How to draw this finite automate?

Question

I would like to verify if i have the good approach to this problem, while looking at my solution it seems ok but i am not sure. Thank you.

I am using this tool to draw if you wanna help out : http://madebyevan.com/fsm/

Here's the question :

Build a finite automata ( it can be deterministic or not) that accept this language on the alphabet $\{0,1\}$ :

$$L=\{w : w \neq 11 \text{ and } w \neq 101 \}$$

In other words, L includes all sequences except 11 and 101

Here's what i tried :

Answer 1

Your detailed question deserves a detailed answer. It is indeed easier to take the complement of the language, that is, $L^c = \{11, 101\}$, and first compute its minimal automaton. Note that the method suggested by Eric Towers would give a deterministic automaton, but not the minimal one. The minimal deterministic incomplete automaton of $L^c$ is represented below

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Now, to get the minimal deterministic automaton of $L$, just add the sink state $0$ and swap the final states.

$\hskip 100pt$

P.S. As you indicated your source to draw automata, here is mine. These automata were obtained using the $\LaTeX$ package gastex.

Answer 2

You might benefit from constructing a complete binary tree of depth three (each internal node has one child consuming a "0" and one consuming a "1"), determining which nodes are rejecting, which are accepting, and then simplify the tree.

Answer 3

Your DFA fails to accept the string $1001$. It would be better if you draw a DFA for $L=\{11,101\}$ and then take the compliment.

Answer 4

We want to avoid $11$ and $101$