相关论文: Breaking Symmetries

We study the distributed message-passing model in which a communication network is represented by a graph G=(V,E). Usually, the measure of complexity that is considered in this model is the worst-case complexity, which is the largest number…

The problem of scheduling conflicting jobs on parallel machines consists in assigning a set of jobs to a set of machines so that no two conflicting jobs are allocated to the same machine, and the maximum processing time among all machines…

For the brain to recognize local orientations within images, neurons must spontaneously break the translation and rotation symmetry of their response functions -- an archetypal example of unsupervised learning. The dominant framework for…

The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear…

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…

This paper focuses on studying the message complexity of implicit leader election in synchronous distributed networks of diameter two. Kutten et al.\ [JACM 2015] showed a fundamental lower bound of $\Omega(m)$ ($m$ is the number of edges in…

We define the symmetric Post Correspondence Problem (PCP) and prove that it is undecidable. As an application we show that the original proof of undecidability of the freeness problem for 3-by-3 integer matrix semigroups works for the…

In this work, we explore the trade-offs of explicit structural priors, particularly group equivariance. We address this through theoretical analysis and a comprehensive empirical study. To enable controlled and fair comparisons, we…

Leader Election is an important primitive for programmable matter, since it is often an intermediate step for the solution of more complex problems. Although the leader election problem itself is well studied even in the specific context of…

We investigate, in a four photon interference experiment in a laser-written waveguide structure, how symmetries control the suppression of many-body output events of a $J_x$ unitary. We show that totally destructive interference does not…

Sortition, the random selection of political representatives, is increasingly being used around the world to choose participants of deliberative processes like Citizens' Assemblies. Motivated by sortition's practical importance, there has…

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…

We consider leader election in anonymous radio networks modeled as simple undirected connected graphs. Nodes communicate in synchronous rounds. Nodes are anonymous and execute the same deterministic algorithm, so symmetry can be broken only…

Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for…

Since the very beginning of the theory of linear logic it is known how to represent the $\lambda$-calculus as linear logic proof nets. The two systems however have different granularities, in particular proof nets have an explicit notion of…

Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt…

We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that state on the other layer. Despite the model's simplicity,…

In content-oblivious computation, n nodes wish to compute a given task over an asynchronous network that suffers from an extremely harsh type of noise, which corrupts the content of all messages across all channels. In a recent work,…

Population protocols are a relatively novel computational model in which very resource-limited anonymous agents interact in pairs with the goal of computing predicates. We consider the probabilistic version of this model, which naturally…

Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms.…