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###### Advanced Computer Architecture-II:

The two most famous documents in this regard are 1. Alonzo Church, “An Insoluble Problem in Elementary Number Theory”, American Journal of Mathematics, 58 (1936), pp. 345–363 2. Alan Turing, “On Computable Numbers, with an Application to Entscheidung.”

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**CS704 **FINAL TERM** PAST PAPERS:**

We will work with the Turing model. Turing came up with the idea of the computing machines that we are now called Turing machines. He suggested that every calculation we can make mechanically could be performed by a Turing machine. The good thing about Turing machines was: that Turing machines are not intuitive concepts like an algorithm.

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But they are mathematically defined objects. So something can be proven about them. Their existence and non-existence can also be proved. They can be studied using mathematical tools and asserted precisely about them.

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Complexity theory will address the following questions: 1. Given a problem, can we design an efficient algorithm to solve this problem? 2. Can we characterize problems that have efficient algorithms? 3. We can characterize problems that are effectively solvable at the border unyielding? 4. Can we prove that problems, even if they are quantifiable, are intractable? 5. Can we prove that certain problems of practical importance are intractable? 6. Is there a unified theory of problems that are difficult to solve?