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5,200 recordsLinked to original sources
arXiv2026

GUI-CC: Benchmarking Contextual Consistency of GUI World Models as Agent Environments

GUI world models are increasingly evaluated as one-step next-screen predictors, yet their intended use is often as multi-step environments for GUI agents. This mismatch leaves a key requirement under-tested: generated states must remain contextually consistent when they are repeatedly reused for future interaction. We introduce GUI-CC, a benchmark that evaluates contextual consistency of GUI world models as agent environments rather than isolated next-screen predictors. GUI-CC contains two complementary tracks: an offline reference-action track that rolls models along real mobile GUI trajectories, and an online agent-loop track that lets fixed probing agents interact with model-generated UIs. We construct 500 offline trajectory tasks from GUIOdyssey and 200 emulator-verified online tasks across 30 mobile apps. GUI-CC evaluates transition fidelity, transition plausibility, contextual consistency, and task progress. Experiments show that plausible single-step generation does not guarantee reliable environment simulation: current models often produce usable-looking screens while failing to preserve task-relevant context or support executable multi-step rollouts.

cs.CL↗
arXiv2026

CC-4DGS: Computational Deformation and Point-Cloud Compression for Storage-Efficient Dynamic Gaussian Splatting

Dynamic four-dimensional (4D) Gaussian Splatting has emerged as a powerful explicit representation for high-quality view synthesis, yet existing methods still require tens to hundreds of megabytes per scene due to their heavy reliance on large multi-resolution hash tables and high-dimensional Gaussian attributes. This paper presents CC-4DGS, a storage-efficient and scalable framework that rethinks both deformation modeling and canonical attribute storage. First, we introduce a computational deformation field (CDF) that replaces large multi-resolution learnable hash tables with deterministic dense hash encoding and compact neural decoders, enabling on-the-fly synthesis of deformation features while reducing deformation storage to only 1--3 MB per scene. Second, we propose a compression of canonical point-cloud attributes (CCA) pipeline that compresses high-dimensional spherical harmonic appearance terms and auxiliary Gaussian attributes via conditional autoencoding, selective quantization, and residual codebooks, achieving 3--5$\times$ point-cloud reduction with negligible quality loss. Together, these components yield a unified representation that preserves real-time rendering performance while reducing total storage to 20--30 MB. Extensive experiments across the N3DV and Technicolor Light Field datasets demonstrate that CC-4DGS achieves reconstruction accuracy comparable to state-of-the-art methods such as Swift4D, while offering significantly improved storage efficiency and favorable runtime-memory trade-offs.

cs.CV↗
arXiv2026

It's Hard to PArcK

We show that Partizan Arc Kayles (PArcK), a generalization of Domineering to graphs, is PSPACE-complete via a reduction from Positive CNF and with recently-discovered techniques for creating PArcK positions with high temperature. The reduction uses only red and blue edges.

cs.CC↗
arXiv2026

Completely Reachable Road Coloring

We characterize the digraphs that admit an edge labeling by letters from a finite alphabet such that the resulting labeled digraph is a completely reachable automaton. This class of digraphs can be recognized in polynomial time. In contrast, we show that, for every fixed alphabet size, the problem of deciding whether a digraph admits an edge labeling with the same property is NP-complete. We also classify the digraphs for which every edge labeling results in a completely reachable automaton.

cs.FL↗
arXiv2026

Upper and lower bounds on the OBDD-width of a special integer multiplication

We consider the Boolean function ${\rm SMul}_{n-1}^n(\boldsymbol{x},\boldsymbol{y})$, which computes the middle bit of the multiplication of two natural numbers represented as $n$-bit binary strings $\boldsymbol{x}$ and $\boldsymbol{y}$, drawn from a restricted domain. We investigate the width of OBDDs computing ${\rm SMul}_{n-1}^n$. We introduce a combinatorially defined function $s_*(n)$ and show that the width of such OBDDs is $Θ(2^{s_*(n)})$.

cs.CC↗
arXiv2026

A note on the $Σ_2^P$-completeness of the Frobenius number

Given a finite set $A$ of natural numbers whose greatest common divisor is one, the Frobenius number $g(A)$ is the largest integer that is not a non-negative integer combination of the numbers in $A$. In a 2016 preprint, Matsubara states that given $A$ and $k$, deciding if $g(A) \geq k$ is $Σ_2^P$-complete. A decade has passed since without peer-reviewed publication of this result. At the same time, the community has found it difficult to verify this result. In this note, we give a write-up of the completeness proof based on Matsubara (2016).

cs.CC↗
arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗
arXiv2026

On the Complexity of Bayesian Signal Processing

We develop a computational framework for Bayesian decision-making. We show that as long as no action is optimal in every state, Bayes-optimal choice is intractable. This hardness need not arise from large action, state, or signal spaces, nor from a complicated represented utility function: extracting enough information from a hard-to-interpret signal to act optimally can itself be computationally hard. We also characterize tractability across approximation notions and identify their sources of difficulty. Under the probably approximately correct criterion, sample-based Bayesian learning is tractable if and only if the signal support is bounded. Our results provide justifications for bounded rationality, costly Bayesian inference, and sample-based Bayesian learning.

econ.TH↗
arXiv2026

Quantified propositional calculi and narrow implicit proofs

In the implicit version of a propositional proof system Q, we work with Q-proofs that are not written down directly, but are succinctly encoded by circuits. Thus implicit Q-proofs are potentially exponentially shorter than usual Q-proofs. We study narrow implicit proofs, a restricted version of this notion, in which lines in the encoded proof can only have polynomial size. We use a cut-elimination construction to show that G_{i+1} is equivalent to narrow implicit G_i, for i >= 1, where G_i is the extension of Frege allowing reasoning with Sigma^q_i quantified propositional formulas. We show that G_1 is equivalent to implicit resolution.

cs.LO↗
arXiv2026

Goal Staying Makes Sum-of-Costs Anonymous Multi-Agent Path Finding NP-Hard

Anonymous Multi-Agent Path Finding (AMAPF) admits polynomial-time network-flow algorithms for several objectives, including makespan, total distance, and sum-of-costs (SoC) when agents disappear upon reaching goals. We show that standard goal-staying AMAPF is fundamentally different. We first formulate SoC minimization by augmenting the standard time-expanded flow model with goal-settlement constraints and show that the resulting linear programming relaxation is non-integral. We then prove that minimizing SoC in goal-staying AMAPF is NP-hard via a reduction from 3-SAT. Together with the polynomial-time result for the disappearing variant, this establishes a sharp complexity boundary determined by whether completed agents remain at their goals.

cs.MA↗
arXiv2026

Improved Subexponential Upper Bounds for $3$-Restricted Matching Vector Families

Matching Vector families (MVFs) are defined by two ordered lists of vectors in $\mathbb{Z}_m^n$ whose inner products satisfy specific residue patterns modulo an integer $m$. Most famously, restricted MVFs are used to construct the best-known constant-query Locally Decodable codes (LDCs). We prove an upper bound of $2^{O\left(\sqrt{n\log n \log m}\right)}$ on the size of $3$-restricted MVFs in $\mathbb{Z}_m^n$ for $m \leq \sqrt{n}$, substantially improving on the previous best bound of $2^{O(n/\log n)}$ by Bhowmick, Dvir and Lovett (STOC'13, SICOMP'14). Our proof relies on a new polynomial method argument that controls collisions in sumsets of matching vectors.

cs.CC↗
arXiv2026

Constructive solvability and the P versus NP problem

The relation between the computational complexity class NP and other complexity classes is addressed in the context of provability and limitations on the possibility of finding sound axioms for formal theories. We construct a family D of decision problems and show that under a certain finiteness condition, D contains a problem which is in NP. Further, it is shown that if the term ``constructible theory'' is defined in a way satisfying a specific natural condition, then no constructible and sound theory verifies a solution algorithm for any of the problems in D. Arguably, this solves the P versus NP problem under a constructive interpretation. The relation to classical proofs of NP $\subseteq$ EXPTIME is discussed. These proofs tacitly use an assumption which may fail for problems in D.

cs.CC↗
arXiv2026

Quantum Computing: Lecture Notes

This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 4 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, a chapter about quantum machine learning, one about stabilizer states and Clifford circuits, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C.

quant-ph↗
arXiv2026

Quantum Blind Rotation for Fast Functional Bootstrapping

Fully homomorphic encryption (FHE) enables privacy-preserving cloud computation, but its efficiency is often limited by the cost of bootstrapping. In particular, existing functional bootstrapping techniques have complexity exponential in the plaintext size. In this work, we show that employing a single quantum server can reduce this dependence. We propose a quantum functional bootstrapping algorithm that allows to evaluate any efficiently computable function in time polynomial in the plaintext size. For general functional bootstrapping over $l$-bit plaintexts, we obtain a time--space tradeoff: poly($l$)-time evaluation can be achieved with O$(2^l)$ qubits, while reducing the space complexity increases the time complexity. Technically, we extend a key classical cryptographic operation, known as \emph{blind rotation}, to the quantum setting by replacing polynomial-exponent encoding with quantum phase encoding. Underlying our extension are insights for the quantum extension of polynomial-based cryptographic tools that may gain dramatic speedups.

quant-ph↗
arXiv2026

Discrepancy of geometric incidences

We study the combinatorial (red-blue) discrepancy of finite point sets with respect to hyperplanes and, more generally, bounded-complexity affine algebraic sets. We prove that every $n$-point set in a real Euclidean space admits a red-blue coloring for which every affine algebraic set of dimension at most $D$ and degree at most $k$ has discrepancy at most $n^{\frac12-\frac{1}{2(D+1)}-\varepsilon}$ for some $\varepsilon=\varepsilon(D,k)>0$. This gives a polynomial improvement over the straightforward VC-dimension bound $\tilde O(n^{\frac12-\frac{1}{2(D+1)}})$. In the opposite direction, we construct $n$-point sets in $\mathbb R^d$ whose discrepancy with respect to hyperplanes is $\tildeΩ(n^{\frac12-\frac{1}{d+1}}),$ extending the point-line discrepancy lower bound of Chazelle and Lvov. We present further applications of our methods in communication complexity, concerning separation between randomized communication cost and deterministic communication cost with access to equality oracle.

math.CO↗
arXiv2026

Hardness of Approximation of Rank Aggregation on Ulam Metric

We study the approximability of rank aggregation under the Ulam metric. In the \emph{Ulam median} problem, the goal is to find a permutation minimizing the sum of its Ulam distances to the input permutations, while in the \emph{Ulam center} problem the objective is to minimize the maximum such distance. Both problems are known to be NP-hard, but no explicit approximation hardness was previously known. We prove that, for every $\varepsilon>0$, it is NP-hard to approximate either Ulam median or Ulam center within a factor of $51/50-\varepsilon$, even when the input consists of only four permutations. We further show that unless P = NP, neither problem admits a polynomial-time additive approximation scheme. The hardness result for Ulam median is established via a reduction from MAX-E3-LIN-2. The corresponding hardness for Ulam center is then obtained through a reduction from Ulam median.

cs.CC↗
arXiv2026

Criterion-Conditional In-Context Learning: Evaluating Criterion-Shift Adaptation in Vision-Language Models

Vision-language models can perform new tasks without parameter updates through in-context learning (ICL), whose core mechanism is utilizing the support set for task induction. In the standard ICL setting, once the task is induced, its decision criterion remains fixed. However, in real-world applications, many tasks exhibit a stable high-level intent, while their decision criteria shift according to specific requirements. Thus, we introduce a new setting, denoted as Criterion-Conditional In-Context Learning (CC-ICL), where models must infer the latent criterion from context and adjust predictions accordingly under fixed task semantics. To evaluate this capability, we propose two complementary metrics, Criterion Invariance and Criterion Sensitivity, capturing the model's robustness and adaptability under criterion shifts. We further construct CC-Bench, a multi-domain benchmark that supports evaluation under the CC-ICL setting. By employing a dual-level data hierarchy, CC-Bench enables legitimate ground-truth variation conditioned on the active criterion even when the task remains fixed. Experiments on CC-Bench reveal that most models exhibit a rigid boundary bias, struggling to align their decisions with the latent criterion. We also find that even a simple multi-criterion training strategy can significantly reduce this bias, improving Criterion Sensitivity and enabling 7B-scale models to surpass proprietary models without degrading general multimodal performance.

cs.CV↗