I need help on this question. Please provide the solution with explaination. Tha

Question

I need help on this question. Please provide the solution with explaination. Thank you!

We learned that a problem is a language. For instance, consider the following problem: Given: a graph G, is G connected? This problem corresponds to the language that puts all the string encodings of the positive instances of the problem into: {(G): G is a connected graph}, where (G) is a string encoding of graph G. Please indicate the languages corresponding to the following four problems: Given: a number n and two primes p, q, Question: is it the case that n = p middot q? Given: a number n, Question: is it the case that n = p middot q for some primes p and q? Given: an NFA A and a word w Question: Does A accept w ? Given: an NFA A Question: Is there any word w such that A accepts w ?

Explanation / Answer

1.

A graph G said to be connected when there is a path between every pair of vertices. There are no unreachable vertices in connected graph.

2.

A number n and two primes p,q is it the case that n=p.q

Yes,because c onsider n=6

P=15,q=10

Primes of p,q are 3 and 2

N=3*2=6

3.

No,generally it is possible for all primes.

4.

AN NFA A and word w accepts .

Yes,

iff there is at least one computation path starting from the start state to an accepting state than it is accepted by NFA.

AN NFA A and is there any word w that accepts A.

5.

Yes,word w accepts . iff there is at least one computation path starting from the start state to an accepting state than it is accepted by NFA.

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