相关论文: On monotone circuits with local oracles and clique…

The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…

We study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $n \cdot \tilde{O}(k^2)$,…

A standard model in network synchronised distributed computing is the LOCAL model. In this model, the processors work in rounds and, in the classic setting, they know the number of vertices of the network, $n$. Using $n$, they can compute…

It is shown that the behavior of an $m$-port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a structured skew-symmetric linear operator…

We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite…

We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…

The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is…

In this work we contribute to the study of the fine-grained complexity of problems parameterized by multi-clique-width, which was initiated by F\"urer [ITCS 2017] and pursued further by Chekan and Kratsch [MFCS 2023]. Multi-clique-width is…

Recently, Forbes, Kumar and Saptharishi [CCC, 2016] proved that there exists an explicit $d^{O(1)}$-variate and degree $d$ polynomial $P_{d}\in VNP$ such that if any depth four circuit $C$ of bounded formal degree $d$ which computes a…

We analyze maximum entropy random graph ensembles with constrained degrees, drawn from arbitrary degree distributions, and a tuneable number of 3-loops (triangles). We find that such ensembles generally exhibit two transitions, a clustering…

We show that any depth-$d$ circuit for determining whether an $n$-node graph has an $s$-to-$t$ path of length at most $k$ must have size $n^{\Omega(k^{1/d}/d)}$. The previous best circuit size lower bounds for this problem were…

We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al.,…

In the \emph{$k$-Diameter-Optimally Augmenting Tree Problem} we are given a tree $T$ of $n$ vertices as input. The tree is embedded in an unknown \emph{metric} space and we have unlimited access to an oracle that, given two distinct…

Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must…

In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…

In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…

Assuming the Generalised Riemann Hypothesis (GRH), we show that for all k, there exist polynomials with coefficients in $\MA$ having no arithmetic circuits of size O(n^k) over the complex field (allowing any complex constant). We also build…

The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…

We study circuits for computing depth-2 linear transforms defined by Kronecker power matrices. Recent works have improved on decades-old constructions in this area using a new ''rebalancing'' approach [Alman, Guan and Padaki, SODA'23;…

The graph parameter treedepth is minor-monotone; hence, the class of graphs with treedepth at most $k$ is minor-closed. By the Graph Minor Theorem, such a class is characterized by a finite set of forbidden minors. A conjecture of…