frac{1}τ\sum_{k=1}^τ P^k, $ where $τ$ is of order $π(m)HT(m)$. Using a coupling with the original walk and Kac's lemma, we prove directly that the averaged walk hits the marked state in $O(1/π(m))$ checks in expectation. The resulting search cost is \[ S + O(HT(m))U + O(1/π(m))C \] in expectation, where $S$, $U$, and $C$ denote setup, update, and checking costs.

Abstract: Query containment and equivalence drive database query optimization and rewriting. For plain conjunctive queries, both are decided by evaluating one query over a single canonical database of the other. This classical test breaks down in two settings that pervade real queries: databases with null values under SQL's three-valued semantics, and queries with order comparisons. In both, deciding containment is $Π_2^p$-complete, and the known characterizations replace it by an exponential family of test databases, leaving no practical route to certifying equivalence. We ask how the family of test databases can be shrunk. For conjunctive queries over databases with nulls, we shrink the family to one that is exponential only in a special set of variables, and place containment in NP when that set has constant size. For queries with comparisons, we construct canonical values that decide containment, and then shrink the family by decomposing the test into independent components and by splitting it along the order conflicts. Finally, we combine the two features, and prove that the number of test databases is fixed-parameter tractable in three local parameters of the two queries, with the null-only and comparison-only tests as special cases. Each test evaluates the containing query over a family of databases, an operation native to any database system.

Abstract: Large Language Model (LLM) applications often transfer domain concepts into the model's context informally, through prompt prose, schema dumps, and examples. We show that for database queries, data model concepts pass to LLMs more effectively through representations whose vocabulary terms carry declared, machine-readable semantics (controlled semantics). NLKGQ is a working system and reusable framework that does this for data modeled in a knowledge graph. A formal OWL ontology serves as the transfer mechanism, concentrating the meaning of the data into semantically precise tokens the model can use directly. In a single LLM call, NLKGQ places in the context a system prompt instructing on SPARQL, the complete domain OWL ontology, and a domain-specific prompt addition, together with the user's natural language query. The model then generates the SPARQL query directly, zero-shot. Where the native vocabulary of an existing database or federation of databases is opaque, a wrapper ontology substitutes clean terms and a runtime rewriter restores the native forms. Evaluating on DBLP-QuAD 2.0 showed that its scores depend on the graph snapshot, the endpoint used, and the wording of its machine-generated questions, so we propose DBLP-QuAD 3.1, which maintains the intent of 2.0 while making reference results deterministic, revising reference SPARQL where needed, and rewriting the natural language questions, with a frontier model, to state each reference query's intent clearly and completely. We evaluate on the DBLP-QuAD 2.0 benchmark (57.6% Match under deterministic re-scoring), DBLP-QuAD 3.1 (89.9% Match on 1,000 questions), SemOpenAlex (98% Match against a published baseline's 86% on the identical test set), and neuroimaging metadata (100%).

Abstract: Agentic systems commit state-changing actions, but additional verifiers can inherit the same upstream fault. We present VP-CONTROL, a runtime-assurance design and deterministic benchmark for cost-aware commit gates. Its 48 task templates yield 2,880 scenarios across six fault regimes. A fixed-call 2 x 2 experiment separates verifier-model diversity from evidence-source diversity. On frozen proposals from two local actor families, a cross-model vote over shared evidence approves 62.9% of unsafe proposals, versus 22.9% with an independent source. The source effect is 40.9 percentage points, compared with 11.3 for model diversity. A portfolio controller selects verification plans using only deployment-observable metadata. Approximate cluster-adjusted calibration at a nominal 5% per-task target yields 1.9% unsafe execution and 38.2% automated safe coverage on the locked test. Matched-budget portfolios also improve on fixed verification policies. Transfer remains conditional: unseen fault families yield 16-26% risk, and a FinQA check fails to reproduce the source effect with the tested small verifiers. A preregistered live HTTP/SQLite study tests concurrent writes and lost responses. After-check races defeat verifier-only gates; transactional partial guards prevent only covered failures, while a full atomic guard records no unsafe effects across 216 episodes. Idempotent request identifiers prevent duplicate effects after lost responses. The results motivate explicit evidence lineage, cost-aware selection, and commit-time enforcement, while exposing the limits of approximate calibration and local-tool generalization.