Topic: Full List of Theory

THEORY

1. Algebra

1.1. Relations
1.2. Partitions

1.2.1. Definition
1.2.2. Sample partition
1.2.3. Operations with partitions
1.2.4. Examples of operations
1.2.5. Applet on partitions

2. Abstract Automata

2.1. Definition
2.2. Subautomaton
2.3. Isomorphism
2.4. Homomorphism

2.4.1. Example of homomorphism
2.4.2. Applet on homomorphism

2.5. Equivalence

2.5.1. Equivalence of states
2.5.2. Equivalence of automata
2.5.3. Reduced automaton
2.5.4. Realization

3. Abstract Network

3.1. Definition
3.2. Drawing
3.3. Automaton Defined by Network
3.4. Realization
3.5. Decomposition
3.6. Main Theorem of Decomposition

4. Partition Pairs and Pair Algebra

4.1. Partition Pair
4.2. Mapping of the Blocks
4.3. Examples
4.4. Lemma
4.5. Operators m and M
4.6. Pair Algebra
4.7. Lemma
4.8. Another Definition for Operator m
4.9. S-S, I-S, S-O, I-O pairs
4.10. Applet on Operator M

5. Construction of an Abstract Network

5.1. Drawing
5.2. Construction
5.3. Example
5.4. Applet on the Construction of an Abstract Network

6. Structured Network

6.1. Definition of Structured Automaton
6.2. Construction of a Structured Network

7. First Decomposition Model

7.1. Initial Automaton
7.2. Definition of States in Component Automata
7.3. Set of Input and Output Variables
7.4. Definition of Transition and Output Functions
7.5. Reduced Procedure of Decomposition
7.6. Result of Decomposition
7.7. Applet on Decomposition