Consider the DFA given below
Which of the regular expressions given below represents the above DFA ?
$(0+1)*00$
To find the regular expression that represents the given DFA, we need to analyze its structure and transitions.
- The DFA starts and ends in different states, indicating specific strings that will result in acceptance. We need to find the path that leads to the accepting state.
- The starting state is represented by the leftmost state. From the start state, the DFA can follow these paths:
- On input '0', move to the second state.
- On input '1', stay in the start state.
- The second state transits:
- On '0', it moves to the accepting state.
- On '1', it loops back to the start state or the second state depending on the DFA structure.
- The accepting state requires two '0's in succession, represented by the string "00". Since any combination of '0's and '1's can be in the prefix, we use the Kleene star operator for "0+1": \((0+1)^*00\).
Therefore, the correct regular expression corresponding to the given DFA is:
(0+1)*00
Explanation of Options:
- (0+1)*00 correctly represents the DFA as it requires a string to end with "00".
- (0+1)*0 is incorrect because it allows any string ending in a single '0', which is not accepted by the DFA.
- (0+1)* is incorrect because it allows any string, not ensuring the "00" pattern required by the DFA.
- (0+1)*00(0+1)* is incorrect because it suggests "00" can appear anywhere, but in the DFA, "00" should appear at the end.
Hence, the correct answer is (0+1)*00.
Important Questions from Finite Automata
Consider the following deterministic finite automaton (DFA) defined over the alphabet, Σ = {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 H 0 0 1 H G A 1 0 - Let $\Sigma = \{1,2,3,4\}$. For $x \in \Sigma^*$, let $prod(x)$ be the product of symbols in $x$ modulo 7. We take $prod(\epsilon) = 1$, where $\epsilon$ is the null string.
For example, $prod(124) = (1 \times 2 \times 4)$ mod 7 = 1.
Define $L = \{x \in \Sigma^* \mid prod(x) = 2\}$.
The number of states in a minimum state DFA for L is ____________ (Answer in integer) Consider the following two finite automata $D_1$ and $D_2$.
Which of the following statements is/are true?- Let $M$ be a nondeterministic finite automaton (NFA) with 6 states over a finite alphabet.
Which of the following options CANNOT be the number of states in the minimal deterministic finite automaton (DFA) that is equivalent to $M$ ?
