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cs.CC: explore 100 source-linked works published from 2023 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-16. Counts describe this index, not the complete source archives.

arXiv2026

A Note on Binary Quadratic Systems and their relation to complexity theory

Deciding whether a system of multivariate quadratic equations over $\mathbb F_2$ has a solution is a classical NP-complete problem, and remains so for square systems, with as many equations as variables. The hardness of this problem is one of the cornerstones of nowadays post-quantum cryptography. Let $\MQ_0(n)$ and $\MQ_1(n)$ denote the sets of square quadratic systems in $n$ variables having respectively no solutions and exactly one solution. $\cup_{n\geq 2} \MQ_0(n)$ is a coNP-complete language, while $\cup_{n\geq 2} \MQ_1(n)$ lies in DP. It is known that $\lim_{n\to \infty} |\MQ_1(n)|/|\MQ_0(n)|=1$. Here we prove the explicit finite-$n$ bounds \[ |\MQ_0(n)|<|\MQ_1(n)| \le \left(1+\frac{1}{2^n-1}\right)|\MQ_0(n)|, \] More generally, let $Q_d$ be the space of polynomial functions $(\FF_2)^n\to\mathbb F_2$ of degree at most $d$, and let $α_k$ count square systems in $(Q_d)^n$ having exactly $k$ solutions. Then \[ α_0<α_1 \le \left(1+\frac{1}{2^n-1}\right)α_0\,, \qquad 2\le d\le n \,. \] The proof combines matroid and coding-theoretic methods. We interpret $(\FF_2)^n$ as the ground set of the evaluation matroid of $Q_d$, express $α_0$ and $α_1$ through characteristic polynomials, and use a Whitney-type sign-reversing involution to show that the only terms that can push $α_1-α_0$ below $α_1/2^n$ come from the elements of a matroid port. These are identified with minimal-support words of the Reed--Muller code $\RM(n-d-1,n)=\RM(d,n)^\perp$; the required estimate then follows from the MacWilliams identity, the minimum-distance bound $2^{d+1}$, and the even-weight structure of the code.

cs.IT↗
arXiv2026

Promises should be taken seriously: On relativization with promise problems

Relativization is concerned with comparing computational models with black-box access to an oracle. For promise problems, black-box access is not canonical due to inputs outside of the promise being unconstrained. We study two semantics for such access. Under robust queries, a machine must correctly answer regardless of the completion of the problem,, while loose access requires that the internal choices of a machine do not change based on off-promise queries. Our first result separates the language and promise settings. Namely, we construct an oracle $O$ such that $\mathsf{P}^O = \mathsf{BQP}^O = \mathsf{AWPP}^O$, but $\mathsf{PromiseBQP}^O\not\subseteq\mathsf{PromiseP}^O_{\mathsf{/poly}}$. In particular, $\mathsf{BPP}^O = \mathsf{BQP}^O$, but $\mathsf{PromiseBQP}^O \neq \mathsf{PromiseBPP}^O$, showing that results for languages need not transfer to promises. Next, we use loose queries to strengthen the upper bound on the Quantum-Classical Polynomial Hierarchy from $\mathsf{P}^{\mathsf{PP}^{\mathsf{PP}}}$ to $\mathsf{QCPH} \subseteq \mathsf{BP\cdot PP} \subseteq \mathsf{PromiseBPP}^{\mathsf{PP}}$. The same proof also shows $\mathsf{PP}^\mathsf{PromiseBQP} = \mathsf{PP}$. Additionally, we show that $\mathsf{PromiseBQP}$, even when given quantum advice, is self-low under robust queries. Finally, we exhibit an obstruction to transferring language-level counting results to promise classes. Although $\mathsf{AWPP}$ and $\mathsf{APP}$ are low for $\mathsf{PP}$, a corresponding promise analogue would collapse the counting hierarchy as $\mathsf{GapP} \subseteq \mathsf{FP}^{\mathsf{PromiseAWPP}}$. This motivates the introduction of $\mathsf{PromisePostBQP^*}$, which restricts $\mathsf{PostBQP}$ to input-indepencent postselection. By showing that it is low for \PP, we obtain $\mathsf{PP}^{\mathsf{PromiseYQP^*}} = \mathsf{PP}$.

cs.CC↗
arXiv2026

Accelerating Fourier--Motzkin elimination: redundancy removal and the choice of variable elimination order

Fourier-Motzkin elimination computes an inequality description of the projection of a polyhedron onto a subset of its coordinates by eliminating one variable at a time. It is used in several areas of optimisation and computer science, and it is a standard way of obtaining the entropic constraints of a causal structure, where the marginalisation over the latent variables produces such a projection. Its limitation is the growth of the intermediate systems of inequalities, which can be doubly exponential in the number of eliminated variables even though the projection itself grows only as a single exponential. In practice the computational overload of the method therefore depends on two choices: how the redundant inequalities are removed after each step, and the order in which the variables are eliminated. We consider both. We first show, by an explicit example, that Imbert's redundancy test cannot be interleaved with redundancy removal by linear programming. We show that the two methods, however, can be combined soundly if the derivation records used by Imbert's test are re-initialised after every step at which linear programming is used. We then propose a rule for choosing the elimination order of the variables that gives a significant computational advantage, however, at the cost of increased resource usage. We demonstrate this advantage on some random polytopes, where the rule reduces the running time by factors of between 6 and 25 compared with the same elimination under a fixed order. For entropic descriptions of causal structures, with more than 250 inequalities and more than 100 variables to eliminate, our rule keeps the number of inequalities handled at each step one to two orders of magnitude lower than a fixed order.

cs.CC↗
arXiv2026

A note on the partition bound for one-way classical communication complexity

We present a linear program for a one-way version of the partition bound of Jain and Klauck, denoted $\mathsf{prt}^1_\varepsilon(f)$, and show that it characterizes the one-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ with shared randomness and worst-case error $\varepsilon$ of any relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. More precisely, for all $\varepsilon,δ\in(0,1/2)$, $\mathsf{R}_\varepsilon^1(f) \geq \log\mathsf{prt}_\varepsilon^1(f)$ and $\mathsf{R}_{\varepsilon+δ}^1(f) \leq \lceil\log\mathsf{prt}_\varepsilon^1(f) + \log\log(1/δ)\rceil$. This improves upon the characterization of $\mathsf{R}_\varepsilon^1(f)$ in terms of the rectangle bound due to Jain, Klauck, and Nayak [STOC'08], which is tight only up to an additive $O(\log(1/δ))$ term.

cs.CC↗
arXiv2026

Improved Small Set Expansion in High Dimensional Expanders

Small set high dimensional expansion over general sheaves has recently became central to several major breakthroughs. These include the construction of classical locally testable and quantum LDPC codes with constant rate and linear distance, $Ω(n)$-levels lower bounds for the Sum-of-Squares hierarchy, and the proof of the NLTS conjecture. In this work, we improve upon the state-of-the-art results for small set expansion in simplicial complexes, for both constant and general sheaves. Compared to one line of work (e.g., [KM22, DD24]), we improve upon their result by obtaining \emph{strong expansion} for small sets. Compared to another line of work (e.g., [KKL14, EK16, KM21, FK22]), we get an \emph{exponential improvement} in the size of sets for which expansion is guaranteed. Our result is based on a novel technique that bridges these two lines of work via a ``local vs. global'' case analysis: for ``local'' sets, which are concentrated within small links, we adapt ideas from the ``fat machinery'' of [KKL14, EK16]; for ``global'' sets, which are spread across the complex, we exploit global averaging operators in the spirit of [KM22, DD24].

cs.CC↗
arXiv2026

Hardness of Regular Expression Matching with Extensions

Regular expression matching asks whether a given regular expression of length $m$ matches a given string of length $n$, and its time complexity is fairly well understood. Meanwhile, regular expressions have been extended to support various extensions for both theoretical and practical reasons, which can substantially change the time complexity of the matching problem. In this work, we consider four well-known extensions to regular expressions called intersection, squaring, complement and backreference, and we prove a number of novel conditional time complexity lower bounds for the regular expression matching problems with these extensions under the Orthogonal Vectors Conjecture, the $k$-Orthogonal Vectors Conjecture or the $k$-Clique hypotheses. Our lower bounds significantly narrow the gaps to the known upper bounds, with some even being (conditionally) optimal in that the dependence on $n$ cannot be polynomially reduced while keeping the dependence on $m$ polynomial (or even elementary, for complement). Additionally, to obtain our results for intersection, squaring and complement in a unified manner, we introduce novel problems called Dyck Selection, Orthogonal Dyck Selection and Generalized Dyck Selection. They are arguably natural formal language and stringology problems that are based on Greibach's hardest context-free language and capture the essence of why the regular expression matching problems with these extensions are hard.

cs.CC↗
arXiv2026

Fault-tolerant quantum processing of physical experiments

Quantum computers may reveal features of Nature inaccessible to conventional experiments, but manipulating raw quantum data introduces noise that degrades inference even when the processor is fault-tolerant, creating a data-input bottleneck for robust quantum learning. Here we show that quantum fault tolerance can substantially improve the sample complexity of learning from noisy experiments. We encode unknown quantum states from physical experiments into protected quantum memory, enabling fault-tolerant implementations of quantum learning algorithms otherwise degraded by errors. Using this quantum uploading procedure, we prove that noisy randomized measurement and multi-copy learning tasks can be performed exponentially faster than by any adaptive strategy that does not immediately encode physical states into error-corrected memory. These separations are not simply due to a reduced effective noise rate: they hold even when uploading is substantially noisier than the bare experimental interface, rigorously establishing immediate encoding as the optimal approach to noise-robust learning. We numerically illustrate the speedups in astronomical imaging, where quantum processing of uploaded photons locates an exoplanet obscured by a bright star using orders of magnitude fewer shots than unencoded baselines. Our results establish a robust interface between quantum computers and natural systems, enabling powerful and practical quantum-enhanced experiments.

quant-ph↗
arXiv2026

Exponential Sampling Lower Bounds for Polynomial Sources

A degree-$d$ polynomial source is the output of a polynomial map of degree at most $d$ over $\mathbb{F}_2$ on arbitrarily many uniform random bits. Khodabandeh and Shinkar (FOCS '26) proved that $\mathrm{Ber}(1/3)^{\otimes N}$ has statistical distance $1-o(1)$ from every constant-degree polynomial source and conjectured exponentially small overlap. Independently of Khodabandeh and Shinkar, Byramji, Kane, Morris, and Ostuni (RANDOM '26) asked for an explicit target distribution at distance $1-\exp(-N^{Ω_d(1)})$. We resolve both questions. For every fixed $d\geq1$, every degree-$d$ polynomial source has overlap at most $\exp(-c_dN)$ with $\mathrm{Ber}(1/3)^{\otimes N}$, where $c_d>0$ is independent of the seed length. For quadratics, $c_2=2^{-26}$ suffices. We amplify Khodabandeh and Shinkar's uniform separation of acceptance probabilities from non-dyadic parameters (numbers not of the form $a/2^b$ for integers $a$ and $b\geq0$). The result extends to other non-dyadic Bernoulli parameters and to coordinates that are Boolean functions of boundedly many bounded-degree polynomials. We also give a uniform deterministic hierarchy between adjacent degrees. Appending the outputs of disjoint AND gates on $d+1$ inputs to uniform seed bits yields flat degree-$(d+1)$ target distributions of entropy $k$ with overlap $\exp(-Ω_d(\min\{k,N-k\}))$ against every degree-$d$ source, for $\min\{k,N-k\}\geq2(d+1)$. This entropy dependence is optimal up to constants in the exponent among flat target distributions for fixed $d$. The construction has locality $d+1$ and uses $O(N)$ field operations to sample. At $k=\lfloor N/2\rfloor$, it handles $d\leq(1-\varepsilon)\log_2N/3$ with overlap $\exp(-N^{\varepsilon-o(1)})$ for fixed $0<\varepsilon<1$. The proof combines monotonicity of Gowers uniformity norms, pairwise independence of points in a random affine cube, and relative entropy.

cs.CC↗
arXiv2026

A Near-Linear Element Kernel for \(d\)-Hitting Set

In \(d\)-\textsc{Hitting Set}, the input consists of a finite universe \(U\), a family \(\mathcal S\) of subsets of \(U\) with size at most \(d\), and an integer \(k\). The task is to decide whether at most \(k\) elements of \(U\) can intersect every set in \(\mathcal S\). For every fixed \(d\geq3\), we give a one-sided randomized kernel with \(O(k\log^3k)\) elements and a deterministic kernel with \(O(k^2\log k)\) elements for \(d\)-\textsc{Hitting Set}. In the one-sided randomized kernel, every NO-instance is always mapped to a NO-instance, and a YES-instance is mapped to a YES-instance with constant probability. The previously known kernels for \(d\)-\textsc{Hitting Set} contain \(O(k^{d-1})\) elements and \(O(k^d)\) sets. It has been asked in the literature whether \(d\)-\textsc{Hitting Set} allows kernels with \(O(k^{d-1-\varepsilon})\) elements for some constant \(\varepsilon>0\). In this paper, we answer this question affirmatively by giving near-linear element-kernels through a re-encoding of the instance. On the other hand, our kernel may still contain \(k^{O(d)}\) sets and the parameter $k$ may grow polynomially.

cs.DS↗
arXiv2026

Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters

Convex optimization on polytopes arises in many areas of science. When the polytope is given implicitly or has exponentially many vertices and facets, standard methods may not apply or be ineffective. This is the case for moment polytopes, such as the entanglement polytopes, which play a foundational role in quantum information and algebraic complexity. They give rise to important entanglement measures and tensor parameters such as the quantum functionals, yet general effective methods for computing these quantities have been elusive. In this paper we address this challenge. We develop a first-order framework called Hadamard mirror descent to optimize suitable convex functions over moment polytopes and, more generally, the gradient sets of geodesically convex functions. It operates locally and does not rely on any explicit description of the polytope. Our framework extends mirror descent, an effective and widely used framework for convex optimization, from the Euclidean setting to Hadamard manifolds, and is motivated by a recent work by Hirai, which we interpret as a Hadamard version of mirror flow. Applying the framework to entanglement polytopes yields the first efficient first-order algorithms to compute the quantum functionals, the symmetric quantum functional, and the G-stable ranks, as well as a new direct algorithm for the non-commutative rank.

cs.CC↗
arXiv2026

Improved Multilayered PCPs and Hypergraph Vertex Cover

We present two elementary constructions of multilayered PCPs that improve upon prior constructions in two ways. Specifically, we give one construction of quasi-linear size, and another one with $2$-to-$2$ constraints. Using these constructions we obtain the following results for the hypergraph vertex cover problem: $\bullet$ For $k=3$, for all $\varepsilon>0$, approximating the minimum vertex cover of a given $3$-uniform hypergraph within factor $1+\sqrt{2}-\varepsilon$ is NP-hard. Previously, the best known result due to [Dinur, Guruswami, Khot, Regev, SICOMP 2005] achieved a factor of $2-\varepsilon$. $\bullet$ For $k\geq 4$, for all $\varepsilon>0$, approximating the minimum vertex cover of a given $k$-uniform hypergraph within factor $k-\varepsilon$ is NP-hard, which is tight. Previous works established this result assuming the Unique-Games Conjecture [Khot, Regev, JCSS 2008], and a weaker factor of $k-1-\varepsilon$ for standard NP-hardness [Dinur, Guruswami, Khot, Regev, SICOMP 2005]. $\bullet$ Assuming the Exponential Time Hypothesis, for all $k\geq 3$ and $\varepsilon>0$ there is $C>0$ such that no $2^{n/\log^C n}$-time algorithm approximates the minimum vertex cover in a $k$-uniform, $n$-vertex hypergraph within factor $k-1-\varepsilon$. The proofs were obtained using ChatGPT 5.6 Pro and subsequently rewritten by the communicators.

cs.CC↗
arXiv2026

How to Verify Probabilistic Consistency of Predictive Models

When a probabilistic predictor answers many conditional-probability queries, are its answers self-consistent, and can this be verified in polynomial time? This problem is of interest for AI safety, where safety is derived from honesty about probabilistic predictions of unwanted outcomes potentially caused by an AI action. We construct an interactive PCP as follows. Let a predictive model be specified by a probability circuit P and a circuit Q which outputs confidence in predictions. Together, P and Q implicitly specify exponentially many probabilistic claims. We show a protocol in which a polynomial-time verifier can verify the approximate consistency of (P,Q). The verifier is given the pair of circuits (P,Q), which it evaluates at only a few points; alongside them it is given a proof oracle, an encoding of a witnessing probability distribution allegedly consistent with the predictions of (P,Q), which it reads at a few locations while interacting with a single untrusted prover. En route, we must ensure the existence of a sparse witnessing distribution consistent with the model's predictions. To do so, we first consider witness distributions for the consistency of explicit probabilistic claims, rather than claims specified by a predictor: say m claims, each of the form Pr[Y = 1 | X = x] = p, over n Boolean variables. Building on work initiated by Nilsson (Artif. Intell., 1986), we place l_2-approximate probabilistic consistency of explicit claims in NP, with certificates of length O(mn + log B) in the input bit-precision B; we further show how a small additive completeness-soundness gap removes the dependence on B. Together these results provide a complexity-theoretic foundation for certifying the self-consistency of probabilistic predictors. We view our interactive PCP as a first step toward training predictive models to prove their own consistency.

cs.CC↗
arXiv2026

Ulam Rank Aggregation Is Hard to Approximate for Four Rankings

We study the approximability of rank aggregation under the Ulam metric. In the \emph{Ulam median} problem, the goal is to find a ranking (permutation) minimizing the sum of its Ulam distances to the input rankings, while in the \emph{Ulam center} problem, the objective is to minimize the maximum such distance. We prove that, for every $0<\varepsilon< 1/34$, it is $\mathrm{NP}$-hard to approximate either Ulam median or Ulam center within a factor of $35/34-\varepsilon$, even when the input consists of only four rankings. We further show that unless P = NP, neither problem admits a polynomial-time additive approximation scheme. Prior to our work, only the exact versions of both problems were known to be $\mathrm{NP}$-hard, and that too only when the number of input rankings is unbounded [Fischer et al., ESA'25 and Bachmaier et al., J. of Discrete Algorithms'15]. Furthermore, our inapproximability results are optimal in terms of the number of input rankings since for three inputs it is already known to be polynomial-time solvable [Chakraborty, Das, Krauthgamer, SODA'21]. En route, we introduce a new general framework for reducing Boolean constraint satisfaction problems (CSP) to the Ulam median with only four inputs. As a specific instantiation of the reduction framework, we obtain our hardness-of-approximation results. The corresponding hardness for the Ulam center follows from a reduction from the Ulam median.

cs.CC↗
arXiv2026

A characterization of efficiently compilable constraint languages

A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation formats studied in this area range from ordered binary decision diagrams (OBDDs) to circuits in decomposable negation normal form (DNNFs). While it is known that there exist CNF formulas that require exponential size representations, the situation is less well studied for other types of constraints than Boolean disjunctive clauses. The constraint satisfaction problem (CSP) is a powerful framework that generalizes CNF-SAT by allowing arbitrary sets of constraints over any finite domain. The main goal of our work is to understand for which type of constraints (also called the constraint language) it is possible to efficiently compute representations of polynomial size. We answer this question completely and prove two tight characterizations of efficiently compilable constraint languages, depending on whether target format is structured. We first identify the combinatorial property of ``strong blockwise decomposability'' and show that if a constraint language has this property, we can compute DNNF representations of linear size. For all other constraint languages we construct families of CSP-instances that provably require DNNFs of exponential size. For a subclass of ``strong uniformly blockwise decomposable'' constraint languages we obtain a similar dichotomy for structured DNNFs. In fact, strong (uniform) blockwise decomposability even allows efficient compilation into multi-valued analogs of OBDDs and FBDDs, respectively. Thus, we get complete characterizations for all knowledge compilation classes between O(B)DDs and DNNFs.

cs.LO↗
arXiv2026

Revisiting average case complexity of multilevel syllogistic

We describe a Lean~4 formalization revisiting NYU Courant Technical Report TR1995-711 on the average-case complexity of Multilevel Syllogistic (MLS). The development encodes Reischuk--Schindelhauer average-case classes, an axiomatic MLS/EMLS semantics layer, a partial Ferro--Omodeo--Schwartz decision procedure with proved soundness and partial completeness on a membership-free fragment, serialization and step budgets, and conditional NP-average completeness and non-AvP hardness corollaries modulo explicitly documented structural axioms. Full Lean sources are inlined in the appendix modules.

cs.LO↗
arXiv2026

Fine-Grained $\mathrm{AC}^0$ Lower Bounds for $k$-$\mathrm{OV}$, $k$-$\mathrm{XOR}$, and $k$-$\mathrm{SUM}$ via Colored Subgraph Isomorphism

We prove lower bounds for $k$-OV, $k$-XOR, and $k$-SUM in nonuniform $\mathrm{AC}^0$, tracking how the circuit-size exponent scales with $k$ and using no running-time hypothesis. Our framework gives depth-zero projections from colored subgraph isomorphism to the three targets at dimension, row count, or bit width $O(k \log n)$, without increasing depth or size, and preserving gate orientation. For every fixed depth and sufficiently large fixed $k$, we obtain unconditional bounds $n^{Ω(k)}$ for $k$-OV and $(n/k)^{Ω(k)}$ for $k$-XOR and $k$-SUM, with an absolute exponent-rate constant independent of both $k$ and the depth. For growing $k = n^{o(1)}$ and every fixed depth $d$, we obtain the unconditional floor $n^{Ω_d(\min\{\sqrt{k},\log n\})}$. This strengthens to $n^{Ω(k)}$ at depth two for both top-gate orientations, and at depth three for top-disjunction (OR-AND-OR) circuits, with no restriction on fan-in or polarity. The depth-three argument rests on a minterm bound for a single CNF: a fixed CNF is very unlikely to become true for the first time exactly when a randomly planted copy is completed. Assuming a pattern-uniform strengthening of the Li-Razborov-Rossman source lower bound, the same projections complete the $k = n^{o(1)}$ frontier with $n^{Ω_d(k)}$ for the missing top-conjunction depth-three orientation and for every fixed depth $d \geq 4$. The framework is modular in the source bound, so improved source bounds pass directly to all three targets. All direct $k$-XOR bounds concern odd $k$; a black-box lift covers even $k$, and the $k$-SUM projection works for both parities. At the bit width $m = Θ(k \log(\mathrm{e}n/k))$ used by our projection, a block-carry $Σ_3$ upper bound of size $(n/k)^{O(k)}$ matches the depth-three lower bound up to constants in the exponent. Gaps remain at depth two and for top-conjunction depth three.

cs.CC↗
Compare source metadata on this page
WorkPublishedSource identifierSource
A Note on Binary Quadratic Systems and their relation to complexity theory2026-09-072609.07769arxiv
Promises should be taken seriously: On relativization with promise problems2026-09-072609.07945arxiv
Accelerating Fourier--Motzkin elimination: redundancy removal and the choice of variable elimination order2026-09-072609.07960arxiv
Algorithmic List Decoding of Reed-Solomon Codes up to Capacity2026-09-072609.08005arxiv
A note on the partition bound for one-way classical communication complexity2026-09-062302.10431arxiv
Improved Small Set Expansion in High Dimensional Expanders2026-09-062512.10385arxiv
Hardness of Regular Expression Matching with Extensions2026-09-062601.03020arxiv
Fault-tolerant quantum processing of physical experiments2026-09-062605.02057arxiv
Exponential Sampling Lower Bounds for Polynomial Sources2026-09-062609.06371arxiv
A Near-Linear Element Kernel for \(d\)-Hitting Set2026-09-062609.06512arxiv
Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters2026-09-062609.06633arxiv
Improved Multilayered PCPs and Hypergraph Vertex Cover2026-09-062609.06775arxiv
How to Verify Probabilistic Consistency of Predictive Models2026-09-052608.11181arxiv
On the sample complexity of the generalized hidden shift problem over arbitrary finite groups2026-09-052609.05828arxiv
Ulam Rank Aggregation Is Hard to Approximate for Four Rankings2026-09-052609.05874arxiv
A characterization of efficiently compilable constraint languages2026-09-042311.10040arxiv
Revisiting average case complexity of multilevel syllogistic2026-09-042606.16134arxiv
Fine-Grained $\mathrm{AC}^0$ Lower Bounds for $k$-$\mathrm{OV}$, $k$-$\mathrm{XOR}$, and $k$-$\mathrm{SUM}$ via Colored Subgraph Isomorphism2026-09-042608.08578arxiv

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