Related papers: Lower Bounds for Alternating Online State Complexi…
We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by…
In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann…
Online bipartite matching and its variants are among the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) introduced an elegant algorithm for the unweighted problem that achieves an…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
We build on the work of Berg, Boyar, Favrholdt, and Larsen, who developed a complexity theory for online problems with and without predictions (IJTCS-FAW, volume 15828 of LNCS, Springer, 2025) where they define a hierarchy of complexity…
Multiplication is indispensable and is one of the core operations in many modern applications including signal processing and neural networks. Conventional right-to-left (RL) multiplier extensively contributes to the power consumption, area…
We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…
Suppose we have many copies of an unknown $n$-qubit state $\rho$. We measure some copies of $\rho$ using a known two-outcome measurement $E_{1}$, then other copies using a measurement $E_{2}$, and so on. At each stage $t$, we generate a…
The graph state formalism is a useful abstraction of entanglement. It is used in some multipartite purification schemes and it adequately represents universal resources for measurement-only quantum computation. We focus in this paper on the…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower…
Online bipartite matching with one-sided arrival and its variants have been extensively studied since the seminal work of Karp, Vazirani, and Vazirani (STOC 1990). Motivated by real-life applications with dynamic market structures, e.g.…
We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data. The bound is valid for any offline exploration policy that consists of a stabilizing controller and an energy bounded…
In a 1989 paper titled "shortest paths without a map", Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed…
We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs…