arXiv subjects

Faruk Alpay

Publications and source records attributed to Faruk Alpay.

At least 55 records · Page 3Linked to original sources

arXiv2026

Residual-Entropy Accounting for Routed Atom-Budgeted Learned Indexes

We study exact predecessor and rank search in a routed, atom-budgeted, certified-repair learned-index architecture. An ordered directory routes each query to a contiguous interval, a counted local predictor returns a certified rank window, and exact repair resolves the remaining uncertainty by comparisons. The result is scoped to this architecture and does not claim guarantees for arbitrary learned-index designs such as unconstrained RMI dispatch, hash routing, neural routing, or exact-payload indexes without additional accounting. The main parameter is conditional residual answer entropy: the entropy of the exact answer after the leaf, predictor output, certificate, and charged pre-repair information are observed. We prove a two-sided accounting theorem showing that this functional gives the query-time scale under the stated architecture and local predictor-atom budget. Directory space, sorted-array storage, and transcript-indexed repair-program space are treated as separate system costs, so the theorem is not a byte-level space lower bound or a compact implementation recipe. We also give a rank-spread specialization in which the radius term log(1 + Delta) is valid only when many residual ranks remain likely after the predictor transcript is known. For counted piecewise-linear segments, we make the profile term non-oracular, derive a shadow-price allocation rule, compute finite-instance RGapM and GapM values on real SOSD and Zenodo samples, and report benchmarks against PGM-index, RadixSpline, and binary search. The benchmarks expose overheads and bottlenecks rather than claiming speed for the shadow prototype.

cs.DS↗

arXiv2026

Cone-Induced Observation Congruences for Vector-Valued Quantitative Languages

We study the observation congruences induced by rational polyhedral cones on vector-valued quantitative languages. The extreme rays of the dual cone define intrinsic covectors, and these covectors classify every incremental residual future by a finite sign cell: negative, tight, or positive along each extremal Farkas direction. The resulting carrier is the right-stable carrier of this cone-induced observation family, whose source is canonical: the restricted covector geometry of the order cone on the residual span of the language. We organize this construction through an observation-refinement correspondence, a cone-refinement calculus, and a separation between the qualitative conic observation quotient and the numerical residual carrier needed for potential certificates. A bounded-horizon fragment is fully computable by enumeration of accumulated futures, and reproducible evaluation runs show how the conic layer detects qualitative obstruction cells before numerical refinement.

cs.FL↗

arXiv2026

AgentSecBench: Measuring Prompt Injection, Privacy Leakage, and Tool-Use Integrity in LLM Agents

LLM agents process trusted instructions, retrieved records, and tool observations through a common generative channel. This conflates data flow with authority: an untrusted string can affect a secret-bearing response or an action proposal even when no application policy authorizes that influence. We introduce AgentSecBench as an empirical instantiation of a formal security framework for this problem. The framework defines three games-instruction-integrity, retrieval-confidentiality, and capability-integrity-under a common notion of intent-to-execution noninterference with permitted leakage. It represents an application policy as a projection onto authorized observations and capabilities, distinguishes prompt annotations from enforcing projections, and measures both adversarial advantage and whether a defense closes the relevant model-visible channel before generation. The exact-marker experiments are intentionally one observable instantiation of the games rather than a complete semantic security claim: they test disclosure and forbidden-action distinguishers with unambiguous ground truth. We evaluate six defense classes with Qwen3-0.6B and Qwen3-1.7B on paired adversarial and benign-control executions. The measurements show when risk reduction follows channel closure and when a model-visible adversarial capability remains exploitable. The result is a security-oriented evaluation method: prompt text can describe a boundary, whereas provenance projection, capability restriction, and output validation can enforce one.

cs.CR↗

arXiv2026

Budgeted Dynamic Trace Structures for Token-Efficient Sequential Computation

Sequential computation increasingly produces long traces containing nested branches, status transitions, textual payloads, and compact summaries of earlier execution. This paper introduces budgeted dynamic trace structures (BDTS), a data-structural framework for maintaining rooted trace graphs and append-only histories under an explicit byte or token budget. BDTS combines status-filtered reachability, cursor pagination, soft-capped recency logs, reference-counted observation keys, delta overlays, bounded cost caches, and summary-plus-suffix compaction. We give formal invariants, asymptotic bounds, and an ancillary Rust implementation with reproducible benchmarks. Across synthetic traces with 10,000-40,000 vertices, the prototype builds graphs in 0.58-2.72 ms, enumerates all descendants in 0.24-1.42 ms, and compacts histories of 350k-2.71M approximate tokens to 1,048-4,120 approximate tokens. Tokenizer and forward measurements with three public model targets reduce 3,359-3,360 trace tokens to 432-433 tokens.

cs.DC↗

arXiv2026

Executable Boundary Contracts for Sound Event Traces

Sound event reports often compress timed boundary behavior into frame, segment, or event scores. This paper defines executable boundary contracts for finite sound event traces. The frame fragment is a bounded Boolean fragment embeddable in STL after grid projection. The event layer adds declared interval matching, duration clauses, fragmentation clauses, and obligation restricted vector scoring. The aim is measurement, not a new general temporal logic and not a challenge leaderboard. The artifact evaluates controlled Mini LibriSpeech seeded scenes, MAESTRO Real soundscapes, frozen pretrained timing probes, and an official DCASE 2024 Task 4 baseline track. Across these tracks, standard scores and contract coordinates disagree in interpretable ways. The strongest real corpus finding is that union activity can hide typed boundary failure, while external DCASE outputs provide a class indexed challenge level reference. Code, generated tables, manifests, and Lean checks for the finite frame core are supplied as ancillary material.

cs.LO↗

arXiv2026

Biprofile Deviation Logic: Report-Replacement Frames and Audit Witnesses

Biprofile deviation logic models strategic social choice states as pairs $(R,P)$, where $R$ is the true profile used for welfare comparisons and $P$ is the submitted report profile used by the rule. Coalition modalities replace only the reports of the coalition, and their relations satisfy the fixed law $E_C \circ E_D = E_{C \cup D}$. The paper proves soundness and completeness of $H_{\mathrm{bp}}$ for the abstract frame class $\mathrm{Dev}(N)$, with the reverse-composition midpoint displayed inside the canonical proof. It then separates abstract $\mathrm{Dev}(N)$-components from genuine report-coordinate products by coordinate separation. On the social-choice side, the classical facts supply the source notions; the paper-specific contribution is the audit layer for representation changes: typed manipulation witnesses, a boundary-row theorem for off-domain extensions, and a factor-closure criterion for public deletions. The ancillary material contains the input formats, an executable certificate checker, Lean and Alloy companions for the finite relational lemmas and update patterns, recorded run logs, and checksums.

cs.LO↗

arXiv2026

Composable Post-Quantum Security for FADEC-Coupled Dual-Spool Turbofan Cyber-Physical Systems

We develop a unified mathematical formulation for post-quantum authenticated telemetry and actuation in FADEC-coupled dual-spool turbofan cyber-physical systems. The formulation integrates lattice-based key establishment under LWE/SIS-style assumptions, PUF-derived attestation entropy, authenticated encryption, radar-altimeter integrity, avionics-bus timing, and Kalman residual monitoring in a stochastic hybrid model. Within this model, plant evolution, communication latency, leakage, adversarial channel quality, and cryptographic state evolve under a common filtration. We show that channel uncertainty tightens admissible key-renewal periods, that ciphertext expansion enters bus-level schedulability constraints, and that sensing and actuator limits shape integrity thresholds and allowable control delay. We further relate PUF smooth min-entropy to distinguishing advantage and connect innovation statistics to conservative alarm design. Overall, the results characterize how post-quantum security, real-time schedulability, and closed-loop stability interact in safety-critical aerospace control architectures within a defensive analytical treatment that does not provide operational guidance for interference with real platforms.

cs.CR↗

arXiv2026

Finite-Horizon First-Order Rank Profiles of Regular Languages

We introduce the finite-horizon first-order rank profile of a language $L \subseteq Σ^*$: the least quantifier rank needed by an $\mathrm{FO}[<]$ sentence to classify membership in $L$ correctly on all words of length at most $n$. The invariant measures quantifier depth only; formula size is deliberately not bounded. First, we prove a rank calculus that is independent of regularity. Every language satisfies $ρ_L(n) \le \lceil \log_2 n \rceil + 4$, via balanced first-order distance formulas and exact-word definitions. Moreover, $\sup_n ρ_L(n) < \infty$ holds exactly when $L$ is globally $\mathrm{FO}[<]$-definable, and the supremum equals the minimum quantifier rank of such a definition. Second, for regular languages we prove a sharp aperiodicity gap: if the syntactic monoid of $L$ is aperiodic, then $ρ_L(n) = O(1)$; otherwise $ρ_L(n) = \log_2 n + O_L(1)$. The lower bound extracts a nontrivial cyclic component from the syntactic monoid and combines it with an Ehrenfeucht-Fraisse power lemma for long repetitions of a fixed word. Thus, for full $\mathrm{FO}[<]$ quantifier rank, regular languages admit no intermediate finite-horizon growth between bounded and logarithmic rank.

cs.FL↗

arXiv2026

LatticeBridge: Rare-Event Sequential Inference for Faithful Structured Sequence Synthesis

Structured sequence generation often requires a model to satisfy several input-derived constraints in a single output. Standard decoding methods may assign high probability to fluent continuations while placing low mass on continuations that realize all required anchors jointly. We study this regime as a rare-event sequential inference problem. LatticeBridge combines a compact prefix language model, instance-compiled surface automata, and a twisted sequential Monte Carlo (SMC) decoder with resampling, multilevel splitting, and a source-support proposal term derived from instance-provided phrases. The constraint representation is compiled from each input instance and does not rely on manually curated lexical classes. On 2,610 attainable validation tasks spanning CommonGen, E2E NLG, and WikiBio, the particle decoder improves exact anchor satisfaction and mean anchor coverage over greedy, beam-filtered, and best-of-k ancestral baselines under a shared proposal model. Since exact anchor satisfaction alone does not rule out unsupported attribute substitutions, the evaluation reports required-anchor coverage, source coverage, source-intrusion diagnostics, overlap, runtime, and particle statistics jointly. The benchmark characterizes the faithfulness-overlap-latency frontier under a fixed proposal model.

cs.CL↗

arXiv2026

Coordinatewise Balanced Covering for Linear Gain Graphs, with an Application to Coset-List Min-2-Lin over Powers of Two

We study a list-constrained extension of modular equation deletion over powers of two, called Coset-List Min-2-Lin$^{\pm}$ over $\mathbb{Z}/2^d\mathbb{Z}$. Each variable is restricted to a dyadic coset $a+2^{\ell}(\mathbb{Z}/2^d\mathbb{Z})$, each binary constraint is of the form $x_u=x_v$, $x_u=-x_v$, or $x_u=2x_v$, and the goal is to delete a minimum number of constraints so that the remaining system is satisfiable. This problem lies between the no-list case and the poorly understood fully conservative list setting. Our main technical result is a coordinatewise balanced covering theorem for linear gain graphs labeled by vectors in $\mathbb{F}_2^r$. Given any balanced subgraph of cost at most $k$, a randomized procedure outputs a vertex set $S$ and an edge set $F$ such that $(G-F)[S]$ is balanced and, with probability $2^{-O(k^2r)}$, every hidden balanced subgraph of cost at most $k$ is contained in $S$ while all incident deletions are captured by $F$. The proof tensors the one-coordinate balanced-covering theorem of Dabrowski, Jonsson, Ordyniak, Osipov, and Wahlström across coordinates, and is combined with a rank-compression theorem replacing the ambient lifted dimension by the intrinsic cycle-label rank $ρ$. We also develop a cycle-space formulation, a cut-space/potential characterization of balancedness, a minimal-dimension statement for equivalent labelings, and an explicit bit-lifting analysis for dyadic coset systems. These yield a randomized one-sided-error algorithm running in \[ 2^{O(k^2ρ+k\log(kρ+2))}\cdot n^{O(1)}+\widetilde{O}(md+ρ^ω), \] and the same framework returns a minimum-weight feasible deletion set among all solutions of size at most $k$.

cs.DS↗

arXiv2026

Algorithmic Barriers to Detecting and Repairing Structural Overspecification in Adaptive Data-Structure Selection

We study algorithmic barriers to detecting and repairing a systematic form of structural overspecification in adaptive data-structure selection. An input instance induces an implied workload signature, such as ordering, sparsity, dynamism, locality, or substring structure, and candidate implementations may be preferred because they match that full signature even when the measured workload evidence supports only a strict subset of it. Under a model in which pairwise evaluators favor implementations that realize the implied signature, we show that this preference propagates through both benchmark aggregation and Bradley-Terry-Luce fitting. We then establish two main results. First, determining whether a representation-selection pipeline exhibits structural commitment beyond measured warrant is undecidable on unbounded input domains, by reduction from the halting problem, but decidable by exhaustive enumeration on finite domains. Second, under a conservative repair constraint requiring already evidence-aligned pipelines to remain unchanged, any total computable repair operator admits an overspecified fixed point via Kleene's recursion theorem. These barriers are qualitatively different from classical lower bounds in data-structure design: they do not limit efficiency on finite workloads, but the possibility of uniformly detecting and repairing overspecification across pipeline families.

cs.CC↗

arXiv2026

Attention Meets Reachability: Structural Equivalence and Efficiency in Grammar-Constrained LLM Decoding

We study grammar-constrained decoding (GCD) as a coupling between an autoregressive next-token distribution and a reachability oracle over a pushdown system compiled from a context-free grammar (CFG). We prove an oracle invariance theorem: language-equivalent grammars induce identical admissible next-token sets for every prefix, hence identical logit masks, yet can yield provably different compiled state spaces and online ambiguity costs. We give exact control-state blowup counts for the canonical $a^n b^n$ language under redundant nonterminal delegation, and introduce a left-to-right structural ambiguity cost (SAC) measuring incremental packed-parse-forest growth per token. For two equivalent grammars over all finite strings, SAC is $O(1)$ per token under right-recursion but $Θ(t^2)$ per token and $Θ(n^3)$ cumulatively under concatenation. We establish engine-independent lower bounds: any sound, retrieval-efficient, parse-preserving online masking engine must incur $Ω(t^2)$ work per token on a specific constant-size CFG family, unconditionally within this model. We define decoding-cost equivalence classes of grammars and prove existence of minimal-SAC representatives within bounded rewrite families. Finally, we characterize the true conditional sampler via a Doob $h$-transform and derive sharp one-step KL and total-variation distortion bounds for hard-masked decoding in terms of survival-probability spread among admissible next tokens. We integrate these results with Transformer and Mixture-of-Experts architectures, derive latency envelopes in terms of vocabulary size, active state sets, and beam width, and connect SAC to instrumentation-based predictive performance models and automated grammar optimization.

cs.CL↗

arXiv2026

Grammar-Constrained (CFL) Reachability: Subcubic Preprocessing, Indexing Trade-offs, and Structured Decoding Semantics

We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free grammars, and analyze its theoretical runtime bounds. To complement our theoretical results, we conduct an extensive empirical evaluation on a comprehensive benchmark of real-world schemas, comparing different algorithmic variants and reporting performance trade-offs. Our results highlight the impact of grammar structure and graph characteristics on reachability computation, and provide guidance for selecting efficient approaches in practice.

cs.DS↗

arXiv2026

Latent Objective Induction and Diversity-Constrained Selection: Algorithms for Multi-Locale Retrieval Pipelines

We present three algorithms with formal correctness guarantees and complexity bounds for the problem of selecting a diverse, multi-locale set of sources from ranked search results. First, we formulate weighted locale allocation as a constrained integer partition problem and give an $O(n \log n)$ algorithm that simultaneously satisfies minimum-representation, budget-exhaustion, and proportionality-bound constraints; we prove all three hold with a tight deviation bound of $< 1$. Second, we define a cascaded country-code inference function as a deterministic priority chain over heterogeneous signals (TLD structure, model-inferred metadata, language fallback) and prove it satisfies both determinism and graceful degradation. Third, we introduce a $κ$-domain diversity constraint for source selection and give an $O(|K| \cdot R)$ algorithm that maintains the invariant via hash-map lookup, eliminating the aggregator monopolization pathology present in URL-level deduplication. We further formalize Latent Objective Induction (LOI), an environment-shaping operator over prompt spaces that steers downstream model behavior without restricting the feasible output set, and prove its convergence under mild assumptions. Applied to a multi-locale retrieval pipeline, these algorithms yield 62% improvement in first-party source ratio and 89% reduction in same-domain duplication across 120 multilingual queries.

cs.DS↗

arXiv2026

Asymptotic Semantic Collapse in Hierarchical Optimization

Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics, yielding near-uniform behavior across agents. We study this effect under the name Asymptotic Semantic Collapse in Hierarchical Optimization. In a closed linguistic setting with a Dominant Anchor Node whose semantic state has effectively infinite inertia, we show that repeated interactions with Peripheral Agent Nodes drive an asymptotic alignment that minimizes a global loss. We model semantic states as points on a Riemannian manifold and analyze the induced projection dynamics. Two consequences follow. First, the limiting semantic configuration is insensitive to the optimization history: both smooth gradient-style updates and stochastic noisy updates converge to the same topological endpoint, establishing path independence at convergence. Second, the degree of context dependence controls information content: moving from atomic (independent) representations to fully entangled (context-bound) representations forces the node entropy, interpreted as available degrees of freedom, to vanish in the limit. The theory connects information-theoretic quantities with differential-geometric structure and suggests an interpretation as an immutable consensus rule that constrains agents to a shared semantic grammar. A lightweight dataset-free benchmark on an RWKV-7 13B GGUF checkpoint complements the analysis, reporting zero hash collisions, mean compliance of 0.50 under greedy decoding and 0.531 under stochastic decoding, and final Jaccard-to-anchor similarity values of 0.295 and 0.224, respectively.

cs.CL↗

arXiv2026

Stochastic Indexing Primitives for Non-Deterministic Molecular Archives

Random access remains a central bottleneck in DNA-based data storage. Existing systems typically retrieve records by PCR enrichment or other multi-step biochemical procedures, which do not naturally support fast, massively parallel, content-addressable queries. We introduce the Holographic Bloom Filter (HBF), a probabilistic indexing primitive that stores key-pointer associations as a single high-dimensional memory vector. HBF binds a key vector and a value (pointer) vector using circular convolution and superposes bindings across all records. A query decodes by correlating the memory with the query key and selecting the best matching value using a margin-based decision rule. We give construction and decoding algorithms and a probabilistic analysis under explicit noise models (memory corruption and query/key mismatches). The analysis provides concentration bounds for match and non-match score distributions, explicit threshold and margin settings for a top K decoder, and exponential error decay in the vector dimension under standard randomness assumptions. HBF offers a concrete, analyzable alternative to pointer-chasing molecular data structures, enabling one-shot associative retrieval while quantifying trade-offs among dimensionality, dataset size, and noise.

cs.DS↗

arXiv2026

Topological Relational Theory: A Simplicial-Complex View of Functional Dependencies, Lossless Decomposition, and Acyclicity

We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological invariants (Betti numbers) to diagnose cyclic dependency structure. We define Simplicial Normal Form (SNF) as homological acyclicity of the dependency complex in positive dimensions, i.e., vanishing reduced homology for all $n \ge 1$. SNF is intentionally weaker than contractibility and does not identify homology with homotopy. For decompositions, we give a topological reformulation of the classical binary lossless-join criterion: assuming dependency preservation, a decomposition is lossless exactly when the intersection attributes form a key for at least one component. Topologically, this yields a strong deformation retraction that trivializes the relevant Mayer--Vietoris boundary map. For multiway decompositions, we show how the nerve of a cover by induced subcomplexes provides a computable certificate: a 1-cycle in the nerve (detected by $H_1$) obstructs join-tree structure and aligns with cyclic join behavior in acyclic-scheme theory. Finally, we discuss an algorithmic consequence: Betti numbers of the dependency complex (or of a decomposition nerve) can be computed from boundary matrices and used as a lightweight schema diagnostic to localize "unexplained" dependency cycles, complementing standard FD-chase tests.

cs.DB↗

arXiv2026

Latent Object Permanence: Topological Phase Transitions, Free-Energy Principles, and Renormalization Group Flows in Deep Transformer Manifolds

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where $C^{(\ell)}=\mathbb{E}[h^{(\ell)}h^{(\ell)\top}]$, and track deviations from a random-matrix bulk. Across model scales (1.5B--30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, $Ω(h)=1-\|h\|_1/(\sqrt{d}\|h\|_2)$, exhibits a discontinuity near a critical normalized depth $γ_c\approx 0.42$ in sufficiently large models. We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics. The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space, which we call Transient Class Objects (TCOs). We provide theoretical conditions connecting logical separability to spectral decay and validate the predicted signatures with layerwise probes on multiple open-weight model families.

cs.LG↗