hw7 - CSE4/586 (Spring 2009): Homework 7 Due by May 5...

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CSE4/586 (Spring 2009): Homework 7 Due by May 5 Tuesday, in class. 1. (40 points) Consider an undirected and connected (but not fully-connected) graph of n nodes. (In other words, the nodes are in a multihop network.) Execution of nodes is assumed to be synchronous— in each step/round, every node j executes its program action (given below) with respect to one of its neighbors, that is chosen in a fixed cyclic ordering, nxt , of all of its neighbors. Program Unison var x.j : int r.j : any value from the set { k | k is a neighbor of j } assign x.j,r.j := min ( x.j,x. ( r.j )) + 1 ,nxt. ( r.j ) 1. Show that this program satisfies the property of Unison: Starting from any unison state , i.e., one where all x variables have equal values, the value of each x variable is incremented by one in every following step/round of the system. (This implies that all states following a unison state are also unison states.) 2. Prove the stabilization of the program. Hint: show that “true leads to unison states”.
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This note was uploaded on 01/04/2010 for the course CSE 123 taught by Professor Qwerty during the Spring '09 term at École Normale Supérieure.

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hw7 - CSE4/586 (Spring 2009): Homework 7 Due by May 5...

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