# hw2 - CS 267 Spring 2011 Homework Assignment 2 Due Friday...

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CS 267 – Spring 2011 – Homework Assignment 2 Due Friday, April 29th Do not discuss the problems with anyone other than the instructor. 1. Write the following CTL formulas using fixpoints: AFAG p , p EU(AG q ), EGF p , EFG p . 2. Consider the following transition system M = ( AP, S, R, S 0 , L ) with the set of states S = { 0 , 1 , 2 , 3 } , the initial set of states S 0 = { 0 } , the transition relation R = { (0 , 1) , (1 , 2) , (2 , 3) , (1 , 0) , (3 , 3) } , the set of atomic propositions AP = { p, q } and the labeling function L : S 2 AP where L (0) = { p } , L (1) = { q } , L (2) = { p } , and L (3) = { p, q } . Based on the above transition system, show the iterative fixpoint computations (show the set of states for each iteration) and the results for the following μ -calculus formulas: νz . ( p EX z )) μz . ( q ( p AX z )) μy . νz . (( q EX z ) EX y ) 3. Consider the following transition system M = ( AP, S, R, S 0 , L ) with the set of states S = { 0 , 1 , 2 , 3 } , the initial set of states S 0 = { 0 } , the transition relation R = { (0 , 1) , (0 , 2) , (1 , 3) , (2 , 3) , (3 , 3) } and the set of atomic propositions AP = { p } and the labeling function L : S 2 AP where L (0) = , L (1) = , L (2) = , L

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