The document defines key concepts in theory of computation including symbols, alphabets, strings, languages, finite state machines, and regular languages. It explains that a finite state machine is defined using 5 tuples and has limited memory. Deterministic finite automata and nondeterministic finite automata are described as being different based on their transition functions. Regular languages are those recognized by a finite state machine and cannot require storing strings. Operations on regular languages like union, intersection, and Kleene closure are also covered.

1. Theory of Computation
by
Savita Baban Ghatte

2.  Symbol -
e.g. –a,b,c,0,1,2,3,………
 Alphabel -
Collection of symbols denoted by ∑
e.g. {a,b}, {0,1}, {0,1,2}, {a,b,c} ,{b,c,d,e}
 String-
Sequence of symbols
e.g.- a,b,0,1,aa,bb,abcd, 01, 0123

3.  Language
Set of strings
e.g. ∑= {a,b}
L1= { Set of all strings of length 2}
={aa,bb,ab,ba}
L2={ Set of all strings of length 3}
={aaa,aab,aba,baa,
abb,bba,bbb,bba,bab}

4. Finite State Machine
 FSM is simplest model of computation
 FSM is an abstract mathematical
model
 It has very limited memory

5. Finite State Machine
 Mathematically FSM is defined using
Five tuples (Q, ∑, q0, F, δ)
1.Q: finite set of states
2. ∑: finite set of input symbol
3. q0: initial state
4. F: final state
5. δ: Transition function

6.  Transition function can be define as
 δ: Q x ∑ →Q
 FA has two states:
accept state or reject state.

7. Types of Finite State Machine
 Finite Automata
 Finite Automata with output
1) Moore Machine
2) Mealy Machine
 Finite Automata without output
1) Deterministic Finite Automata (DFA)
2) Non deterministic Finite Automata
(NFA)
3) Epsilon NFA

8. DFA
 DFA stands for Deterministic Finite
Automata.
 In DFA, the input character goes to
one state only
 DFA doesn't accept the null move that
means the DFA cannot change state
without any input character.
 DFA is defined using five tuples
 {Q, ∑, q0, F, δ}

9. DFA
 DFA has five tuples {Q, ∑, q0, F, δ}
 Q: set of all states
∑: finite set of input symbol where
 δ: Q x ∑ →Q
 q0: initial state
 F: final state
 δ: Transition function

10. NDFA
 NDFA refer to the Non Deterministic
Finite Automata.
 It is used to transit the any number of
states for a particular input.
 NDFA accepts the NULL move that
means it can change state without
reading the symbols.

11. NDFA
 NDFA also has five states same as
DFA. But NDFA has different transition
function.
 Transition function of NDFA can be
defined as:
 δ: Q x ∑ →2Q

12. Regular Language
 A language is regular language if
some Finite State Machine (FSM)
recognizes it.
 The memory of Finite State Machine
is very limited.
 FSM cannot store string.

13. Regular Language
 Not regular language
- The language which require memory
to store string.
- The language which are not
recognized by any Finite state
machine.
- E.g. abab, 011011, anbn

14. Operations on Regular
Language
 The operations on regular language
are:
 Union: If L1and L2 are two regular
languages then their union L1 U L2 is
also a union.
L1 U L2 = {s | s is in L1 or s is in L2}
 Intersection: If L1 and L2 are two
regular languages then their
intersection is also an intersection.
 L1 ⋂ L2 = {st | s is in L1 and t is in L2}

15. Operations on Regular
Language
 Kleene closure:
If L is a regular language then its kleene
closure.
L* = Zero or more occurrence of langua
ge L.
Here L is a regular language.