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Recent questions tagged turingrecognizablelanguages
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Michael Sipser Edition 3 Exercise 5 Question 36 (Page No. 242)
Say that a $CFG$ is minimal if none of its rules can be removed without changing the language generated. Let $MIN_{CFG} = \{\langle G \rangle \mid \text{G is a minimal CFG}\}$. Show that $MIN_{CFG}$ is $T$recognizable. Show that $MIN_{CFG}$ is undecidable.
asked
Oct 20
in
Theory of Computation
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Lakshman Patel RJIT
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turingrecognizablelanguages
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Michael Sipser Edition 3 Exercise 5 Question 35 (Page No. 242)
Say that a variable $A$ in $CFG \:G$ is necessary if it appears in every derivation of some string $w \in G$. Let $NECESSARY_{CFG} = \{\langle G, A\rangle \mid \text{A is a necessary variable in G}\}$. Show that $NECESSARY_{CFG}$ is Turingrecognizable. Show that $NECESSARY_{CFG} $is undecidable.
asked
Oct 20
in
Theory of Computation
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Lakshman Patel RJIT
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Michael Sipser Edition 3 Exercise 5 Question 24 (Page No. 240)
Let $J = \{w \mid \text{either $w = 0x$ for some $x \in A_{TM},$ or $w = 1y\:$ for some $y \in \overline{A_{TM}}\:\:$}\}$. Show that neither $J$ nor $\overline{J}$ is Turingrecognizable.
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Oct 19
in
Theory of Computation
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Lakshman Patel RJIT
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Michael Sipser Edition 3 Exercise 5 Question 22 (Page No. 240)
Show that $A$ is Turingrecognizable iff $A \leq_{m} A_{TM}$.
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Oct 19
in
Theory of Computation
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Lakshman Patel RJIT
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Michael Sipser Edition 3 Exercise 5 Question 7 (Page No. 239)
Show that if $A$ is Turingrecognizable and $A\leq_{m} \overline{A},$ then $A$ is decidable.
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Oct 19
in
Theory of Computation
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Lakshman Patel RJIT
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54.9k
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theoryofcomputation
turingrecognizablelanguages
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Michael Sipser Edition 3 Exercise 5 Question 2 (Page No. 239)
Show that $EQ_{CFG}$ is coTuringrecognizable.
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Oct 17
in
Theory of Computation
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7
Michael Sipser Edition 3 Exercise 4 Question 30 (Page No. 212)
Let $A$ be a Turingrecognizable language consisting of descriptions of Turing machines, $\{ \langle M_{1}\rangle,\langle M_{2}\rangle,\dots\}$, where every $M_{i}$ is a decider. Prove that some decidable language $D$ is not ... $A$. (Hint: You may find it helpful to consider an enumerator for $A$.)
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Oct 17
in
Theory of Computation
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Lakshman Patel RJIT
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8
Michael Sipser Edition 3 Exercise 4 Question 20 (Page No. 212)
Let $A$ and $B$ be two disjoint languages. Say that language $C$ separates $A$ and $B$ if $A \subseteq C$ and $B \subseteq \overline{C}$. Show that any two disjoint coTuringrecognizable languages are separable by some decidable language.
asked
Oct 17
in
Theory of Computation
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9
Michael Sipser Edition 3 Exercise 4 Question 18 (Page No. 212)
Let $C$ be a language. Prove that $C$ is Turingrecognizable iff a decidable language $D$ exists such that $C = \{x \mid \exists y (\langle{ x, y \rangle} \in D)\}$.
asked
Oct 17
in
Theory of Computation
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Lakshman Patel RJIT
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54.9k
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michaelsipser
theoryofcomputation
turingrecognizablelanguages
decidability
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10
Michael Sipser Edition 3 Exercise 4 Question 5 (Page No. 211)
Let $E_{TM} = \{\langle{ M \rangle } \mid M\: \text{is a TM}\: \text{and}\: L(M) = \phi\}$. Show that $E_{TM}$, the complement of $E_{TM}$, is Turingrecognizable.
asked
Oct 17
in
Theory of Computation
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Lakshman Patel RJIT
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michaelsipser
theoryofcomputation
turingmachine
turingrecognizablelanguages
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11
Michael Sipser Edition 3 Exercise 3 Question 20 (Page No. 190)
Show that singletape $TMs$ that cannot write on the portion of the tape containing the input string recognize only regular languages.
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Oct 15
in
Theory of Computation
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Lakshman Patel RJIT
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theoryofcomputation
turingmachine
turingrecognizablelanguages
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12
Michael Sipser Edition 3 Exercise 3 Question 19 (Page No. 190)
Show that every infinite Turingrecognizable language has an infinite decidable subset.
asked
Oct 15
in
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Lakshman Patel RJIT
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13
Michael Sipser Edition 3 Exercise 3 Question 17 (Page No. 189)
Let $B = \{\langle {M_{1}\rangle},\langle{ M_{1}\rangle} , \dots \}$ be a Turingrecognizable language consisting of $TM$ descriptions. Show that there is a decidable language $C$ consisting of $TM$ descriptions such that every machine described in $B$ has an equivalent machine in $C$ and vice versa.
asked
Oct 15
in
Theory of Computation
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Lakshman Patel RJIT
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theoryofcomputation
turingmachine
turingrecognizablelanguages
descriptive
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14
Michael Sipser Edition 3 Exercise 3 Question 16 (Page No. 189)
Show that the collection of Turingrecognizable languages is closed under the operation of union. concatenation. star. intersection. homomorphism.
asked
Oct 15
in
Theory of Computation
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Lakshman Patel RJIT
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54.9k
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theoryofcomputation
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turingrecognizablelanguages
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15
Michael Sipser Edition 3 Exercise 3 Question 14 (Page No. 189)
A queue automaton is like a pushdown automaton except that the stack is replaced by a queue. A queue is a tape allowing symbols to be written only on the lefthand end and read only at the righthand end. ... at any time. Show that a language can be recognized by a deterministic queue automaton iff the language is Turingrecognizable.
asked
Oct 15
in
Theory of Computation
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Lakshman Patel RJIT
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54.9k
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theoryofcomputation
turingmachine
turingrecognizablelanguages
descriptive
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16
Michael Sipser Edition 3 Exercise 3 Question 13 (Page No. 189)
A Turing machine with stay put instead of left is similar to an ordinary Turing machine, but the transition function has the form $\delta: Q\times \Gamma \rightarrow Q\times \Gamma \times \{R,S\}$ At each ... that this Turing machine variant is not equivalent to the usual version. What class of languages do these machines recognize?
asked
Oct 15
in
Theory of Computation
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descriptive
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17
Michael Sipser Edition 3 Exercise 3 Question 12 (Page No. 189)
A Turing machine with left reset is similar to an ordinary Turing machine, but the transition function has the form $\delta: Q\times \Gamma \rightarrow Q\times \Gamma \times \{R,RESET\}$ ... to move the head one symbol left. Show that Turing machines with left reset recognize the class of Turingrecognizable languages.
asked
Oct 15
in
Theory of Computation
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Lakshman Patel RJIT
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54.9k
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theoryofcomputation
turingmachine
turingrecognizablelanguages
descriptive
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18
Michael Sipser Edition 3 Exercise 3 Question 11 (Page No. 189)
A Turing machine with doubly infinite tape is similar to an ordinary Turing machine, but its tape is infinite to the left as well as to the right. The tape is initially filled with blanks except for the portion ... tape as it moves leftward. Show that this type of Turing machine recognizes the class of Turingrecognizable languages.
asked
Oct 15
in
Theory of Computation
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Lakshman Patel RJIT
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54.9k
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2
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