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Recent questions tagged ullman
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121
Ullman (Compiler Design) Edition 2 Exercise 1.6 Question 1 (Page No. 35 - 36)
For the block-structured C code, indicate the values assigned to $w, x, y$, and $z$. int w,x,y,z; int i = 4; int j = 5; { int j = 7; i = 6; w = i + j; } x = i + j; { int i = 8; y = i + j; } z = i + j;
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Compiler Design
Jul 26, 2019
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admin
154
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ullman
compiler-design
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0
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122
Ullman (Compiler Design) Edition 2 Exercise 1.3 Question 1 (Page No. 14 - 15)
Indicate which of the following terms: imperative declarative von Neumann object-oriented functional third-generation fourth-generation scripting apply to which of the following languages: C C++ Cobol Fortran Java Lisp ML Perl Python VB.
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Compiler Design
Jul 26, 2019
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admin
332
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ullman
compiler-design
1
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123
Ullman (TOC) Edition 3 Exercise 9.5 Question 3 (Page No. 418 - 419)
It is undecidable whether the complement of a CFL is also a CFL. Exercise $9.5.2$ can be used to show it is undecidable whether the complement of a CFL is regular, but that is not the same thing. To prove our initial ... ;s lemma to force equality in the lengths of certain substrings as in the hint to Exercise $7.2.5(b)$.
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Theory of Computation
Jul 26, 2019
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admin
346
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ullman
theory-of-computation
context-free-language
pcp
descriptive
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124
Ullman (TOC) Edition 3 Exercise 9.5 Question 2 (Page No. 418)
Show that the language $\overline{L_A}\cup \overline{L_B}$ is a regular language if and only if it is the set of all strings over its alphabet;i.e., if and only if the instance $(A,B)$ of PCP has no ... homomorphism, complementation and the pumping lemma for regular sets to show that $\overline{L_A}\cup \overline{L_B}$ is not regular.
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Theory of Computation
Jul 26, 2019
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admin
408
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ullman
theory-of-computation
regular-language
pcp
descriptive
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125
Ullman (TOC) Edition 3 Exercise 9.5 Question 1 (Page No. 418)
Let $L$ be the set of (codes for) context-free grammars $G$ such that $L(G)$ contains at least one palindrome. Show that $L$ is undecidable. Hint: Reduce PCP to $L$ by constructing, from each instance of PCP a grammar whose language contains a palindrome if and only if the PCP instance has a solution.
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Theory of Computation
Jul 26, 2019
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admin
228
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ullman
theory-of-computation
context-free-grammar
pcp
descriptive
0
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0
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126
Ullman (TOC) Edition 3 Exercise 9.4 Question 4 (Page No. 412)
A Post tag system consists of a set of pairs of strings chosen from some finite alphabet $\Sigma$ and a start string. If $(w,x)$ is a pair, and $y$ is any string over $\Sigma$, we say that $wy\vdash yx$. That is ... . If $M$ enters an accepting state, arrange that the current strings can eventually be erased, i.e., reduced to $\epsilon$.
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Theory of Computation
Jul 21, 2019
by
admin
324
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ullman
theory-of-computation
turing-machine
undecidable
descriptive
0
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127
Ullman (TOC) Edition 3 Exercise 9.4 Question 3 (Page No. 412)
Suppose we limited $PCP$ to a one-symbol alphabet, say $\Sigma = \left\{0\right\}$. Would this restricted case of $PCP$ still be undecidable?
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Theory of Computation
Jul 21, 2019
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admin
158
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ullman
theory-of-computation
undecidable
post-correspondence-problem
descriptive
0
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128
Ullman (TOC) Edition 3 Exercise 9.4 Question 2 (Page No. 412)
We showed that $PCP$ was undecidable, but we assumed that the alphabet $\Sigma$ could be arbitrary. Show that $PCP$ is undecidable even if we limit the alphabet to $\Sigma = \left\{0,1\right\}$ by reducing $PCP$ to this special case of $PCP$.
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Theory of Computation
Jul 21, 2019
by
admin
186
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ullman
theory-of-computation
undecidable
post-correspondence-problem
descriptive
0
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0
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129
Ullman (TOC) Edition 3 Exercise 9.4 Question 1 (Page No. 412)
Tell whether each of the following instances of $PCP$ has a solution. Each is presented as two lists $A$ and $B$, and the $i^{th}$ strings on the two lists correspond for each $i = 1,2,\cdot\cdot\cdot\cdot$ $A=(01,001,10); \ B = (011,10,00).$ $A=(01,001,10); \ B = (011,01,00).$ $A=(ab,a,bc,c); \ B = (bc,ab,ca,a).$
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Theory of Computation
Jul 21, 2019
by
admin
171
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ullman
theory-of-computation
post-correspondence-problem
descriptive
0
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130
Ullman (TOC) Edition 3 Exercise 9.3 Question 8 (Page No. 401)
Tell whether each of the following are recursive, RE-but-not-recursive, or non-RE. The set of all $TM$ codes for $TM's$ that halt on every input. The set of all $TM$ codes for $TM's$ that halt on no input. The set of ... halt on at least one input. The set of all $TM$ codes for $TM's$ that fail to halt on at least one input.
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Theory of Computation
Jul 21, 2019
by
admin
226
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ullman
theory-of-computation
turing-machine
recursive-and-recursively-enumerable-languages
descriptive
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131
Ullman (TOC) Edition 3 Exercise 9.3 Question 7 (Page No. 400 - 401)
Show that the following problems are not recursively enumerable: The set of pairs $(M,w)$ such that $TM \ M$, started with input $w$, does not halt. The set of pairs $(M_{1},M_{2})$ ... $TM's$.
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Theory of Computation
Jul 21, 2019
by
admin
240
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ullman
theory-of-computation
turing-machine
recursive-and-recursively-enumerable-languages
descriptive
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132
Ullman (TOC) Edition 3 Exercise 9.3 Question 6 (Page No. 400)
Show that the following questions are decidable: The set of codes for $TM's \ M$ such that when started with blank tape will eventually write some nonblank symbol on its tape. Hint: If $M$ has $m$ states, consider the first $m$ ... $(M,w)$ such that $TM \ M$, started with input $w$, never scans any tape cell more than once.
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Theory of Computation
Jul 21, 2019
by
admin
170
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ullman
theory-of-computation
turing-machine
decidability
descriptive
0
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133
Ullman (TOC) Edition 3 Exercise 9.3 Question 5 (Page No. 400)
Let $L$ be the language consisting of pairs of $TM$ codes plus an integer, $(M_{1},M_{2},k)$, such that $L(M_{1})\cap L(M_{2})$ contains at least $k$ strings. Show that $L$ is $RE$, but recursive.
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Theory of Computation
Jul 21, 2019
by
admin
174
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ullman
theory-of-computation
turing-machine
recursive-and-recursively-enumerable-languages
descriptive
0
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1
answer
134
Ullman (TOC) Edition 3 Exercise 9.3 Question 4 (Page No. 400)
We know by Rice's theorem that none of the following problems are decidable. However are they recursively enumerable,or non-RE? Does $L(M)$ contain at least two strings? Is $L(M)$ infinite? Is $L(M)$ a context-free language? Is $L(M) = (L(M))^{R}$?
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Theory of Computation
Jul 21, 2019
by
admin
370
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ullman
theory-of-computation
rice-theorem
descriptive
0
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135
Ullman (TOC) Edition 3 Exercise 9.3 Question 3 (Page No. 400)
Show that the language of codes for $TM's\ M$ that, when started with blank tape, eventually write a $1$ somewhere on the tape is undecidable.
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Theory of Computation
Jul 21, 2019
by
admin
191
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ullman
theory-of-computation
turing-machine
undecidable
descriptive
0
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136
Ullman (TOC) Edition 3 Exercise 9.3 Question 2 (Page No. 400)
The Big Computer Corp. has decided to bolster its sagging market share by manufacturing a high-tech version of the Turing machine called, $BWTM$ that is equipped with bells and whistles. The $BWTM$ is basically the same as your ordinary ... that it is undecidable whether a given $BWTM \ M$, on given input $w$, ever blows the whistle.
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Theory of Computation
Jul 21, 2019
by
admin
239
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ullman
theory-of-computation
turing-machine
descriptive
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137
Ullman (TOC) Edition 3 Exercise 9.3 Question 1 (Page No. 400)
Show that the set of Turing-machine codes for TM's that accept all inputs that are palindromes (possibly along with some other inputs) is undecidable.
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Theory of Computation
Jul 21, 2019
by
admin
313
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ullman
theory-of-computation
turing-machine
undecidable
descriptive
0
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138
Ullman (TOC) Edition 3 Exercise 9.2 Question 6 (Page No. 392)
We have not discussed closure properties of the recursive languages or the RE languages other than our discussion of complementation in Section $9.2.2.$ Tell whether the recursive languages and/or the RE ... , constructions to show closure. Union. Intersection. Concatenation. Kleene closure(star). Homomorphism. Inverse homomorphism.
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Theory of Computation
Jul 21, 2019
by
admin
197
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ullman
theory-of-computation
recursive-and-recursively-enumerable-languages
descriptive
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139
Ullman (TOC) Edition 3 Exercise 9.2 Question 5 (Page No. 392)
Let $L$ be recursively enumerable and let $\overline{L}$ be non-RE. Consider the language $L' = \left\{0w\mid w\ \text{is in}\ L \right\}$ Can you say for certain whether $L'$ or its complement are recursive, RE, or non-RE? Justify your answer.
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Theory of Computation
Jul 21, 2019
by
admin
151
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ullman
theory-of-computation
recursive-and-recursively-enumerable-languages
descriptive
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140
Ullman (TOC) Edition 3 Exercise 9.2 Question 4 (Page No. 391)
Let $L_{1},L_{2},\cdot\cdot\cdot,L_{k}$ be a collection of languages over alphbet $\Sigma$ such that: For all $i\neq j$, $L_{i}\cap L_{j}=\phi$ ... languages $L_{i}$, for $i=1,2,\cdot\cdot\cdot,k$ is recursively enumerable. Prove that each of the languages is therefore recursive.
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Theory of Computation
Jul 21, 2019
by
admin
210
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ullman
theory-of-computation
recursive-and-recursively-enumerable-languages
0
votes
1
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141
Ullman (TOC) Edition 3 Exercise 9.2 Question 3 (Page No. 391)
Informally describe multitape Turing machines that enumerate the following sets of integers, in the sense that started with blank tapes, it prints on one of its tapes $10^{i_{1}}10^{i_{2}}1\cdot\cdot\cdot$ ... $s$ steps, then we shall eventually discover each $M_{i}$ that accepts $w_{i}$ and enumerate $i$.
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Theory of Computation
Jul 21, 2019
by
admin
587
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ullman
theory-of-computation
turing-machine
recursive-and-recursively-enumerable-languages
descriptive
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142
Ullman (TOC) Edition 3 Exercise 9.2 Question 2 (Page No. 390 - 391)
In the box "Why 'Recursive'?" in Section $9.2.1$ we suggested that there was a notion of "recursive function" that competed with the Turing machine as a model for what can be computed. In this exercise, we shall explore ... : Evaluate $A(2,1).$ What function of $x$ is $A(x,2)$? Evaluate $A(4,3)$.
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Theory of Computation
Jul 21, 2019
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admin
294
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ullman
theory-of-computation
turing-machine
ackermanns-function
descriptive
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143
Ullman (TOC) Edition 3 Exercise 9.2 Question 1 (Page No. 390)
Show that the halting problem, the set of $(M,w)$ pairs such that $M$ halts (with or without accepting) when given input $w$ is $RE$ but not recursive.$ ($See the box on "The Halting Problem" in Section $9.2.4)$
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Theory of Computation
Jul 21, 2019
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admin
203
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ullman
theory-of-computation
halting-problem
0
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144
Ullman (TOC) Edition 3 Exercise 9.1 Question 4 (Page No. 383)
We have considered only Turing machines that have input alphabet $\left\{0,1\right\}$. Suppose that we wanted to assign an integer to all Turing machines, regardless of their input alphabet. That is not quite possible because ... could assign an integer to all $TM's$ that had a finite subset of these symbols as its input alphabet.
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Theory of Computation
Jul 21, 2019
by
admin
206
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ullman
theory-of-computation
turing-machine
descriptive
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145
Ullman (TOC) Edition 3 Exercise 9.1 Question 3 (Page No. 382)
Here are two definitions of languages that are similar to the definition of $L_{d}$, yet different from that language. For each, show that the language is not accepted by a Turing machine, using a diagonalization-type argument. Note that you cannot develop ... $w_{i}$ such that $w_{2i}$ is not accepted by $M_{i}$.
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Theory of Computation
Jul 21, 2019
by
admin
523
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ullman
theory-of-computation
turing-machine
diagonalization
descriptive
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146
Ullman (TOC) Edition 3 Exercise 9.1 Question 2 (Page No. 382)
Write one of the possible codes for the Turing machine of Fig.$8.9.$
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Theory of Computation
Jul 21, 2019
by
admin
401
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ullman
theory-of-computation
turing-machine
0
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147
Ullman (TOC) Edition 3 Exercise 9.1 Question 1 (Page No. 382)
What strings are: $w_{37}$? $w_{100}$?
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Theory of Computation
Jul 21, 2019
by
admin
176
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ullman
theory-of-computation
srtings
0
votes
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148
Ullman (TOC) Edition 3 Exercise 8.5 Question 2 (Page No. 362)
The purpose of this exercise is to show that a one-stack machine with an endmarker on the input has no more power than a deterministic $PDA$. $L\$ is the concatenation of language $L$ with the language containing only the one string $\$ ... $q$ such that $P$,started in $ID\ (q,a,X_{i}X_{i+1}\cdot \cdot X_{n})$ will accept.
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Theory of Computation
Jul 21, 2019
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admin
188
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ullman
theory-of-computation
turing-machine
dpda
descriptive
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149
Ullman (TOC) Edition 3 Exercise 8.5 Question 1 (Page No. 361)
Informally but clearly describe counter machines that accept the following languages. In each case, use as few counters as possible,but not more than two counters. $\left\{0^{n}1^{m} \mid n\geq m\geq 1\right\}.$ ... $\left\{a^{i}b^{j}c^{k} \mid i=j \ \text{or} \ i=k \ \text{or}\ j=k\right\}.$
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Theory of Computation
Jul 21, 2019
by
admin
217
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ullman
theory-of-computation
turing-machine
descriptive
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150
Ullman (TOC) Edition 3 Exercise 8.4 Question 10 (Page No. 352)
A two-dimensional Turing machine has the usual finite-state control but a tape that is a two-dimensional grid of cells, infinite in all directions. The input is placed on one row of the grid, with the head at ... Prove that the languages accepted by two-dimensional Turing machines are the same as those accepted by ordinary $TM's$.
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Theory of Computation
Jul 21, 2019
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admin
465
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ullman
theory-of-computation
turing-machine
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