Homework Answers
If L1 and L2 are NP languages , then we can say that L1
So L1\L2 is NP-Complete. So, here option 3 can be chose as appropriate answer.
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(10 pts.) Now assume that L and L2 are NP-complete languages. Which of the following statements...
For each of the following statements, where L1, L2, and L are languages over some alphabet...
For each of the following statements, where L1, L2, and L are languages over some alphabet Σ, state whether it is true or false. Prove your answer. • ∀L,(∅ or L+) = L∗ • ∀L1,L2,(L1 or L2)∗ = (L2 or L1)∗
Exercise 1 Define a language L to be co-NP-complete if it is in co-NP and a languages in co-NP ca...
Hi, this question is from
Theory of Computation. Kindly help if you can.
Exercise 1 Define a language L to be co-NP-complete if it is in co-NP and a languages in co-NP can be polynomial-time reduced to L. Say that a formula of quantified boolean logic is a universal sentence if it is a sentence (i.e., has no free variables) of the form Vai... Vxn(V) where> is a propositional logic formula (contains no quantifiers). Show that the language to I...
13. (1 point) Which of the following statement could be false where Lį and L2 are...
13. (1 point) Which of the following statement could be false where Lį and L2 are decidable lan- guages? A. Li · L2 is decidable. B. Li Lis undecidable. C. Lin L2 is decidable. D. LI U L2 is decidable. E. None of the above. 14. (1 point) Which of the following statement could be false where Lj is decidable and L2 is recognizable? A. Li · L2 is recognizable. B. Li · L2 is decidable. C. Lin L2 is...
2. If L1 and L2 are regular languages, which of the following are regular languages? Provide...
2. If L1 and L2 are regular languages, which of the following are regular languages? Provide justification for your answers. a. L1 U L2 b. L1L2 c. L1 n L2
If L1 and L2 are Regular Languages, then L1 ∪ L2 is a CFL. Group of answer choices...
If L1 and L2 are Regular Languages, then L1 ∪ L2 is a CFL. Group of answer choices True False Flag this Question Question 61 pts If L1 and L2 are CFLs, then L1 ∩ L2 and L1 ∪ L2 are CFLs. Group of answer choices True False Flag this Question Question 71 pts The regular expression ((ac*)a*)* = ((aa*)c*)*. Group of answer choices True False Flag this Question Question 81 pts Some context free languages are regular. Group of answer choices True...
Consider the following languages Li and L2, respectively, and construct a context free grammar for it...
Consider the following languages Li and L2, respectively, and construct a context free grammar for it if it is a context free language; if not, using the pumping lemma to disprove it. Let na(w) denote the number if a is w, same notation for to now) and nc(w). • L1 = {w we {a,b}* and na(w) = nb(w)} • L2 = {w I w€ {a,b,c}* and na(w) = n5(w) = nc(w)}
Exercise 7.3.2: Consider the following two languages: Li = {a"b2ncm n,m >0} L2 = {a" mc2m...
Exercise 7.3.2: Consider the following two languages: Li = {a"b2ncm n,m >0} L2 = {a" mc2m | n,m >0} a) Show that each of these languages is context-free by giving grammars for each. ! b) Is L; n L, a CFL? Justify your answer.
= {a,b}: 1. (9 pts) Consider the following three languages, all subsets of S* where •...
= {a,b}: 1. (9 pts) Consider the following three languages, all subsets of S* where • L = {w w is a word such that we is divisible by 3). . L2 = {w w is a word whose length is divisible by 4 }. • L3 = {w w is a word such that wla >3}. (a) For each language construct a DFA that recognizes that language. (b) Construct an automaton that recognizes Lin L2. If the constructed automaton...
3. (3 pts) Two well-known NP-complete problems are 3-SAT and TSP, the traveling salesman problem. The...
3. (3 pts) Two well-known NP-complete problems are 3-SAT and TSP, the traveling salesman problem. The 2-SAT problem is a SAT variant in which each clause contains at most two literals. 2-SAT is known to have a polynomial-time algorithm. Is each of the following statements true or false? Justify your answer. a. 3-SAT sp TSP. b. If P NP, then 3-SAT Sp 2-SAT. C. If P NP, then no NP-complete problem can be solved in polynomial time.
5. (1 point) Which of the following statements is true? A. Recognizable languages are a subset...
5. (1 point) Which of the following statements is true? A. Recognizable languages are a subset of the decidable languages. B. Some decidable languages may not be recognizable. C. A decider for a language must accept every input. D. A recognizer for a language doesn't halt. E. A decider halts on every input by either going to an accept state or a reject state. 6. (1 point) Which of the following could be false for the language L = {abclixj...
Hi, this question is from
Theory of Computation. Kindly help if you can.
Exercise 1 Define a language L to be co-NP-complete if it is in co-NP and a languages in co-NP can be polynomial-time reduced to L. Say that a formula of quantified boolean logic is a universal sentence if it is a sentence (i.e., has no free variables) of the form Vai... Vxn(V) where> is a propositional logic formula (contains no quantifiers). Show that the language to I...
13. (1 point) Which of the following statement could be false where Lį and L2 are decidable lan- guages? A. Li · L2 is decidable. B. Li Lis undecidable. C. Lin L2 is decidable. D. LI U L2 is decidable. E. None of the above. 14. (1 point) Which of the following statement could be false where Lj is decidable and L2 is recognizable? A. Li · L2 is recognizable. B. Li · L2 is decidable. C. Lin L2 is...
2. If L1 and L2 are regular languages, which of the following are regular languages? Provide justification for your answers. a. L1 U L2 b. L1L2 c. L1 n L2
Consider the following languages Li and L2, respectively, and construct a context free grammar for it if it is a context free language; if not, using the pumping lemma to disprove it. Let na(w) denote the number if a is w, same notation for to now) and nc(w). • L1 = {w we {a,b}* and na(w) = nb(w)} • L2 = {w I w€ {a,b,c}* and na(w) = n5(w) = nc(w)}
Exercise 7.3.2: Consider the following two languages: Li = {a"b2ncm n,m >0} L2 = {a" mc2m | n,m >0} a) Show that each of these languages is context-free by giving grammars for each. ! b) Is L; n L, a CFL? Justify your answer.
= {a,b}: 1. (9 pts) Consider the following three languages, all subsets of S* where • L = {w w is a word such that we is divisible by 3). . L2 = {w w is a word whose length is divisible by 4 }. • L3 = {w w is a word such that wla >3}. (a) For each language construct a DFA that recognizes that language. (b) Construct an automaton that recognizes Lin L2. If the constructed automaton...
3. (3 pts) Two well-known NP-complete problems are 3-SAT and TSP, the traveling salesman problem. The 2-SAT problem is a SAT variant in which each clause contains at most two literals. 2-SAT is known to have a polynomial-time algorithm. Is each of the following statements true or false? Justify your answer. a. 3-SAT sp TSP. b. If P NP, then 3-SAT Sp 2-SAT. C. If P NP, then no NP-complete problem can be solved in polynomial time.
5. (1 point) Which of the following statements is true? A. Recognizable languages are a subset of the decidable languages. B. Some decidable languages may not be recognizable. C. A decider for a language must accept every input. D. A recognizer for a language doesn't halt. E. A decider halts on every input by either going to an accept state or a reject state. 6. (1 point) Which of the following could be false for the language L = {abclixj...
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