arXiv subjects

Matthew Gray

Publications and source records attributed to Matthew Gray.

10 recordsLinked to original sources

arXiv2026

ETH-Hardness of Learning Monotone Circuits and Approximating Their Size

We show the following hardness results for monotone learning and approximation of monotone circuit size: 1. Under the Randomised Exponential-Time Hypothesis (rETH), it requires time $n^{\Omega(\log n)}$ to PAC-learn monotone formulas with $n$ input bits and size $s(n) = n$ by monotone circuits of size $n^{(\log n)^{1-\epsilon}}$, for every $\epsilon > 0$. 2. Under the Randomised Exponential-Time Hypothesis (rETH), for any $\delta > 0$, there is a polynomially bounded function $m$ such that $m^{1-\delta}$-multiplicatively approximating the minimum monotone circuit size of a monotone function consistent with a sequence of $m(n)$ labelled examples $\{(x_i, b_i)\}$ over $n$-bit inputs requires time $m^{\Omega(\log(m))}$. Our results are shown by a novel application of lifting arguments in proof and communication complexity to hardness of monotone learning, by building on the seminal result of Atserias and M\"uller (J. ACM, 2020) on hardness of automating Resolution proofs.

cs.CC↗

arXiv2026

Sonar-GPS Fusion for Seabed Mapping in Turbid Shallow Waters with an Autonomous Surface Vehicle

Accurate seabed mapping is essential for habitat monitoring and infrastructure inspection. In turbid, shallow coastal waters, such as shellfish aquaculture farms, the effectiveness of traditional optical methods is limited. Autonomous surface vehicles (ASVs) equipped with forward-looking sonar (FLS) offer a promising alternative. However, existing sonar-based systems face challenges in achieving fine resolution mapping over long trajectories due to low-resolution positioning measurements and accumulated drift over long trajectories. In this paper, we present a drift-resilient seabed mapping framework that integrates local FLS frame alignment using the Fourier-Mellin transform (FMT) with global trajectory optimization based on an extended Kalman filter (EKF) that fuses global positioning system (GPS), inertial measurement unit (IMU), and compass data. A variance-based image blending strategy is used to further reduce visual artifacts in overlapping regions. Field trials on a structured oyster farm site show that our framework helps reduce drift in RMSE by 9.5% relative to the FMT-only baseline. This framework also enables sub-meter reconstruction accuracy and preservation of high-resolution textures needed for oyster inventory estimation within the mapped areas.

cs.RO↗

arXiv2025

A Meta-Complexity Characterization of Minimal Quantum Cryptography

We give a meta-complexity characterization of EFI pairs, which are considered the "minimal" primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the problem of estimating a certain Kolmogorov-like complexity measure is hard given a single copy. A key technical step in our proof, which may be of independent interest, is to show that the existence of EFI pairs is equivalent to the existence of non-uniform single-copy secure pseudorandom state generators (nu 1-PRS). As a corollary, we get an alternative, arguably simpler, construction of a universal EFI pair.

quant-ph↗

arXiv2025

Cryptographic Conditions for Efficient Testing of Distributions and Quantum States

One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When $\mathcal{D}$ is a distribution over $\bit^n$, the optimal sample complexity of identity testing is known to be $\Omega(\sqrt{2^n})$. Furthermore, most existing results assume that the samples $x_1,\ldots,x_s$ are generated independently from an unknown distribution. In this work, we overcome both of these limitations by initiating study of distribution testing in a more realistic setting. In our model, the unknown distribution is promised to be efficiently samplable, while allowing the observed samples $x_1,\ldots,x_s$ to be adversarially generated and arbitrarily correlated. Under this model, we show that polynomially many samples suffice to verify distributions. We further characterize the computational complexity of verifying classically- and quantumly-samplable distributions. Our techniques also extend to verifications of quantum states. In establishing some of our results, we employ Kolmogorov complexity techniques in a novel manner. We also present multiple applications of Kolmogorov complexity that are of independent interest. In particular, we show that certified randomness with a classical efficient prover can be achieved without computational assumptions when inefficient verification is allowed. Furthermore, we also show that a natural quantum extension of a well-studied Kolmogorov complexity measure provides a good benchmark for certifying sampling-based quantum advantage.

quant-ph↗

arXiv2024

A Meta-Complexity Characterization of Quantum Cryptography

We prove the first meta-complexity characterization of a quantum cryptographic primitive. We show that one-way puzzles exist if and only if there is some quantum samplable distribution of binary strings over which it is hard to approximate Kolmogorov complexity. Therefore, we characterize one-way puzzles by the average-case hardness of a uncomputable problem. This brings to the quantum setting a recent line of work that characterizes classical cryptography with the average-case hardness of a meta-complexity problem, initiated by Liu and Pass. Moreover, since the average-case hardness of Kolmogorov complexity over classically polynomial-time samplable distributions characterizes one-way functions, this result poses one-way puzzles as a natural generalization of one-way functions to the quantum setting. Furthermore, our equivalence goes through probability estimation, giving us the additional equivalence that one-way puzzles exist if and only if there is a quantum samplable distribution over which probability estimation is hard. We also observe that the oracle worlds of defined by Kretschmer et. al. rule out any relativizing characterization of one-way puzzles by the hardness of a problem in NP or QMA, which means that it may not be possible with current techniques to characterize one-way puzzles with another meta-complexity problem.

cs.CR↗

arXiv2024

3D Water Quality Mapping using Invariant Extended Kalman Filtering for Underwater Robot Localization

Water quality mapping for critical parameters such as temperature, salinity, and turbidity is crucial for assessing an aquaculture farm's health and yield capacity. Traditional approaches involve using boats or human divers, which are time-constrained and lack depth variability. This work presents an innovative approach to 3D water quality mapping in shallow water environments using a BlueROV2 equipped with GPS and a water quality sensor. This system allows for accurate location correction by resurfacing when errors occur. This study is being conducted at an oyster farm in the Chesapeake Bay, USA, providing a more comprehensive and precise water quality analysis in aquaculture settings.

cs.RO↗

arXiv2024

On Central Primitives for Quantum Cryptography with Classical Communication

Recent work has introduced the "Quantum-Computation Classical-Communication" (QCCC) (Chung et. al.) setting for cryptography. There has been some evidence that One Way Puzzles (OWPuzz) are the natural central cryptographic primitive for this setting (Khurana and Tomer). For a primitive to be considered central it should have several characteristics. It should be well behaved (which for this paper we will think of as having amplification, combiners, and universal constructions); it should be implied by a wide variety of other primitives; and it should be equivalent to some class of useful primitives. We present combiners, correctness and security amplification, and a universal construction for OWPuzz. Our proof of security amplification uses a new and cleaner version construction of EFI from OWPuzz (in comparison to the result of Khurana and Tomer) that generalizes to weak OWPuzz and is the most technically involved section of the paper. It was previously known that OWPuzz are implied by other primitives of interest including commitments, symmetric key encryption, one way state generators (OWSG), and therefore pseudorandom states (PRS). However we are able to rule out OWPuzz's equivalence to many of these primitives by showing a black box separation between general OWPuzz and a restricted class of OWPuzz (those with efficient verification, which we call EV-OWPuzz). We then show that EV-OWPuzz are also implied by most of these primitives, which separates them from OWPuzz as well. This separation also separates extending PRS from highly compressing PRS answering an open question of Ananth et. al.

cs.CR↗

arXiv2024

Quantum Automating $\mathbf{TC}^0$-Frege Is LWE-Hard

We prove the first hardness results against efficient proof search by quantum algorithms. We show that under Learning with Errors (LWE), the standard lattice-based cryptographic assumption, no quantum algorithm can weakly automate $\mathbf{TC}^0$-Frege. This extends the line of results of Kraj\'i\v{c}ek and Pudl\'ak (Information and Computation, 1998), Bonet, Pitassi, and Raz (FOCS, 1997), and Bonet, Domingo, Gavald\`a, Maciel, and Pitassi (Computational Complexity, 2004), who showed that Extended Frege, $\mathbf{TC}^0$-Frege and $\mathbf{AC}^0$-Frege, respectively, cannot be weakly automated by classical algorithms if either the RSA cryptosystem or the Diffie-Hellman key exchange protocol are secure. To the best of our knowledge, this is the first interaction between quantum computation and propositional proof search.

cs.CC↗

arXiv2023

On the Computational Hardness of Quantum One-Wayness

There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent computational assumptions to be realized. Furthermore, the existence of either of these primitives implies that $\rm{P} \neq \rm{NP}$, which gives a lower bound on the necessary hardness. One can also define versions of each of these primitives with quantum output: respectively one-way state generators and pseudorandom state generators. Unlike in the classical setting, it is not known whether either primitive can be built from the other. Although it has been shown that pseudorandom state generators for certain parameter regimes can be used to build one-way state generators, the implication has not been previously known in full generality. Furthermore, to the best of our knowledge, the existence of one-way state generators has no known implications in complexity theory. We show that pseudorandom states compressing $n$ bits to $\log n + 1$ qubits can be used to build one-way state generators and pseudorandom states compressing $n$ bits to $\omega(\log n)$ qubits are one-way state generators. This is a nearly optimal result since pseudorandom states with fewer than $c \log n$-qubit output can be shown to exist unconditionally. We also show that any one-way state generator can be broken by a quantum algorithm with classical access to a $\rm{PP}$ oracle. An interesting implication of our results is that a $t(n)$-copy one-way state generator exists unconditionally, for every $t(n) = o(n/\log n)$. This contrasts nicely with the previously known fact that $O(n)$-copy one-way state generators require computational hardness. We also outline a new route towards a black-box separation between one-way state generators and quantum bit commitments.

cs.CR↗

arXiv2019

"LOADS of Space": Local Order Agnosticism and Bit Flip Efficient Data Structure Codes

Algorithms, data structures, coding techniques, and other methods that reduce bit-flips are being sought to best utilize hardware where flipping bits is the dominating cost. Write efficient memories were introduced by Ahlswede and Zhang as a model for storage systems with these kinds of arbitrary read, write, and update costs. The introduction of non-volatile Random Access Memories like phase-change RAM, which have asymmetric read-write costs has re-motivated the field. Our work focuses on potential bit-flip efficiencies to be gained at the data structure layer. We examine Local Order Agnostic Data Structures (LOADS), data structures in which local order does not convey information and in which cells are modified individually. We found that because these data structures have a limited set of valid values and transitions, that bit flipping wins should be possible without the use of additional hardware.

cs.DS↗