1. Non Deterministic Finite Auotmata
Abhineet Anand
Assistant Professor
Dept. of Computer Science And Engineering,
College of Engineering Studies.
University of Petroleum and Energy Studies, Dehradun.
January 24, 2013
Abhineet Anand (UPES, Dehradun) Non Deterministic Finite Auotmata January 24, 2013 1/7
2. Outline
1 Why Nondeterminism
2 Definition
Abhineet Anand (UPES, Dehradun) Non Deterministic Finite Auotmata January 24, 2013 2/7
3. Nondeterministic
Nondeterministic means a choice of moves for an auotmaton.
Set of possible moves is given rather than unique move.
Formally, it is achieved by defining the transition function so that its
range is a set of possible states.
Abhineet Anand (UPES, Dehradun) Non Deterministic Finite Auotmata January 24, 2013 3/7
4. Why Nondeterministic
A ”nondeterministic” finite automation(NFA) has the power to be in
several states at once.
Each NFA accepts a language that is also accepted by some DFA.
NFA can be converted to DFA.
Though nondeterministic is a feature which is normally not associated
with real computers, it is an extension of the behaviour of DFA.
Moreover, nondeterministic is an essential feature of FA, every NFA is
equivalent to FA.
Abhineet Anand (UPES, Dehradun) Non Deterministic Finite Auotmata January 24, 2013 4/7
5. Definition
A non deterministic finite automata is a quintuple
M=(Q, Σ, δ , q0 , F)
1 Q : Is a non-empty finite set of states presents in the finite control.
(q0 , q1 , q2 , q3 , ...)
2 Σ : Is a non-empty finite set of input symbols which can be passed to
the finite state machine. (a, b, c, d, ....)
3 q0 : Is a Starting state, One of the state in Q.
4 F : Is a non-empty set of final states or accepting states, set of final
states belongs to Q.
5 δ : Is a Function called transition function that takes two argument : a
state and input symbol, and it return a a sub set of state Q.
that is Q x (ΣU {ϸ }) → 2Q
Abhineet Anand (UPES, Dehradun) Non Deterministic Finite Auotmata January 24, 2013 5/7
6. Non Deterministic Finite Automata
The transition function is : Q x (ΣU {ϸ }) → 2Q .
Transition Table for the above automata:
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