The presentation topic is on computational models. It will be presented by Md. Touhidur Rahman. The document discusses four computational models: finite automata (DFA and NFA), context free grammar, pushdown automata, and Turing machines. Finite automata are defined using states, symbols, transitions, a start state, and accepting states. Context free grammars are defined using variables, terminals, productions, and a start symbol. Pushdown automata extend NFAs with a stack. Turing machines are formally defined but also described at a higher level for understanding.

1. Presentation Topic is:
To Our Theory of Computing Presentation

2. Group Member List:
Name ID
Md. Touhidur Rahman 152-15-6232

3. Computational Models
Computational Model are four type:
 Finite Automata - DFA & NFA
 Context Free Grammar
 Push Down Automata
 Turing Machine

4. Finite Automata - DFA & NFA
Definition: A deterministic finite automaton (DFA) consists of
• 1. a finite set of states (often denoted Q)
• 2. a finite set of symbols (alphabet)
• 3. a transition function that takes as argument a state and a
• symbol and returns a state (often denoted )
• 4. a start state often denoted q0
• 5. a set of final or accepting states (often denoted F)

5. Finite Automata - DFA & NFA
How to present a DFA? With a transition table
• The ! indicates the start state: here q0
• The indicates the final state(s) (here only one final state q1)
• This defines the following transition diagram

6. Finite Automata - DFA & NFA
Formal Definition:

7. Finite Automata - DFA & NFA
How to present a NFA? With a transition table

8. Context Free Grammar
What is a grammar?:
A grammar consists of one or more variables that represent
classes of strings (i.e., languages)
There are rules that say how the strings in each class are
constructed. The construction can use :
1. symbols of the alphabet
2. strings that are already known to be in one of the
classes
3. or both

9. Context Free Grammar
Definition of Context-Free Grammar:
A CFG (or just a grammar) G is a tuple G = (V, T, P, S) where
1. V is the (finite) set of variables (or nonterminal or syntactic
categories). Each variable represents a language, i.e., a set of
strings .
2. T is a finite set of terminals, i.e., the symbols that form the
strings of the language being defined.
3. P is a set of production rules that represent the recursive
definition of the language.
4. S is the start symbol that represents the language being
defined. Other variables represent auxiliary classes of
strings that are used to help define the language of the start
symbol.

10. Context Free Grammar
Examples 1(CFG): The grammar:
1. E → I
2. E → E + E
3. E → E ∗ E
4. E → (E)
5. I → a
6. I → b
7. I → Ia
8. I → Ib
9. I → I 0
10. I → I 1
The Grammar for expression is started formally as,
Grammar G 1 = ( {E, I }, T, P, E)
where: T = { +, ∗, (, ), a, b, 0, 1 } is the set of symbol and P is
the set of productions

11. Context Free Grammar
Derivation:
The sequence of substitutions to generate a string is called a
derivation.
Derivation both are two types:
1.Left-Most Derivation.
2.Right-Most Derivation.
Left-Most Derivation:
A derivation which always replace the leftmost variable in each step is
called a leftmost derivation.
Examples of Left-Most derivation to Previous Examples1:
Derivation of a ∗ (a + b00) by G 1
E ⇒ E ∗ E ⇒ I ∗ E ⇒ a ∗ E ⇒ a ∗ (E) ⇒ a ∗ (E + E) ⇒ a ∗ (I + E) ⇒ a ∗
(a + E) ⇒ a ∗ (a + I) ⇒ a ∗ (a + I0) ⇒ a ∗ (a + I00) ⇒ a ∗ (a + b00)
We can conclude that E ∗ ⇒lm a ∗ (a + b00).

12. Context Free Grammar
Right-Most Derivation:
Rightmost derivation Always replace the rightmost variable by
one of its rule-bodies.
Examples of Right-Most derivation to Previous Examples 1:
E ⇒E ∗ E ⇒ E ∗ (E) ⇒ E ∗ (E + E) ⇒ E ∗ (E + I) ⇒rm E
∗ (E + I0) ⇒ E ∗ (E + I00) ⇒ E ∗ (E + b00) ⇒ E ∗ (I + b00) ⇒ E ∗
(a + b00) ⇒ I ∗ (a + b00) ⇒ a ∗ (a + b00)
We can conclude that E ∗ ⇒rm a ∗ (a + b00).

13. Push Down Automata
Definition:
A pushdown automata (PDA) is essentially an -NFA with a
stack.
• On a transition, the PDA:
1. Consumes an input symbol.
2. Goes to a new state (or stays in the old).
3. Replaces the top of the stack by any string (does nothing,
pops the
stack, or pushes a string onto
the stack)

14. Push Down Automata
Formal Definition:

15. Push Down Automata

16. Turing Machine
Definition:
 We can give a formal description to a particular TM by
specifying each of its seven components.
 This way a TM can become cumbersome.
Note: To avoid this we use higher level descriptions which are
precise enough for the purpose of understanding
 However, every higher level description is actually just a
short hand for its formal counterpart.

17. Turing Machine
Analysis:

18. Turing Machine
Example: