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Michael Sipser Decidability Problem
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Is the following language decidable or not? If you deem it decidable, you need to give an algorithm and analyse its running time. If not decidable, you need to prove it. L = {M | M is a Turing machine and L(M) ∈ TIME(2^n)}
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Michael Sipster Decidability Problems
Prove L = {F | F is a boolean formula and F evaluates to true on every asignment" is decidable (include algorithm and running time in big o notation)
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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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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 Turing-recognizable. Show that $NECESSARY_{CFG} $is undecidable.
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Michael Sipser Edition 3 Exercise 5 Question 34 (Page No. 241)
Let $X = \{\langle M, w \rangle \mid \text{M is a single-tape TM that never modifies the portion of the tape that contains the input $w$ } \}$ Is $X$ decidable? Prove your answer.
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