Electronic Colloquium on Computational Complexity, Report No. 52 (2004) Non-Abelian Homomorphism Testing, and Distributions

Abstract. In this paper, we study two questions related to the problem of testing whether a function is close to a homomorphism. For two finite groups (not necessarily Abelian), an arbitrary map, and a parameter, say that is-close to a homomorphism if there is some homomorphism such that and differ on at most elements of, and say that is-far otherwise. For a given and, a homomorphism tester should distinguish whether is a homomorphism, or if is-far from a homomorphism. When is Abelian, it was known that the test which! "#% picks random & pairs!' and tests that gives a homomorphism tester. Our first result shows $/.0()&1+ that such a test works for all groups. Next, we consider functions that are close to their self-convolutions. 23. Let 5 G6HJILK DMGMN A D 5 G. It is known that 2C.O2 = exactly =A.CB-DFE when is the uniform distribution over a subgroup of. We show that there is 2 a sense in which this characterization is robust – that 2 is, if is close in statistical 2> = distance to 2, then must be close to uniform over some subgroup of

ARA: A Wireless Living Lab Vision for Smart and Connected Rural Communities

The rural US includes 72% of the nation's land and 46 million people, and it serves as major sources of food and energy for the nation. Thus rural prosperity is essential to US wellbeing. As a foundation for next-generation rural economy and communities, broadband connectivity is a key driver of rural prosperity. Yet 39% of the rural US lacks broadband access, and most agriculture (ag) farms are not connected at all. To address the rural broadband challenge, we will develop the ARA rural wireless living lab. ARA will not only serve as a first-of-its-kind, real-world wireless experimental infrastructure for smart and connected rural communities, it will also provide the living lab processes, activities, and organizations to engage the broad wireless and application communities in the research, education, innovation, and pilot of affordable, high-capacity rural broadband solutions. Through this visioning article, we illustrate the community, application, economic, and operational contexts of rural wireless, the design of ARA, ARA-enabled research, and how ARA is expected to make rural broadband as affordable as urban broadband today. This article is also a call-to-action for the broad wireless and application communities to participate in the ARA living lab activities and to join the ARA Consortium of public-private partners in shaping the future of advanced wireless, rural broadband, and rural communities in general.This presentation is published as Zhang, Hongwei, Yong Guan, Ahmed Kamal, Daji Qiao, Mai Zheng, Anish Arora, Ozdal Boyraz et al. "ARA: A Wireless Living Lab Vision for Smart and Connected Rural Communities." In Proceedings of the 15th ACM Workshop on Wireless Network Testbeds, Experimental evaluation & CHaracterization, pp. 9-16. 2022. DOI: 10.1145/3477086.3480837. Copyright 2022 Association for Computing Machinery. Attribution-NonCommercial-ShareAlike 4.0 (CC BY-SA 4.0). Posted with permission