Sipser 1.53 - 1.53) Let = {0,1,+,=}, and ADD = {x = y + z |...

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Unformatted text preview: 1.53) Let = {0,1,+,=}, and ADD = {x = y + z | x,y,z are binary integers, and x is the sum of y and z} *Note: to avoid confusion going forwards for this problem, I've used the word "equal(s)" instead of the equality sign, as that symbol is part of the language in question. Use the pumping lemma; assume that ADD is regular and conforms appropriately (let p be its hypothetical pumping number). Consider the word w equal to 1p=0+1p , |w| equals 2p +3 p. If we parse w as w equal to abc, then we have a equals 1i, b equals 1j, c equals 1p-i-j=0+1 p, and b does not equal . Now consider, if we pump b, then ab0c must be in C. However, ab0c equals 1i1p-i-j=0+1 p, but (i + p i j) = (p j) < p, so the binary equation is not balanced, and w is not in ADD. There is a contradiction of the pumping lemma, so ADD is not regular. ...
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This note was uploaded on 04/06/2008 for the course EECS 376 taught by Professor Stout during the Spring '08 term at University of Michigan.

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