Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Some useful problems
Recent questions tagged finite-automata
7
votes
5
answers
181
ISRO2020-41
Minimum number of states required in DFA accepting binary strings not ending in $\text{“101”}$ is $3$ $4$ $5$ $6$
Minimum number of states required in DFA accepting binary strings not ending in $\text{“101”}$ is$3$$4$$5$$6$
Satbir
7.1k
views
Satbir
asked
Jan 13, 2020
Theory of Computation
isro-2020
theory-of-computation
finite-automata
normal
+
–
1
votes
0
answers
182
Michael Sipser Edition 3 Exercise 5 Question 27 (Page No. 241)
A two-dimensional finite automaton $(2DIM-DFA)$ is defined as follows. The input is an $m \times n$ rectangle, for any $m, n \geq 2$ ... of determining whether two of these machines are equivalent. Formulate this problem as a language and show that it is undecidable.
A two-dimensional finite automaton $(2DIM-DFA)$ is defined as follows. The input is an $m \times n$ rectangle, for any $m, n \geq 2$. The squares along the boundary of th...
admin
467
views
admin
asked
Oct 20, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
turing-machine
decidability
proof
+
–
0
votes
0
answers
183
Michael Sipser Edition 3 Exercise 5 Question 26 (Page No. 240)
Define a two-headed finite automaton $(2DFA)$ to be a deterministic finite automaton that has two read-only, bidirectional heads that start at the left-hand end of the input tape and can be independently controlled to move in either direction. The tape ... $E_{2DFA}$ is not decidable.
Define a two-headed finite automaton $(2DFA)$ to be a deterministic finite automaton that has two read-only, bidirectional heads that start at the left-hand end of the in...
admin
395
views
admin
asked
Oct 20, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
turing-machine
decidability
proof
+
–
0
votes
0
answers
184
Michael Sipser Edition 3 Exercise 4 Question 27 (Page No. 212)
Let $E = \{\langle M \rangle \mid \text{ M is a DFA that accepts some string with more 1s than 0s}\}$. Show that $E$ is decidable. (Hint: Theorems about $CFLs$ are helpful here.)
Let $E = \{\langle M \rangle \mid \text{ M is a DFA that accepts some string with more 1s than 0s}\}$. Show that $E$ is decidable. (Hint: Theorems about $CFLs$ are helpfu...
admin
232
views
admin
asked
Oct 17, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
decidability
proof
+
–
0
votes
1
answer
185
Michael Sipser Edition 3 Exercise 4 Question 26 (Page No. 212)
Let $PAL_{DFA} = \{ \langle M \rangle \mid \text{ M is a DFA that accepts some palindrome}\}$. Show that $PAL_{DFA}$ is decidable. (Hint: Theorems about $CFLs$ are helpful here.)
Let $PAL_{DFA} = \{ \langle M \rangle \mid \text{ M is a DFA that accepts some palindrome}\}$. Show that $PAL_{DFA}$ is decidable. (Hint: Theorems about $CFLs$ are helpfu...
admin
320
views
admin
asked
Oct 17, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
decidability
proof
+
–
0
votes
0
answers
186
Michael Sipser Edition 3 Exercise 4 Question 25 (Page No. 212)
Let $BAL_{DFA} = \{ \langle M \rangle \mid \text{ M is a DFA that accepts some string containing an equal number of 0s and 1s}\}$. Show that $BAL_{DFA}$ is decidable. (Hint: Theorems about $CFLs$ are helpful here.)
Let $BAL_{DFA} = \{ \langle M \rangle \mid \text{ M is a DFA that accepts some string containing an equal number of 0s and 1s}\}$.Show that $BAL_{DFA}$ is decidable. (Hin...
admin
236
views
admin
asked
Oct 17, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
decidability
proof
+
–
0
votes
0
answers
187
Michael Sipser Edition 3 Exercise 4 Question 23 (Page No. 212)
Say that an $NFA$ is ambiguous if it accepts some string along two different computation branches. Let $AMBIG_{NFA} = \{ \langle N \rangle \mid \text{ N is an ambiguous NFA}\}$. Show that $AMBIG_{NFA}$ is decidable. (Suggestion: One elegant way to solve this problem is to construct a suitable $DFA$ and then run $E_{DFA}$ on it.)
Say that an $NFA$ is ambiguous if it accepts some string along two different computation branches. Let $AMBIG_{NFA} = \{ \langle N \rangle \mid \text{ N is an ambiguous N...
admin
353
views
admin
asked
Oct 17, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
decidability
proof
+
–
0
votes
0
answers
188
Michael Sipser Edition 3 Exercise 4 Question 17 (Page No. 212)
Prove that $EQ_{DFA}$ is decidable by testing the two DFAs on all strings up to a certain size. Calculate a size that works.
Prove that $EQ_{DFA}$ is decidable by testing the two DFAs on all strings up to a certain size. Calculate a size that works.
admin
256
views
admin
asked
Oct 17, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
decidability
proof
+
–
0
votes
0
answers
189
Michael Sipser Edition 3 Exercise 4 Question 3 (Page No. 211)
Let $ALL_{DFA} = \{ \langle{ A }\rangle \mid A \text{ is a DFA and}\: L(A) = \Sigma^{\ast}\}.$ Show that $ALL_{DFA}$ is decidable.
Let $ALL_{DFA} = \{ \langle{ A }\rangle \mid A \text{ is a DFA and}\: L(A) = \Sigma^{\ast}\}.$ Show that $ALL_{DFA}$ is decidable.
admin
211
views
admin
asked
Oct 15, 2019
Theory of Computation
michael-sipser
theory-of-computation
turing-machine
finite-automata
decidability
proof
+
–
0
votes
0
answers
190
Michael Sipser Edition 3 Exercise 4 Question 2 (Page No. 211)
Consider the problem of determining whether a DFA and a regular expression are equivalent. Express this problem as a language and show that it is decidable.
Consider the problem of determining whether a DFA and a regular expression are equivalent. Express this problem as a language and show that it is decidable.
admin
512
views
admin
asked
Oct 15, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
regular-expression
decidability
proof
+
–
0
votes
0
answers
191
Michael Sipser Edition 3 Exercise 4 Question 1 (Page No. 210)
admin
516
views
admin
asked
Oct 15, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
turing-machine
descriptive
+
–
0
votes
0
answers
192
Michael Sipser Edition 3 Exercise 3 Question 9 (Page No. 188)
Let a $k-PDA$ be a pushdown automaton that has $k$ stacks. Thus a $0-PDA$ is an $NFA$ and a $1-PDA$ is a conventional $PDA$. You already know that $1-PDAs$ are more powerful (recognize a larger class of languages) than ... $3-PDAs$ are not more powerful than $2-PDAs$. (Hint: Simulate a Turing machine tape with two stacks.)
Let a $k-PDA$ be a pushdown automaton that has $k$ stacks. Thus a $0-PDA$ is an $NFA$ and a $1-PDA$ is a conventional $PDA$. You already know that $1-PDAs$ are more power...
admin
278
views
admin
asked
Oct 15, 2019
Theory of Computation
michael-sipser
theory-of-computation
pushdown-automata
finite-automata
descriptive
+
–
1
votes
2
answers
193
CMI2019-A-2
Let $A$ be an $NFA$ with $n$ states. Which of the following is necessarily true? The shortest word in $L(A)$ has length at most $n-1.$ The shortest word in $L(A)$ has length at least $n.$ The shortest word not in $L(A)$ has length at most $n-1.$ The shortest word not in $L(A)$ has length at least $n.$
Let $A$ be an $NFA$ with $n$ states. Which of the following is necessarily true?The shortest word in $L(A)$ has length at most $n-1.$The shortest word in $L(A)$ has lengt...
gatecse
877
views
gatecse
asked
Sep 13, 2019
Theory of Computation
cmi2019
finite-automata
+
–
3
votes
3
answers
194
CMI2019-B-1
Consider an alphabet $\Sigma=\{a,b\}.$ Let $L_{1}$ be the language given by the regular expression $(a+b)^{\ast}bb(a+b)^{\ast}$ and let $L_{2}$ be the language $baa^{\ast}b.$ Define $L:=\{u\in\Sigma^{\ast}\mid \exists w\in L_{2}\: s.t.\: uw\in L_{1}\}.$ Give an example of a word in $L.$ Give an example of a word not in $L.$ Construct an NFA for $L.$
Consider an alphabet $\Sigma=\{a,b\}.$Let $L_{1}$ be the language given by the regular expression $(a+b)^{\ast}bb(a+b)^{\ast}$ and let $L_{2}$ be the language $baa^{\ast}...
gatecse
1.6k
views
gatecse
asked
Sep 13, 2019
Theory of Computation
cmi2019
regular-expression
regular-language
finite-automata
+
–
1
votes
2
answers
195
CMI2018-B-1
Consider the following non-deterministic finite automata(NFA) $A_{1}$ and $A_{2}:$ Give an example of a word which is accepted by both $A_{1}$ and $A_{2}.$ Give an example of a word which is accepted by $A_{1},$ but not by $A_{2}.$ Draw the deterministic finite automaton(DFA) equivalent to $A_{1}.$
Consider the following non-deterministic finite automata(NFA) $A_{1}$ and $A_{2}:$Give an example of a word which is accepted by both $A_{1}$ and $A_{2}.$Give an example ...
gatecse
638
views
gatecse
asked
Sep 13, 2019
Theory of Computation
cmi2018
finite-automata
descriptive
+
–
0
votes
0
answers
196
Ullman (Compiler Design) Edition 2 Exercise 5.2 Question 6 (Page No. 317)
Implement Algorithm $3.23$, which converts a regular expression into a nondeterministic finite automaton, by an L-attributed SDD on a top-down parsable grammar. Assume that there is a token char representing any ... never before returned by this function. Use any convenient notation to specify the transitions of the $NFA$.
Implement Algorithm $3.23$, which converts a regular expression into a nondeterministic finite automaton, by an L-attributed SDD on a top-down parsable grammar. Assume th...
admin
838
views
admin
asked
Sep 6, 2019
Compiler Design
ullman
compiler-design
syntax-directed-translation
regular-expression
finite-automata
parsing
+
–
0
votes
0
answers
197
Ullman (Compiler Design) Edition 2 Exercise 4.6 Question 8 (Page No. 259)
We suggested that individual items could be regarded as states of a nondeterministic finite automaton, while sets of valid items are the states of a deterministic finite automaton (see the box on "Items as States of an NFA" ... the NFA that comes from the valid items for a grammar produces the $LR(0)$ sets of items.
We suggested that individual items could be regarded as states of a nondeterministic finite automaton, while sets of valid items are the states of a deterministic finite ...
admin
275
views
admin
asked
Aug 20, 2019
Compiler Design
ullman
compiler-design
finite-automata
grammar
lr-parser
descriptive
+
–
4
votes
2
answers
198
UGC NET CSE | June 2019 | Part 2 | Question: 75
How many states are there in a minimum state automata equivalent to regular expression given below? Regular expression is $a^*b(a+b)$ $1$ $2$ $3$ $4$
How many states are there in a minimum state automata equivalent to regular expression given below?Regular expression is $a^*b(a+b)$$1$$2$$3$$4$
Arjun
4.6k
views
Arjun
asked
Jul 2, 2019
Theory of Computation
ugcnetcse-june2019-paper2
finite-automata
minimal-state-automata
+
–
2
votes
2
answers
199
Conversion of regular grammar to FA
A->aB/bA/b B->aC/bB C->aA/bC/a If the above regular grammar is converted into DFA then how many final states will be there? According to me there should be 2 final states: A and C But the resource from where I am reading it says only one final state will be there which will be A. Kindly explain.
A->aB/bA/bB->aC/bBC->aA/bC/a If the above regular grammar is converted into DFA then how many final states will be there?According to me there should be 2 final states: A...
Akash Kumar Roy
4.7k
views
Akash Kumar Roy
asked
Jun 3, 2019
Theory of Computation
theory-of-computation
finite-automata
regular-grammar
+
–
3
votes
3
answers
200
Ace Test Series: Theory Of Computation - Finite Automata
How many $2$ state DFA’s with the designated initial state can be constructed over the alphabet over the alphabet $\sum = \{a, b\}$ that accept universal language? $4$ $16$ $20$ $24$
How many $2$ state DFA’s with the designated initial state can be constructed over the alphabet over the alphabet $\sum = \{a, b\}$ that accept universal language?$4$$1...
Hirak
1.4k
views
Hirak
asked
May 22, 2019
Theory of Computation
ace-test-series
theory-of-computation
finite-automata
number-of-dfa
+
–
3
votes
2
answers
201
ACE ACADEMY: TOC
How many 2 state DFA’s with designated initial state can be constructed over the alphabet Σ = {a, b} that accept empty language ϕ ? (a) 4 (b) 16 (c) 20 (d) 24
How many 2 state DFA’s with designated initial state can be constructed over the alphabet Σ = {a, b} that accept empty language ϕ ?(a) 4 (b) 16 (c) 20 ...
Hirak
2.4k
views
Hirak
asked
May 22, 2019
Theory of Computation
theory-of-computation
number-of-dfa
finite-automata
+
–
3
votes
1
answer
202
Self Doubt : Ambiguity
Why is ambiguity in regular language is decidable and not decidable in CFL ? Can you give Example?
Why is ambiguity in regular language is decidable and not decidable in CFL ? Can you give Example?
logan1x
1.1k
views
logan1x
asked
May 10, 2019
Theory of Computation
theory-of-computation
finite-automata
ambiguous
regular-language
context-free-language
context
+
–
0
votes
0
answers
203
Michael Sipser Edition 3 Exercise 1 Question 72 (Page No. 93)
Let $M_{1}$ and $M_{2}$ be $\text{DFA's}$ that have $k_{1}$ and $k_{2}$ states, respectively, and then let $U = L(M_{1})\cup L(M_{2}).$ Show that if $U\neq\phi$ then $U$ contains some string $s,$ where $|s| < max(k1, k2).$ Show that if $U\neq\sum^{*},$ then $U$ excludes some string $s,$ where $|s| < k1k2.$
Let $M_{1}$ and $M_{2}$ be $\text{DFA's}$ that have $k_{1}$ and $k_{2}$ states, respectively, and then let $U = L(M_{1})\cup L(M_{2}).$Show that if $U\neq\phi$ then $U$ c...
admin
326
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
+
–
2
votes
2
answers
204
Michael Sipser Edition 3 Exercise 1 Question 71 (Page No. 93)
Let $\sum = \{0,1\}$ Let $A=\{0^{k}u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$ Show that $A$ is regular. Let $B=\{0^{k}1u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$Show that $B$ is not regular.
Let $\sum = \{0,1\}$Let $A=\{0^{k}u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$ Show that $A$ is regular.Let $B=\{0^{k}1u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}....
admin
510
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
+
–
0
votes
1
answer
205
Michael Sipser Edition 3 Exercise 1 Question 70 (Page No. 93)
We define the $\text{avoids}$ operation for languages $A$ and $B$ to be $\text{A avoids B = {w| w ∈ A and w doesn’t contain any string in B as a substring}.}$ Prove that the class of regular languages is closed under the ${avoids}$ operation.
We define the $\text{avoids}$ operation for languages $A$ and $B$ to be $\text{A avoids B = {w| w ∈ A and w doesn’t contain any string in B as a substring}.}$ Prove t...
admin
489
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
+
–
1
votes
0
answers
206
Michael Sipser Edition 3 Exercise 1 Question 69 (Page No. 93)
Let $\sum=\{0,1\}.$ Let $WW_{k}=\{ww|w\in \sum^{*}$ and $w$ is of length $k\}.$ Show that for each $k,$ no DFA can recognize $WW_{k}$ with fewer than $2^{k}$ states. Describe a much smaller $NFA$ for $\overline{WW_{k}},$ the complement of $WW_{k}.$
Let $\sum=\{0,1\}.$ Let $WW_{k}=\{ww|w\in \sum^{*}$ and $w$ is of length $k\}.$Show that for each $k,$ no DFA can recognize $WW_{k}$ with fewer than $2^{k}$ states.Descri...
admin
336
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
proof
descriptive
+
–
0
votes
0
answers
207
Michael Sipser Edition 3 Exercise 1 Question 66 (Page No. 93)
A $\text{homomorphism}$ is a function $f : Σ→Γ^{*}$ from one alphabet to strings overanother alphabet. We can extend $f$ to operate on strings by defining $f(w) = f(w_{1})f(w_{2})...f(w_{n}),$ ... Is it a DFA in every case$?$ Show, by giving an example, that the class of non-regular languages is not closed under homomorphism.
A $\text{homomorphism}$ is a function $f : Σ→Γ^{*}$ from one alphabet to strings overanother alphabet. We can extend $f$ to operate on strings by defining $f(w) = f(w...
admin
581
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
homomorphism
descriptive
+
–
0
votes
0
answers
208
Michael Sipser Edition 3 Exercise 1 Question 65 (Page No. 93)
Prove that for each $n > 0,$ a language $B_{n}$ exists where $B_{n}$ is recognizable by an $\text{NFA}$ that has $n$ states, and if $B_{n} = A_{1}\cup...\cup A_{k},$ for regular languages $A_{i},$ then at least one of the $A_{i}$ requires a $\text{DFA}$ with exponentially many states$.$
Prove that for each $n 0,$ a language $B_{n}$ exists where$B_{n}$ is recognizable by an $\text{NFA}$ that has $n$ states, andif $B_{n} = A_{1}\cup...\cup A_{k},$ for reg...
admin
305
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
descriptive
+
–
0
votes
0
answers
209
Michael Sipser Edition 3 Exercise 1 Question 64 (Page No. 92)
Let $N$ be an $\text{NFA}$ with $k$ states that recognizes some language $A.$ Show that if $A$ is nonempty, A contains some string of length at most k. Show, by giving an example, that $\text{part (a)}$ is not necessarily ... ;s shortest member strings are of length exponential in $k.$ Come as close to the bound in $(c)$ as you can$.$
Let $N$ be an $\text{NFA}$ with $k$ states that recognizes some language $A.$Show that if $A$ is nonempty, A contains some string of length at most k.Show, by giving an e...
admin
588
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
descriptive
+
–
0
votes
0
answers
210
Michael Sipser Edition 3 Exercise 1 Question 63 (Page No. 92)
Let $A$ be an infinite regular language. Prove that $A$ can be split into two infinite disjoint regular subsets. Let $B$ and $D$ be two languages. Write $B\subseteqq D$ if $B\subseteq D$ and $D$ contains infinitely many ... regular languages where $B\subseteqq D,$ then we can find a regular language $C$ where $B\subseteqq C\subseteqq D.$
Let $A$ be an infinite regular language. Prove that $A$ can be split into two infinite disjoint regular subsets.Let $B$ and $D$ be two languages. Write $B\subseteqq D$ if...
admin
346
views
admin
asked
Apr 30, 2019
Theory of Computation
michael-sipser
theory-of-computation
finite-automata
regular-language
descriptive
+
–
Page:
« prev
1
2
3
4
5
6
7
8
9
10
11
12
...
35
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register