Set of strings of length exactly k
Powers of an alphabet
The objects and notions
Definition
Expresses that some objects
Mathematical statement
Convincing logical argument
Proof
Statement proved true
Theorem
Another more significant statement
Lemma
Concluded from a theorem
Corollaries
Assume that the theorem is false
Proof by contradiction
Proving statements
Proof by induction
Proves that it is true
Basis
how efficiently problems can be solved on a model of computation using algorithm
Theory of computation
3 major branches
Set of allowable operations
Model of computation
Study of abstract machine
Automata theory
Self acting machine
Automata
Recognized by an automaton
Formal language
Different kinds of automata
Finite
Push down
Turing
Finite automata examples
Elevators
Vending machine
Lexical analyzers
3 central areas
Fundamental mathematical properties
TOC
Problems computationally hard
Complexity
Efficiently solvable
Easy
Can’t be solved easily
Hard
degree of computational difficulty
Motivation of complexity theory