Let’s discuss the question: show that class p is closed under union. We summarize all relevant answers in section Q&A of website Abettes-culinary.com in category: MMO. See more related questions in the comments below.
Is the class P closed under union?
P is closed under union. For any two P-language L1 and L2, let M1 and M2 be the TMs that decide them in polynomial time.
What operations is P closed under?
We show that P is closed under the star operation by dynamic programming. Let A be any language in P, and let M be the TM deciding A in polynomial time.
Regular Languages Closed Under Union/Intersection (Product Construction)
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How do you show NP is closed under union?
(a) Show that NP is closed under union. Answer: Let L1 and L2 be languages in NP. Also, for i = 1, 2, let Vi(x, c) be an algorithm that, for a string x and a possible certificate c, verifies whether c is actually a certificate for x ∈ Li. Thus, Vi(x, c) = 1 if certificate c verifies x ∈ Li, and Vi(x, c) = 0 otherwise.
Is P closed under intersection?
If x /∈ A then there is NO proof that x ∈ A. The class P is closed under union, intersection, concatenation, and ∗.
Is Turing recognizable closed under concatenation?
Concatenation Both decidable and Turing recognizable languages are closed under concatenation. I will give the proof for Turing recognizable languages. The proof for decidable languages is similar.
Is NP closed under complement?
NP is closed under union, intersection, and concatenation; but is not known to be closed under complement.
What is NP problem?
That is, co-NP is the set of decision problems where there exists a polynomial p(n) and a polynomial-time bounded Turing machine M such that for every instance x, x is a no-instance if and only if: for some possible certificate c of length bounded by p(n), the Turing machine M accepts the pair (x, c).
Is the complement of a language in p also in p?
Every language in P has its complement also in P, and therefore in NP.
What is Kleene star automata?
Definition − The Kleene star, ∑*, is a unary operator on a set of symbols or strings, ∑, that gives the infinite set of all possible strings of all possible lengths over ∑ including λ.
Is NP equal to P?
Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so P = NP would imply that the apparently hard problems actually have relatively easy solutions.
Is NP a CoNP?
Since P = NP, NP is also closed under complementation. So for every S, if S is in NP, then S is in NP. But remember that CoNP consists of the complements of all problems in NP. So NP = CoNP.
16. Complexity: P, NP, NP-completeness, Reductions
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Is NP closed under star?
NP is closed under Kleene star. Given a NTM N which decides L 2 NP in nondeterministic polynomial time, the following NTM N0 decides L⇤ in nondeterministic polynomial time.
Is linear on?
An algorithm is said to take linear time, or O(n) time, if its time complexity is O(n). Informally, this means that the running time increases at most linearly with the size of the input.
What are Turing recognizable languages closed under?
Turing decidable languages are closed under intersection and complementation.
Are regular languages closed under intersection?
Regular Languages are closed under intersection, i.e., if L1 and L2 are regular then L1 ∩ L2 is also regular.
Are decidable languages closed under reversal?
Then M will either reject w or fail to halt on w, so M does not accept w. Show that the decidable languages are closed under the property of Reversal, that is if L is decidable, then LR = {w | wr is in L} is decidable.
Is co NP closed under intersection?
NP is closed under (finite) unions and intersections, therefore using De Morgan laws, NP∩coNP is closed under unions and intersections.
Is L1 ∪ L2 necessarily in NP?
Ans: Yes, L1 ∪ L2 ∈ NP. We will prove it as follows.
Can NP complete problems be solved in polynomial time?
If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.
What is P and NP class problems?
P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.
Operations on Regular Languages
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What is P and NP class in automata?
Step 1 − If a problem is in class P, it is nothing but we can find a solution to that type of problem in polynomial time. Step 2 − If a problem is in class NP, it is nothing but that we can verify a possible solution in polynomial time.
What is the difference between P and NP?
P = the set of problems that are solvable in polynomial time by a Deterministic Turing Machine. NP = the set of decision problems (answer is either yes or no) that are solvable in nondeterministic polynomial time i.e can be solved in polynomial time by a Nondeterministic Turing Machine[4].
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