turingSept7 - Computability and the Turing Machine Tuesday,...

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Unformatted text preview: Computability and the Turing Machine Tuesday, September 7 th 2010 Tuesday, September 7, 2010 Review cognition might turn out to be merely computation Tuesday, September 7, 2010 Review cognition might turn out to be merely computation what is computation? what are its limits? Tuesday, September 7, 2010 Intuitive notion of algorithm Tuesday, September 7, 2010 Intuitive notion of algorithm Tuesday, September 7, 2010 Polynomials 6 x x x y z z = 6 x 3 yz 2 Tuesday, September 7, 2010 Polynomials 6 x 3 yz 2 + 3 xy 2 x 3 10 6 x x x y z z = 6 x 3 yz 2 Tuesday, September 7, 2010 6 x 3 yz 2 + 3 xy 2 x 3 10 Polynomials root : assignment to x , y , z such that the value of the polynomial is zero Tuesday, September 7, 2010 6 x 3 yz 2 + 3 xy 2 x 3 10 Polynomials root : assignment to x , y , z such that the value of the polynomial is zero x = 5 , y = 3 , z = Tuesday, September 7, 2010 6 x 3 yz 2 + 3 xy 2 x 3 10 Polynomials root : assignment to x , y , z such that the value of the polynomial is zero x = 5 , y = 3 , z = integral root : all variables get integer values Tuesday, September 7, 2010 Hilberts 10 th problem 10. D E T E R M I N A T I O N O F THE SOLVABILITY O F A B I O P H A N- TINE E Q U A T I O N . Given a diophantine equation with any number of u n- known q u a n t i t i e s a n d w i t h r a t i o n a l i n t e g r a l n u m e r i c a l coefficients : To devise a process according to which it can be dete mined by a finite number of operations whether the equation is solvable in rational integers....
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This note was uploaded on 01/30/2011 for the course COGST 1101 taught by Professor Spivey,m during the Fall '07 term at Cornell University (Engineering School).

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turingSept7 - Computability and the Turing Machine Tuesday,...

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