A knowledge-based analysis of global function computation

Consider a distributed system N in which each agent has an input value and each communication link has a weight. Given a global function, that is, a function f whose value depends on the whole network, the goal is for every agent to eventually compute the value f(N). We call this problem global function computation. Various solutions for instances of this problem, such as Boolean function computation, leader election, (minimum) spanning tree construction, and network determination, have been proposed, each under particular assumptions about what processors know about the system and how this knowledge can be acquired. We give a necessary and sufficient condition for the problem to be solvable that generalizes a number of well-known results [Attyia, Snir, and Warmuth 1988; Yamashita and Kameda 1996; Yamashita and Kameda 1999]. We then provide a knowledge-based (kb) program (like those of Fagin, Halpern, Moses, and Vardi [1995, 1997]) that solves global function computation whenever poss...

• Type: Journal
• Year: 2010
• Where: DC
• Authors: Joseph Y. Halpern, Sabina Petride
• Keywords: DC 2001, DC 2010, Global Function, Global Function Computation, Leader Election