Automata theory fundamental, definitions, applications, representations, models

1. Theory of Computation - Introduction

2. What do u mean by computation?
calculation, solving, making decision , any kind of operations/task by any machine
(like computer, calculator)
What do u mean by theory?
Simply speaking ….. A theory is a group of ideas intended to explain something.
logically speaking …. A theory is a fact-based framework for describing a phenomenon.
i.e basic principles behind any concept
Purpose of Theory of computation :
Develop formal mathematical models of computation that reflect real-world computers

3. Definition:
Theory of computation is the branch that deals with how effectively
problems can be solved on a model of computation, using an
algorithm.
Automata Theory:
• Automata is the plural of automaton – means automatic machine
• Is the study of abstract machines and how it could solve the
problems.

4. Representation of Model:
Will be like Flow chart
State / transition diagram

5. Applications of Automata
• Text processing – string search
• Web browsing
• Compiler design
• Operating system
• Game theory (strategy model by decision making)
• NLP
• Artificial intelligence

6. PREREQUISTIES
• Set theory
• Model theory
• Computability theory
• Proof theory

7. CS8501 Theory of Computation
UNIT I AUTOMATA FUNDAMENTALS
UNIT II REGULAR EXPRESSIONS AND LANGUAGES
UNIT III CONTEXT FREE GRAMMAR AND LANGUAGES
UNIT IV PROPERTIES OF CONTEXT FREE LANGUAGES
UNIT V UNDECIDABILITY

8. TEXTBOOK FOR REFERENCE

9. FINITE
AUTOMATA

10. REPRESENTATIONS
Transition function :
syntax: δ(state , input symbol) -> output state
example: δ(q0,1)= q1
2) Transition table
Row ---> states
Column ---> input symbols
1) Transition diagram

11. TYPES OF FA
1. Deterministic Finite Automata (DFA)
2. Non- Deterministic Finite Automata (NFA)
Both are defined by 5 tuples but there is difference in :
Transition function
DFA: Q x Σ -> [Q] - output is single state
NFA : Q x Σ -> {Q} - output is in many states

12. NFA
δ(q0,b)= {q0,q1}
NFA
δ(q0,1)= {q0,q2}
δ(q0,0)= {q0,q1}
δ(q2,1)= {q3}
δ(q2,1)= ∅
DFA
δ(q0,b)= [q0]
δ(q0,a)=[ q0,q1]
∅ - no null transitions
Guess the type of FA