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TOPIC - MINIMIZATION OF DFA - TABLE FILLING METHOD    • MINIMIZATION OF DFA - TABLE FILLING METHOD  

Formal Definition of DFA :

We formally denote a finite automation by a 5 tuples.
M = (Q, ∑, δ, q0,F)
Q = is a finite set of states
∑ = is a finite input alphabet
q0 = is the initial state in Q
F = is the set of final states F ⸦ Q
δ= is the transition function mapping from Q x ∑ = Q

Minimization Algorithm :

Procedure : [table filling method]

An x is placed in the table each time a state that cannot be equivalent.

Initially an x is placed in each entry corresponding to one final state and one non – final state.

Next for each pair of states p and q that are not distinguishable, we consider.
r = δ(p, a)
s = δ(q, a) for each input symbol a

If states r and s have been shown to be distinguishable by some string x, then p and q are distinguishable by string ax.

Thus if the string (r,s) in the table has an x, an x is placed at the entry (p, q)