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NFA to DFA

Write a Java program to convert any given NFA to an equivalent DFA.

NFA files is shown in the following example:

3

a b c d

0: {0} {0,1} {} {} {1,2,0}

1: {} {1} {1} {1} {1}

2: {} {1,2} {1} {1} {2}

0

{1,2}

• The first line contains the number of states of the NFA; in this case, there are 3 states.

• The second line contains Σ = {a, b, c, d}.

• After that, each line is a state and its transition. The number to the left of the colon

is the label of the state. After the colon, each set is the set of next states on the input

alphabet corresponding to the alphabets in Σ in the same order as shown in the second

line plus the λ-transition at the end of the same line.

For example, the transitions of the NFA shown above from state 0 are: δ(0, a) =

{0}, δ(0, b) = {0, 1}, δ(0, c) = {}, δ(0, d) = {}, and δ(0, λ) = {0, 1, 2}.

Note that, the last column is referred to λ-transition, and coming back to self is always

implied; therefore, 0 is included in δ(0, λ) = {0, 1, 2}, although 0 may not be shown in

the last column of state 0.

• After every state’s transitions are specified, there is a line to indicate the starting state.

In this case, 0 is the starting state.

• The last line contains the set of final states. In this case, {1, 2}

I will compile and run the program from the Unix

command line as follows:

javac [url removed, login to view]

java NFA nfa2 [url removed, login to view]

the program should print out the following text:

(1) The original NFA

(2) An equivalent DFA (no need to minimized)

(3) The list of strings in [url removed, login to view] that are accepted by the NFA (don’t list those

that are rejected).

Here is the example output:

Sigma:a b

------

0: (a,{1}) (b,{4}) ( ,{2})

1: (a,{5}) (b,{2}) ( ,{})

2: (a,{5}) (b,{}) ( ,{})

3: (a,{}) (b,{}) ( ,{0})

4: (a,{}) (b,{1}) ( ,{3})

5: (a,{}) (b,{}) ( ,{4})

------

0: Initial State

5: Accepting State(s)

To DFA:

Sigma: a b

------------------

0: 1 2

1: 1 3

2: 1 3

3: 1 3

------------------

0: Initial State

1: Accepting State(s)

The following strings are accepted:

aabaa

aaaaa

Skills: Java

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