# Sheet 7 : Question 2

Question is:

Determinize this automaton by breakpoint construction.

• inputs {a},{};
• outputs ;

Submit the solution in the following form:
labels 0:s1; 1:s2,s3; 2:; 3:s0,s1,s2;     // encode Q
labels 0:; 1:s2,s3; 2:; 3:s2;     // encode Qf
init 0,1;
transitions (0,{a},,1); (0,{},,2); (1,{},,3); (3,{a},,3); (3,{},,3);
accept 2,3;

Solution :

labels 0:s0,s3; 2:s1,s3; 3:s2; 1:; 4:s0;    // encode Q

labels 0:; 2:s1; 3:s2; 1:; 4:;    // encode Qf

init 0;

transitions (0,{a},,1); (0,{},,2); (2,{},,3); (2,{a},,1); (3,{},,4); (3,{a},,1); (4,{},,2);  (4,{a},,1); (1,{},,1); (1,{a},,1);

accept 2,3;

Please tell me where am I wrong?

I have used the teaching tool to verify your result and got a different automaton. The given automaton looks as follows (if I was reading it correctly from your image):

which I encoded as follows for the teaching tool:

```inputs a0,a1;
init 0,3;
transitions
(0,a0,1); (0,a0,3);
(1,a0,2); (1,a1,1);
(2,a0,0);
(3,a1,1);
accept 1,2;```

where a0 means input {} and a1 means input {a}. The breakpoint construction then yields the following deterministic automaton:

by (166k points)
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ok. Thank you so much.