Theory%20of%20Computing

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Theory of Computing

• Topics
• Formal languages
• automata
• computability and related matters

• Purposes
• To know the foundations and principles of
  computer science
• To learn the material that is useful in
  subsequent course

• Prerequisites
• Fundamentals of data structures and algorithms
• Discrete mathematics that includes set,
  functions, relations, logic, and mathematical
  reasoning

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Chapter 1 Introduction to The Theory of
Computation
1.1.1 Sets
Definition 1. A set is a group of objects.The
objects in a set are called the elements, or
members, of the set.
Definition 2. Two sets are equal if and only if
they have the same elements.
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• A set can be described by using a set builder
  notation.

• A set can be described by using a Venn diagram.

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• Set Operations

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• Set Identities

Table 1 Set Identities

Identity
Name
Identity laws
Domination laws
Idempotent laws
Complementation laws
Commutative laws
Associative laws
Distributive laws
De Morgans law
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1.1.2 Functions and Relations
The domain of G is the set AAdams, Chou,
Goodfriend, Rodriguez, Stevens, and the range of
G is the set A,B,C,F.
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Considering the function whose domain and range
are in the set of integers. We are often
interested only in the behavior of these
functions as their arguments become very large.
Example 2
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Definition 3 Let A and B be the sets. A relation
R from A to B is a subset of .

• Functions can be consider as relations, but
  relations are more general than functions.

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1.1.3 Graphs and Trees
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Definition 3 A tree is a directed graph that has
no cycles. There is a one distinct vertex in
tree, called the root.
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1.1.4 A Proof TechniqueMathematical Induction

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