acceptance of a string
a string is accepted by a FA if upon scanning the entire string we rests at a final state.
acceptance of a language
a language is accepted by a FA if all the strings in the language are accepted and all strings
not in the language are rejected by it.
DFA construction
Prob 1
The lang is infinite
Prob 2
The lang is finite
This is minimal automata
1
Given a language ,It is possible to draw many DFA, but a lang will only have one minimal
DFA.
Important trick
Prob 3
This is not minimal
To make it minimal it will look like this
If we divide any no. by 3 the possible remainder is either: -
2
0,1,2 :- therefore we should at least have three states which distinguish the remainder.
Question
What does this mean?
Length of string is congruent to 1 mod 3
Means take length of string divide by 3 the remainder should be 1
Prob
3
More
The transition table
4