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turingSept7

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

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Computability and the Turing Machine Tuesday, September 7 th 2010 Tuesday, September 7, 2010

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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

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Intuitive notion of algorithm Tuesday, September 7, 2010
Intuitive notion of algorithm Tuesday, September 7, 2010

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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

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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 = 0 Tuesday, September 7, 2010

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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 = 0 integral root : all variables get integer values Tuesday, September 7, 2010
Hilbert’s 10 th problem 10. DETERMINATION OF THE SOLVABILITY OF A BIOPHAN- TINE EQUATION. Given a diophantine equation with any number of un- known quantities and with rational integral numerical 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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turingSept7 - Computability and the Turing Machine Tuesday...

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