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• ### Let n be a positive integer. Classify the languages R = { (M) | M is a TM and L(M) contains exactly n strings} S = { (M)...

Let n be a positive integer. Classify the languages R = { (M) | M is a TM and L(M) contains exactly n strings} S = { (M) | M is a TM and L(M) contains more than n strings} as (a) decidable (b) Turing-recognizable but not co-Turing recognizable (c) co-Turing recognizable but not Turing-recognizable (d) neither Turing nor co-Turing recognizable

• ### Classify the language { (G) | G is a CFG, L(G) contains a palindrome}\ as (a) decidable (b) Turing-recognizable but not...

Classify the language { (G) | G is a CFG, L(G) contains a palindrome}\ as (a) decidable (b) Turing-recognizable but not co-Turing recognizable (c) co-Turing recognizable but not Turing-recognizable (d) neither Turing nor co-Turing recognizable Justify your answer

• ### Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection...

Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable lanquages are closed under union and intersection The class of undecidable languages contains the class of recognizable anguages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all that apply) 1 point EDFA-{ «A> 1 A is a DFA and...

• ### Please also note that there might be multiple answers for each question. Q1: Which of the following claims are true?*...

Please also note that there might be multiple answers for each question. Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable languages are closed under union and intersection The class of undecidable languages contains the class of recognizable languages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all...

• ### Help me answer this question plz! 4. Let L = { (A) M is a Turing...

Help me answer this question plz! 4. Let L = { (A) M is a Turing machine that accepts more than one string } a) Define the notions of Turing-recognisable language and undecidable language. b) Is L Turing-recognisable? Justify your answer with an informal argument. c) Justify with a formal proof your answer to b) d) Prove that L is undecidable. (Hint: use Rice's theorem.) e) Modify your answer to b) when instead of L you have the language Ln...

• ### 19. (1 point) Suppose that L is undecidable and L is recognizable. Which of the following...

19. (1 point) Suppose that L is undecidable and L is recognizable. Which of the following could be false? A. I is co-Turing recognizable. B. I is not recognizable. C. I is undecidable. D. L* is not recognizable. E. None of the above. 20. (2 points) Let ETM {(M)|L(M) = 0} and EQTM = {(M1, M2)|L(Mi) = L(M2)}. We want to show that EQTM is undecidable by reducing Etm to EQTM and we do this by assuming R is a...

• ### 1. Let m be a nonnegative integer, and n a positive integer. Using the division algorithm...

1. Let m be a nonnegative integer, and n a positive integer. Using the division algorithm we can write m=qn+r, with 0 <r<n-1. As in class define (m,n) = {mc+ny: I,Y E Z} and S(..r) = {nu+ru: UV E Z}. Prove that (m,n) = S(n,r). (Remark: If we add to the definition of ged that gedan, 0) = god(0, n) = n, then this proves that ged(m, n) = ged(n,r). This result leads to a fast algorithm for computing ged(m,...

• ### 11. Let n be a positive integer and [r], [y e Zn. Show that the following...

11. Let n be a positive integer and [r], [y e Zn. Show that the following conditions are equivalent. (i) []= [v] (ii) - y nr for some integer r. (ii) n/(x-y)

• ### Automata question Categorize the languages as I.                   Type 0 or Recursively Enumerable Languages II.        &n

Automata question Categorize the languages as I.                   Type 0 or Recursively Enumerable Languages II.                Type 1 or CSL III.             Type 2 or CFL IV.             Type 3 or Regular in accordance to the Chomsky hierarchy (select only one of the answers designating the lowest level - Note that Type 3 is the lowest level and Type 0 is the highest level) over the alphabet {0,1} L = {0n10k   |k, n is any integer} i think its type 0.. am i right ?...

• ### 1. Let Rn = = {ver 1.5251+} for each positive integer n. Formally justify your answers...

1. Let Rn = = {ver 1.5251+} for each positive integer n. Formally justify your answers (a picture is not a justification). Provide your answers in interval notation. Find: (a) (5 points) Ü Rn. n=1 m (b) (5 points) ſ Rn. n=1 (c) (5 points) Ü Rn n=1