The One-Way Communication Complexity of Group Membership

This paper studies the one-way communication complexity of the subgroup membership problem, a classical problem closely related to basic questions in quantum computing. Here Alice receives, as input, a subgroup $H$ of a finite group $G$; Bob receives an element $x \in G$. Alice is permitted to send a single message to Bob, after which he must decide if his input $x$ is an element of $H$. We prove the following upper bounds on the classical communication complexity of this problem in the bounded-error setting: (1) The problem can be solved with $O(\log |G|)$ communication, provided the subgroup $H$ is normal; (2) The problem can be solved with $O(d_{\max} \cdot \log |G|)$ communication, where $d_{\max}$ is the maximum of the dimensions of the irreducible complex representations of $G$; (3) For any prime $p$ not dividing $|G|$, the problem can be solved with $O(d_{\max} \cdot \log p)$ communication, where $d_{\max}$ is the maximum of the dimensions of the irreducible \F_p-representations of $G$

Programming with process groups: Group and multicast semantics

Process groups are a natural tool for distributed programming and are increasingly important in distributed computing environments. Discussed here is a new architecture that arose from an effort to simplify Isis process group semantics. The findings include a refined notion of how the clients of a group should be treated, what the properties of a multicast primitive should be when systems contain large numbers of overlapping groups, and a new construct called the causality domain. A system based on this architecture is now being implemented in collaboration with the Chorus and Mach projects

Demographic Faultlines and Creativity In Diverse Groups

Despite the oft made argument that demographic diversity should enhance creativity, little is known about this relationship. We propose that group diversity, measured in terms of demographic faultlines, affects creativity through its effects on group members’ felt psychological safety to express their diverse ideas and the quality of information sharing that takes place across subgroup boundaries. Further, we propose that the relationship between faultlines and creativity will be moderated by task interdependence and equality of subgroup sizes. Finally, we provide suggestions for how organizations can establish norms for self-verification and use accountability techniques to enhance creativity in diverse groups

Construction and abstraction: contrasting methods of supporting model building in learning science

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