by: Er. Sukhwinder kaur

 Computation Computation  Algorithm Algorithm  Objectives Objectives  What do we study in Theory of Computation ? What do we study in Theory of Computation ?  What do we study in Complexity Theory ? What do we study in Complexity Theory ?  History of Theory of Computation History of Theory of Computation

 Computation is a general term for any type of information processing that can be represented as an algorithm precisely (mathematically).  Examples:  Adding two numbers in our brains, on a piece of paper or using a calculator.  Converting a decimal number to its binary presentation or vise versa.  Finding the greatest common divisors of two numbers.  …

A very fundamental and traditional branch of Theory of Computation seeks: 1. A more tangible definition for the intuitive notion of algorithm which results in a more concrete definition for computation. 2. Finding the boundaries (limitations) of computation. back

 A finite sequence of simple instructions that is guaranteed to halt in a finite amount of time.  This is a very abstract definition, since: ◦ We didn’t specify the nature of this simple instructions.  For example an instruction can be “increment a number by one” or “Calculate the triple integral” ◦ We didn’t specify the entity which can execute these instructions.  For example is this entity a person, a computer, …  If it is a computer what is the processor type? How much memory does it have? …. ? back

 Introduce concepts in automata theory and theory of computation  Identify different formal language classes and their relationships  Design grammars and recognizers for different formal languages  Prove or disprove theorems in automata theory using its properties  Determine the decidability and intractability of computational problems back

What is computable, and what is not ? Basis of Algorithm analysis Complexity theory  What a computer can and cannot do  Are you trying to write a non-existing program?  Can you make your program more efficient? back

 What is easy, and what is difficult, to compute ?  What is easy, and what is hard for computers to do?  Is your cryptographic scheme safe? back

 Analysis of algorithms  Complexity Theory  Cryptography  Compilers  Circuit design

 1936 Alan Turing invented the Turing machine, and proved that there exists an unsolvable problem.  1940’s Stored-program computers were built.  1943 McCulloch and Pitts invented finite automata.  1956 Kleene invented regular expressions and proved the equivalence of regular expression and finite automata.

 1956 Chomsky defined Chomsky hierarchy, which organized languages recognized by different automata into hierarchical classes.  1959 Rabin and Scott introduced nondeterministic finite automata and proved its equivalence to (deterministic) finite automata.  1950’s-1960’s More works on languages, grammars, and compilers back

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