Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
No answer
No selected answer
No upvoted answer
Previous GATE
Featured
Recent questions without an upvoted answer
0
votes
0
answers
7741
Ullman (TOC) Edition 3 Exercise 7.1 Question 12 (Page No. 279)
Use the construction of question $11$ to convert the grammar $S\rightarrow AA|0$ $A\rightarrow SS|1$ to $GNF.$
Use the construction of question $11$ to convert the grammar$S\rightarrow AA|0$$A\rightarrow SS|1$to $GNF.$
admin
125
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-grammar
context-free-language
+
–
0
votes
0
answers
7742
Ullman (TOC) Edition 3 Exercise 7.1 Question 11 (Page No. 278 - 279)
In this exercise, we shall show that for every context-free language $L$ containing at least one string other than $\in,$there is a $CFG$ in Greibach normal form that generates $L-\in.$ Recall that a Greibach normal form $(GNF)$ grammar is ... $(a).$ Then fi x the $B_{i}$ productions in any order , again $(a).$
In this exercise, we shall show that for every context-free language $L$ containing at least one string other than $\in,$there is a $CFG$ in Greibach normal form that gen...
admin
301
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
proof
descriptive
+
–
0
votes
0
answers
7743
Ullman (TOC) Edition 3 Exercise 7.1 Question 10 (Page No. 278)
Is it possible to find, for every context-free language without $\in,$ a grammar such that all its productions are either of the form $A\rightarrow BCD$ $($i.e., a body consisting of three variables$),$ or $A\rightarrow a$ $($i.e., a body consisting of a single terminal$)?$ Give either a proof or a counterexample.
Is it possible to find, for every context-free language without $\in,$ a grammar such that all its productions are either of the form $A\rightarrow BCD$ $($i.e., a body ...
admin
240
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
proof
+
–
0
votes
0
answers
7744
Ullman (TOC) Edition 3 Exercise 7.1 Question 9 (Page No. 278)
Provide the inductive proofs needed to complete the following theorems$:$ The part of Theorem $7.4$ where we show that discovered symbols really are generating. Both directions of Theorem $7.6$ where we show the correctness of ... reachable symbols. The part of Theorem $7.11$ where we show that all pairs discovered really are unit pairs.
Provide the inductive proofs needed to complete the following theorems$:$ The part of Theorem $7.4$ where we show that discovered symbols really are generating.Both direc...
admin
317
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
proof
+
–
0
votes
0
answers
7745
Ullman (TOC) Edition 3 Exercise 7.1 Question 8 (Page No. 278)
Let $G$ be an $\in-$production-free grammar whose total length of production bodies is $n.$ We convert $G$ to $CNF.$ Show that the CNF grammar has at most $O(n^{2})$ productions. Show that it is ... $n^{2}.$ Hint$:$Consider the construction that eliminates unit productions.
Let $G$ be an $\in-$production-free grammar whose total length of production bodies is $n.$ We convert $G$ to $CNF.$Show that the CNF grammar has at most $O(n^{2})$ produ...
admin
367
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
+
–
0
votes
0
answers
7746
Ullman (TOC) Edition 3 Exercise 7.1 Question 7 (Page No. 278)
Suppose $G$ is a CFG with $p$ productions, and no production body longer than $n.$Show that if $A\xrightarrow[G]{*}\in,$ then there is a derivation of $\in$ from $A$ of no more than $\frac{(n^{p}-1)}{(n-1)}$ steps. How close can you actually come to this bound$?$
Suppose $G$ is a CFG with $p$ productions, and no production body longer than $n.$Show that if $A\xrightarrow[G]{*}\in,$ then there is a derivation of $\in$ from $A$ of n...
admin
278
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
+
–
0
votes
0
answers
7747
Ullman (TOC) Edition 3 Exercise 7.1 Question 6 (Page No. 278)
Design a CNF grammar for the set of strings of balanced parentheses.You need not start from any particular non-CNF grammar.
Design a CNF grammar for the set of strings of balanced parentheses.You need not start from any particular non-CNF grammar.
admin
266
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
+
–
0
votes
0
answers
7748
Ullman (TOC) Edition 3 Exercise 7.1 Question 5 (Page No. 277 - 278)
Begin with the grammar$:$ $S\rightarrow aAa|bBb|\in$ $A\rightarrow C|a$ $B\rightarrow C|b$ $C\rightarrow CDE|\in$ $D\rightarrow A|B|ab$ Eliminate $\in-$productions. Eliminate any unit productions in the resulting grammar. Eliminate any useless symbols in the resulting grammar. Put the resulting grammar into Chomsky Normal Form.
Begin with the grammar$:$$S\rightarrow aAa|bBb|\in$$A\rightarrow C|a$$B\rightarrow C|b$$C\rightarrow CDE|\in$$D\rightarrow A|B|ab$Eliminate $\in-$productions.Eliminate an...
admin
261
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
+
–
0
votes
0
answers
7749
Admission query for Placement opportunities
My gate score is 600 OBC NCL and Rank is 2184 According to opportunities for placements ….so which college should i prefer among the following and Anyone plz suggest good college aaprt from these according to my Gate score ?? nit surathkal NIT calicut IIT Indore MS IIT ropar IIT patna IIT Gandhinagar IIIT allahabad IIIT Banglore MS
My gate score is 600 OBC NCL and Rank is 2184According to opportunities for placements ….so which college should i prefer among the following and Anyone plz suggest goo...
Gopi Thawre
502
views
Gopi Thawre
asked
Apr 11, 2019
0
votes
0
answers
7750
Ullman (TOC) Edition 3 Exercise 7.1 Question 4 (Page No. 277)
Begin with the grammar$:$ $S\rightarrow AAA|B$ $A\rightarrow aA|B$ $B\rightarrow \in$ Eliminate $\in-$productions. Eliminate any unit productions in the resulting grammar. Eliminate any useless symbols in the resulting grammar. Put the resulting grammar into Chomsky Normal Form.
Begin with the grammar$:$$S\rightarrow AAA|B$$A\rightarrow aA|B$$B\rightarrow \in$ Eliminate $\in-$productions.Eliminate any unit productions in the resulting grammar.El...
admin
209
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
+
–
0
votes
0
answers
7751
Ullman (TOC) Edition 3 Exercise 7.1 Question 3 (Page No. 277)
Begin with the grammar$:$ $S\rightarrow 0A0|1B1|BB$ $A\rightarrow C$ $B\rightarrow S|A$ $C\rightarrow S|\in$ Eliminate $\in-$productions. Eliminate any unit productions in the resulting grammar. Eliminate any useless symbols in the resulting grammar. Put the resulting grammar into Chomsky Normal Form.
Begin with the grammar$:$$S\rightarrow 0A0|1B1|BB$$A\rightarrow C$$B\rightarrow S|A$$C\rightarrow S|\in$Eliminate $\in-$productions.Eliminate any unit productions in the ...
admin
233
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-language
context-free-grammar
+
–
0
votes
0
answers
7752
Ullman (TOC) Edition 3 Exercise 7.1 Question 2 (Page No. 275 - 276 - 277)
Begin with grammar$:$ $S\rightarrow ASB|\in$ $A\rightarrow aAS|a$ $B\rightarrow SbS|A|bb$ Eliminate $\in-$productions. Eliminate any unit productions in the resulting grammar. Eliminate any useless symbols in the resulting grammar. Put the resulting grammar into Chomsky Normal Form.
Begin with grammar$:$$S\rightarrow ASB|\in$$A\rightarrow aAS|a$$B\rightarrow SbS|A|bb$Eliminate $\in-$productions.Eliminate any unit productions in the resulting grammar....
admin
258
views
admin
asked
Apr 11, 2019
Theory of Computation
ullman
theory-of-computation
context-free-grammar
+
–
0
votes
0
answers
7753
Allen Carrer Institute: TOC1
How many no. of states in DFA for the following required expression? $(a + b + c) (a + b + c) (a + b + c) (a + b + c) ……… (n – 2)$ times $(a + b + c)^{+}$ $(1) $ $n – 1$ $(2) $ $n$ $(3) $ $n + 1$ $(4) $ $n + 2$ Plz confirm me the answer . Is it $(n-1)$ or $n ?$
How many no. of states in DFA for the following required expression?$(a + b + c) (a + b + c) (a + b + c) (a + b + c) ……… (n – 2)$ times $(a + b + c)^{+}$$(1) $$n ...
srestha
460
views
srestha
asked
Apr 11, 2019
Theory of Computation
finite-automata
+
–
0
votes
0
answers
7754
Kenneth Rosen Edition 7 Exercise 2.3 Question 74 (Page No. 155)
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lfloor \left \lceil x \right \rceil \right \rfloor = \left \lceil x \right \rceil$ for all real numbers $x.$ ... $x$ and $y.$
Prove or disprove each of these statements about the floor and ceiling functions.$\left \lfloor \left \lceil x \right \rceil \right \rfloor = \left \lceil x \right \rceil...
Pooja Khatri
388
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7755
Kenneth Rosen Edition 7 Exercise 2.3 Question 73 (Page No. 155)
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lceil \left \lfloor x \right \rfloor \right \rceil = \left \lfloor x \right \rfloor$ for all real number $x.$ ... $x.$
Prove or disprove each of these statements about the floor and ceiling functions.$\left \lceil \left \lfloor x \right \rfloor \right \rceil = \left \lfloor x \right \rflo...
Pooja Khatri
297
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
1
answer
7756
Kenneth Rosen Edition 7 Exercise 2.3 Question 72 (Page No. 155)
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $|A|=|B|$. Show that $f$ is one-to-one if and only if it is onto.
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $|A|=|B|$. Show that $f$ is one-to-one if and only if it is onto.
Pooja Khatri
306
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7757
Kenneth Rosen Edition 7 Exercise 2.3 Question 71 (Page No. 155)
Let $S$ be a subset of a universal set $U$. The characteristic function $f_{s}$ of $S$ is the function from $U$ to the set $\left \{ 0,1 \right \}$ such that $f_{S}(x)=1$ if $x$ belongs to $S$ and $f_S(x)=0$ if $x$ does not belong to $S$. Let $A$ ... $f_{A \oplus B}(x) = f_{A}(x) + f_{B}(x)- 2 f_{A}(x) f_{B}(x) $
Let $S$ be a subset of a universal set $U$. The characteristic function $f_{s}$ of $S$ is the function from $U$ to the set $\left \{ 0,1 \right \}$ such that $f_{S}(x)=1$...
Pooja Khatri
277
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7758
Kenneth Rosen Edition 7 Exercise 2.3 Question 70 (Page No. 155)
Suppose that $f$ is an invertible function from $Y$ to $Z$ and $g$ is an invertible function from $X$ to $Y$. Show that the inverse of the composition $fog$ is given by $(fog)^{-1} = g^{-1} o f^{-1}.$
Suppose that $f$ is an invertible function from $Y$ to $Z$ and $g$ is an invertible function from $X$ to $Y$. Show that the inverse of the composition $fog$ is given by $...
Pooja Khatri
227
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
1
votes
2
answers
7759
Kenneth Rosen Edition 7 Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
Find the inverse function of $f(x) = x^3 +1.$
Pooja Khatri
310
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7760
Kenneth Rosen Edition 7 Exercise 2.3 Question 68 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lceil 3x-2 \right \rceil$ $f(x) =$ $\left \lceil 0.2x \right \rceil$ $f(x) =$ $\left \lfloor -1/x \right \rfloor$ $f(x) =$ $\left \lfloor x^2 \right \rfloor$ ... $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$
Draw graphs of each of these functions.$f(x) =$ $\left \lceil 3x-2 \right \rceil$$f(x) =$ $\left \lceil 0.2x \right \rceil$$f(x) =$ $\left \lfloor -1/x \right \rfloor$$f(...
Pooja Khatri
214
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7761
Kenneth Rosen Edition 7 Exercise 2.3 Question 67 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ ... $f(x) =$ $\left \lceil \left \lfloor x-12 \right \rfloor + 1/2\right \rceil$
Draw graphs of each of these functions.$f(x) =$ $\left \lfloor x+1/2 \right \rfloor$$f(x) =$ $\left \lfloor 2x+1 \right \rfloor$$f(x) =$ $\left \lceil x/3 \right \rceil$$...
Pooja Khatri
176
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7762
Kenneth Rosen Edition 7 Exercise 2.3 Question 66 (Page No. 155)
Draw the graph of the function $f(n) =$ $\left \lceil x \right \rceil +\left \lceil x/2 \right \rceil$ from $R$ to $R$
Draw the graph of the function $f(n) =$ $\left \lceil x \right \rceil +\left \lceil x/2 \right \rceil$ from $R$ to $R$
Pooja Khatri
182
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7763
Kenneth Rosen Edition 7 Exercise 2.3 Question 65 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor x \right \rfloor +\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
Draw the graph of the function $f(n) =$$\left \lfloor x \right \rfloor +\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
Pooja Khatri
193
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7764
Kenneth Rosen Edition 7 Exercise 2.3 Question 64 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
Draw the graph of the function $f(n) =$$\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
Pooja Khatri
171
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7765
Kenneth Rosen Edition 7 Exercise 2.3 Question 63 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor 2x \right \rfloor$ from $R$ to $R$
Draw the graph of the function $f(n) =$$\left \lfloor 2x \right \rfloor$ from $R$ to $R$
Pooja Khatri
178
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7766
Kenneth Rosen Edition 7 Exercise 2.3 Question 62 (Page No. 155)
Draw the graph of the function $f(n) = 1-n^2$ from $Z$ to $Z$
Draw the graph of the function $f(n) = 1-n^2$ from $Z$ to $Z$
Pooja Khatri
174
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7767
Kenneth Rosen Edition 7 Exercise 2.3 Question 61 (Page No. 155)
Data are transmitted over a particular Ethernet network in blocks of $1500$ octets (blocks of $8$ bits). How many blocks are required to transmit the following amounts of data over this Ethernet network? (Note that a byte is a synonym for ... $1.544$ $\text{megabytes}$ of data $45.3$ $\text{megabytes of}$ data
Data are transmitted over a particular Ethernet network in blocks of $1500$ octets (blocks of $8$ bits). How many blocks are required to transmit the following amounts of...
Pooja Khatri
388
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7768
Kenneth Rosen Edition 7 Exercise 2.3 Question 60 (Page No. 155)
How many ATM cells (described in Example 28) can be transmitted in $10$ seconds over a link operating at the following rates? $128$ kilobits per second ($1$ kilobit= $1000$ bits) $300$ kilobits per second $1$ megabit per second ($1$ megabit=$1,000,000$ bits)
How many ATM cells (described in Example 28) can be transmitted in $10$ seconds over a link operating at the following rates?$128$ kilobits per second ($1$ kilobit= $1000...
Pooja Khatri
270
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
0
votes
0
answers
7769
Kenneth Rosen Edition 7 Exercise 2.3 Question 59 (Page No. 155)
How many bytes are required to encode $n$ bits of data where $n$ equals $7$ $17$ $1001$ $28800$
How many bytes are required to encode $n$ bits of data where $n$ equals$7$$17$$1001$$28800$
Pooja Khatri
198
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
1
votes
0
answers
7770
Kenneth Rosen Edition 7 Exercise 2.3 Question 58 (Page No. 154)
How many bytes are required to encode $n$ bits of data where $n$ equals $4$ $10$ $500$ $3000$
How many bytes are required to encode $n$ bits of data where $n$ equals$4$$10$$500$$3000$
Pooja Khatri
217
views
Pooja Khatri
asked
Apr 11, 2019
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
Page:
« prev
1
...
254
255
256
257
258
259
260
261
262
263
264
...
1007
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register