Related papers: Imperfect Gaps in Gap-ETH and PCPs
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
Understanding the power of space-bounded computation with access to catalytic space has been an important theme in complexity theory over the recent years. One of the key algorithmic results in this area is that bipartite maximum matching…
Conformal Prediction (CP) is a popular method for uncertainty quantification with machine learning models. While conformal prediction provides probabilistic guarantees regarding the coverage of the true label, these guarantees are agnostic…
Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level $\varepsilon$, CP…
We present a simple deterministic reduction which, assuming the Exponential Time Hypothesis ($\mathsf{ETH}$), yields tight lower bounds for approximating the parameterized Maximum Likelihood Decoding problem ($\mathsf{MLD}$) and the…
Towards predicting patch correctness in APR, we propose a simple, but novel hypothesis on how the link between the patch behaviour and failing test specifications can be drawn: similar failing test cases should require similar patches. We…
Despite the fundamental role the Quantum Satisfiability (QSAT) problem has played in quantum complexity theory, a central question remains open: At which local dimension does the complexity of QSAT transition from "easy" to "hard"? Here, we…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
In 2021, Broadbent and Kazmi developed a gate-teleportation-based protocol for computational indistinguishability obfuscation of quantum circuits. This protocol is efficient for Clifford+T circuits with logarithmically many T-gates, where…
Coherent gate errors are a concern in many proposed quantum computing architectures. These errors can be effectively handled through composite pulse sequences for single-qubit gates, however, such techniques are less feasible for entangling…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
In this work, we focus on several completion problems for subclasses of chordal graphs: Minimum Fill-In, Interval Completion, Proper Interval Completion, Threshold Completion, and Trivially Perfect Completion. In these problems, the task is…
The Strong Exponential Time Hypothesis (SETH) is a standard assumption in (fine-grained) parameterized complexity and many tight lower bounds are based on it. We consider a number of reasonable weakenings of the SETH, with sources from (i)…
This paper proposes a new methodology for early validation of high-level requirements on cyber-physical systems with the aim of improving their quality and, thus, lowering chances of specification errors propagating into later stages of…
Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We…
We consider the problem of estimating from sample paths the absolute spectral gap $\gamma_*$ of a reversible, irreducible and aperiodic Markov chain $(X_t)_{t \in \mathbb{N}}$ over a finite state space $\Omega$. We propose the ${\tt UCPI}$…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
In arXiv:1710.08163 a generalization of Boolean circuits to arbitrary finite algebras had been introduced and applied to sketch P versus NP-complete borderline for circuits satisfiability over algebras from congruence modular varieties.…
In this paper we present a new gap-creating randomized self-reduction for parameterized Maximum Likelihood Decoding problem over $\mathbb{F}_p$ ($k$-MLD$_p$). The reduction takes a $k$-MLD$_p$ instance with $k\cdot n$ vectors as input, runs…
The use of analog classical systems for computation is generally thought to be a difficult proposition due to the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present…