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). Consider the relation RM defined by M. As all states are reachable from the start state, RM has _____ equivalence classes.State 0 1 a b c b a d c e f d e f e e f f f f
6
For a DFA \(M = (Q, \Sigma, \delta, q_0, F)\) the relation \(R_M\) on strings is defined by \(x \, R_M \, y\) if and only if \(\delta(q_0, x) = \delta(q_0, y)\), that is, x and y drive M to the same state. It is a right-invariant equivalence relation, and each of its classes is the set of strings that reach one particular state, so its index equals the number of states reachable from the start state.
Step 1 — The automaton M given in the table has six states a, b, c, d, e, f: start a; a–0→b, b–0→a, a–1→c, b–1→d, c–0→e, d–0→e, e–0→e, and c, d, e on 1 go to f, which loops on 0 and 1; the final states are c, d and e.
Step 2 — Since all six states are reachable, \(R_M\) has six classes: \((00)^*\) (state a), \((00)^*0\) (b), \((00)^*1\) (c), \((00)^*01\) (d), \(0^*100^*\) (e) and \(0^*10^*1(0+1)^*\) (f).
Step 3 — These classes refine the three classes of the language relation \(R_L\) (no 1, exactly one 1, two or more 1s); the minimal DFA would merge a with b and c, d with e.
The smaller counts 2, 4 and 5 do not match the number of reachable states of this automaton, which is what fixes the index of \(R_M\).
6 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 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 :
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’?
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
