What is the deterministic finitite automaton (DFA) for the regex ".*b."
Every language described by a regular expression has a DFA&nbsp;&ndash; this is Kleene's theorem (not to be confused with Kleene's recursion theorems, which are something completely different).  Standard algorithms to translate from regular expressions to automata give nondeterministic automata (NFAs), such as the one you found on the web.  There are standard algorithms to determinize NFAs but they make the state space exponentially larger.

In this case, though, it's straightforward to produce a DFA by thinking about the language you're interested in. The language is all strings whose second-to-last character is&nbsp;$b$. So your automaton needs to accept if it gets to the end of the string and the previous character it saw was a&nbsp;$b$.  I don't have any drawing software to hand but the following textual description is, I think, more useful.  You need four states, corresponding to the combinations of "the character I just read was/was not&nbsp;$b$" and "the character before that was/was not&nbsp;$b$". You start in (not&nbsp;$b$, not&nbsp;$b$), since you haven't read any&nbsp;$b$s before you've read any characters.  The transition function and so on should be pretty obvious.