Almayasa Al-Naimi 15 129-Prof. Harras August 29, 2017 Theory of Computation

In the 1930s, before computers were introduced Alan Turing, an English mathematician, logician, computer scientist aspired to find out the capabilities and limitations of computing machines. He classified problems as either: solvable or unsolvable.

Later on, in 1969, Professor Steven Cook, a computer scientist and mathematician further extended Turing’s ideas by questioning the difficulty and efficiency of the solvable problems. The professor split the solvable problems into two areas: 1. Tractable- a problem that can be solved efficiently 2. Intractable- a problem that cannot be solved by using a computing machine and is therefore inefficient.

Many other mathematicians and logicians researched the theories of computation. One of their main objectives was to find out ‘whether all mathematical problems can be solved in a systematic way.’ Another purpose of theories of computation is to use logic and mathematics to construct and further develop a variety of models for all the computer science sectors.

Theory of computation is made up of:

1. Computational Complexity Theory- deals with how difficult the problem is 2. Computability Theory- is whether the problem can be solved or not 3. Automata Theory- explores the properties and problems of computers and creates theoretical models to help understand them.

References: http://cglab.ca/~michiel/TheoryOfComputation/TheoryOfComputation.pdf https://www.youtube.com/watch?v=6ik0M-AWrn8 https://www.youtube.com/watch?v=pM0w3ue-sjU https://www.youtube.com/watch?v=nqvDdT4h4iQ https://en.wikipedia.org/wiki/Alan_Turing https://en.wikipedia.org/wiki/Stephen_Cook https://en.wikipedia.org/wiki/Theory_of_computation

Questions:

What are some of the computation models used in Automata? What is a Turing machine model? What is Moore’s Law?