How do I construct transition table for the following?

Question

Fig. contains transition diagramDesign Finite Automata which accepts only those strings that start with 1 and ends with 0. Please describe me how to construct transition table because all I need to learn is transition table itself as I can then draw transition diagram from the table.

Answer 1

So from your description we need four states:

• A start state $s_\epsilon$, it signals that nothing has been read
• A state $s_0$ that signals that the word started with a $1$, and the last read symbol was a $0$.
• A state $s_1$ that signals that the word started with a $1$, and the last read symbol was a $1$.
• A state $s_\bot$ that signals that the word started with a $0$.

If we have started with a $0$, nothing ever read can lead to an accepted word, that is we stay in $s_\bot$, that gives the transition table $$ \begin{array}{c|*4c} & s_\epsilon & s_0 & s_1 & s_\bot\\ \hline 0 & s_\bot & s_0 & s_0 & s_\bot\\ 1 & s_1 & s_1 & s_1 & s_\bot \end{array} $$