Conversion of NFA to DFA (Example 4)

TOC: Problem Number 4 on Conversion of Non-deterministic Finite Automata (NFA) to Deterministic Finite Automata (DFA).
Topics discussed:
This lecture shows how to design an NFA that accepts all the strings over {0,1} in which the second last symbol is always '1'. After designing this, it is converted to its equivalent DFA using the Subset Construction Method.

Music:
Axol x Alex Skrindo - You [NCS Release]

#TheoryOfComputation #TOCByNeso #NFAtoDFA #NFA #DFA #AutomataTheory

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[jaenniskaennis]

I sort of understood the concept of subset construction in my lecture, but the tabular method you showed made it really easy to actually perform the NFA->DFA transformation! Thank you so much for another great video!

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[Nomnomnom]

The DFA here can actually be minimised. Good thing that there is a tutorial on DFA minimization right after this 😄

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[kiirnyok]

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[dessmandessstar]

1. Giver DFA’s accepting the following languages over the alphabet {0, 1}
A. The set of all strings such that each block of five consecutive symbols contains at least
two 0’s
B. The set of all strings whose tenth symbol from the right end is a 1.
C. The set of strings that either begin or end (or both) with 01.
D. The set of strings such that the number of 0’s is divisible by five and the number of 1’s
is divisible by 3.
E. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is
multiple of 5 . for example strings 101, 1010 and are in the language ;0, 100, and
111 are not.
F. The set of all strings that, when interpreted in reverse as a binary integer, is divisible by
5.Examples of strings in the language are 0, 10011, 1001100 and 0101.
G. The set of all strings ending in 00.
H. The set of all strings with three consecutive 0’s(Not necessarily at the end)
I. The set of strings with 011 as substring.
2. Design NFA’s to recognize the following sets of strings.
A. abc, abd, and aacd.Assume the alphabet is {a, b, c, d}
B. 0101, 101 and 011
C. ab, bc and cs .Assume the alphabet is {a, b, c}
3. Convert each of your NFA’s from the Q1 to DFA’s.
4. Convert the following NFA to a DFA and informally describe the language it accepts.
5. Write the regular expressions for the following languages.
A. The set of strings over alphabet {a, b, c} containing at least one a and at least one b.
B. The set of strings of 0’s and 1’s whose tenth symbol from the right end is 1.

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