Consider the following deterministic finite automaton (DFA) defined over the alphabet, $\Sigma=\{a, b\}$. Identify which of the following language(s) is/are accepted by the given DFA.
Consider a finite state machine (FSM) with one input $X$ and one output $f$, represented by the given state transition table. The minimum number of states required to realize this FSM is ________ . (Answer in integer)
| Present state | Next state | Output $f$ | ||
|---|---|---|---|---|
| $X = 0$ | $X = 1$ | $X = 0$ | $X = 1$ | |
| A | F | B | 0 | 0 |
| B | D | C | 0 | 0 |
| C | F | E | 0 | 0 |
| D | G | A | 1 | 0 |
| E | D | C | 0 | 0 |
| F | F | B | 1 | 1 |
| G | G | H | 0 | 1 |
| H | G | A | 1 | 0 |
Let M be the 5-state NFA with ε-transitions shown in the diagram below.
Which one of the following regular expressions represents the language accepted by M?
Let L1 be the language represented by the regular expression b*ab*(ab*ab*)* and L2 = { w ∈ (a + b)* | |w| ≤ 4 }, where |w| denotes the length of string w. The number of strings in L2 which are also in L1 is __________.