Table of Contents

#### CS704 FINAL TERM SOLVED PAPERS

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

In the same paper, Turing showed that a very important problem called the “Halting Problem” cannot be solved by an algorithm. That was a breakthrough. It turns out that there are mathematically defined exact problems that have no algorithmic solutions. This shows us that some problems cannot be counted.

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

What is a calculation? We can come up with a precise definition of an algorithm or a calculation? (The answer is yes). Stopping problem. Everything can be calculated. (The answer is no.) We can characterize problems that cannot be counted. (The answer is that it’s hard to do, but in certain cases, we can identify them and prove that they are not quantifiable).

##### CS704 FINAL TERM** PAST PAPERS BY MOAAZ:**

We will study quantifiable and non-quantifiable problems in various fields. We will study computability and logic. We will prove Godel’s incompleteness theorem. Godel’s theorem is the cornerstone of mathematical logic and the foundation of mathematics. It roughly says that: In any (axiomatic) system that contains numbers. There are always statements that are true but unprovable.

##### CS704 FINAL TERM** SOLVED PAPERS:**

This had a profound impact on mathematics. We will prove this theorem in our course using tools from computability theory. We will discuss this in detail when the time comes. Complexity theory is much more practical than computability theory.6. Is there a unified theory of problems that are difficult to solve?