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Michael Sipser Edition 3 Exercise 5 Question 1 (Page No. 239)
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Show that $EQ_{CFG}$ is undecidable.
michaelsipser
theoryofcomputation
contextfreegrammars
decidability
proof
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Oct 18, 2019
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Theory of Computation
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Lakshman Patel RJIT

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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.
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Oct 20, 2019
in
Theory of Computation
by
Lakshman Patel RJIT

163
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michaelsipser
theoryofcomputation
contextfreegrammars
turingrecognizablelanguages
decidability
proof
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Michael Sipser Edition 3 Exercise 5 Question 32 (Page No. 241)
Prove that the following two languages are undecidable. $OVERLAP_{CFG} = \{\langle G, H\rangle \mid \text{G and H are CFGs where}\: L(G) \cap L(H) \neq \emptyset\}$. $PREFIXFREE_{CFG} = \{\langle G \rangle \mid \text{G is a CFG where L(G) is prefixfree}\}$.
asked
Oct 20, 2019
in
Theory of Computation
by
Lakshman Patel RJIT

55
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michaelsipser
theoryofcomputation
contextfreegrammars
turingmachine
decidability
proof
0
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0
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3
Michael Sipser Edition 3 Exercise 5 Question 21 (Page No. 240)
Let $AMBIG_{CFG} = \{\langle G \rangle \mid \text{G is an ambiguous CFG}\}$. Show that $AMBIG_{CFG}$ is undecidable. (Hint: Use a reduction from $PCP$ ... $a_{1},\dots,a_{k}$ are new terminal symbols. Prove that this reduction works.)
asked
Oct 19, 2019
in
Theory of Computation
by
Lakshman Patel RJIT

26
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michaelsipser
theoryofcomputation
contextfreegrammars
reduction
postcorrespondenceproblem
decidability
proof
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Michael Sipser Edition 3 Exercise 5 Question 2 (Page No. 239)
Show that $EQ_{CFG}$ is coTuringrecognizable.
asked
Oct 18, 2019
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Theory of Computation
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Lakshman Patel RJIT

23
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michaelsipser
theoryofcomputation
contextfreegrammars
turingrecognizablelanguages
proof
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