Which of the following languages can be recognized by neither Non-Deterministic Finite Automata (NFA) nor Deterministic Finite Automata (DFA) ? (A) L1 = {w ∈ {0, 1}* | the length of w is even} (B) L2 = {w ∈ {0, 1}* | the length of w is odd} (C) L3 = {w ∈ {0, 1}* | all 0′s come before all 1′s in w} (D) L4 = {w ∈ {0, 1}* | w contains an equal number of 0′s and 1′s} (E) L5 = {w ∈ {0, 1}* | all 1′s come before all 0′s in w} Choose the correct answer from the options given below :
(D) Only
Non-deterministic and deterministic finite automata have exactly the same power: the subset construction converts any NFA into an equivalent DFA. Both recognise precisely the regular languages, so a language is accepted by some NFA if and only if it is accepted by some DFA. The task is therefore to find which listed languages are not regular.
L1 (even length) is regular: a two-state DFA toggles between “even” and “odd” on every symbol and accepts in the even state.
L2 (odd length) is regular: the same two-state DFA with the odd state accepting.
L3 (all 0′s before all 1′s) is the language \(0^*1^*\), given by a regular expression, so it is regular.
L5 (all 1′s before all 0′s) is \(1^*0^*\), also regular.
L4 (equal numbers of 0′s and 1′s) is not regular. By the pumping lemma, take \(w = 0^p1^p\); any split with \(|xy| \le p\) puts y inside the 0-block, and pumping y changes the count of 0′s only, giving a string outside L4. A finite automaton cannot keep an unbounded count.
So only L4 is recognised by neither kind of automaton. Pairs containing L1, L2, L3 or L5 are wrong because each of those is regular.
(D) Only option is correct.
Similar Questions
There are exactly __________ different finite automata with three states x, y and z over the alphabet {a, b} where x is always the start state.
The transition function for the language \(L = \{w \mid n_{a}(w)\) and \(n_{b}(w)\) are both odd\(\}\) is given by :
\(\delta(q_{0}, a) = q_{1}\) ; \(\delta(q_{0}, b) = q_{2}\)
\(\delta(q_{1}, a) = q_{0}\) ; \(\delta(q_{1}, b) = q_{3}\)
\(\delta(q_{2}, a) = q_{3}\) ; \(\delta(q_{2}, b) = q_{0}\)
\(\delta(q_{3}, a) = q_{2}\) ; \(\delta(q_{3}, b) = q_{1}\)
The initial and final states of the automata are :
Minimal deterministic finite automaton for the language \(L = \{0^{n} \mid n \geq 0, n \neq 4\}\) will have :
For the above specified passage, which of the following is DFA for the language represented/accepeted by machine?
For the above mentioned passage which of the following is correct?
Which of the following represented the minimum state DFA for the above specified passage?
Which of the following Finite Automata, recognizes the language L={a,b}* ?
A. M=({q0}, {a,b}, δ, q0, {q0}) where, δ is
a b q0 {q0} {q0} B. M=({q0,q1}, {a,b}, δ, q0, {q0,q1}) where, δ is
a b q0 {q0,q1} {q0,q1} q1 {q1} {q1} C. M=({q0,q1}, {a,b}, δ, q0, {q0,q1}) where, δ is
a b q0 {q0,q1} {q0} q1 - {q1} D. M=({q0,q1,q2 }, {a,b}, δ, q0, {q0}) where, δ is
a b q0 {q0} {q0} q1 {q2} - q2 {q0} {q2} What is the minimum and maximum number of initial, dead, unreachable and final states in a valid ‘n’ state finite automaton, where the language accepted is not ‘φ’?
Let L be the language generated by regular expression 0*10* and accepted by the deterministic finite automata M, whose transition table is given below (start state a; final states c, d and e).
State 0 1 a b c b a d c e f d e f e e f f f f Consider the relation RM defined by M. As all states are reachable from the start state, RM has _____ equivalence classes.
Important Questions from Finite Automata
Consider the DFA given below
Which of the regular expressions given below represents the above DFA ?- 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 $M$ ? 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 Consider the following DFA that generates set of strings over $\Sigma=\{a, b, c\}$
Now identify that which of the followings is the best description of the language for the above DFA
