Define each of the following for a language L.
a) L is in the class P.
b) L is in the class NP.
c) L is reducible to another language L' in polynomial time
d) L is NP-complete
a) This means that L can be solved in polynomial time.
b) This means that L cannot be solved in polynomial time.
c) This means that L is in NP.
d) This means that L an be solved in polynomial time on a non-deterministic Turing machine.
Define each of the following for a language L. a) L is in the class P....
25. (1 point) Suppose A is some language in the class NP and B is NP-complete. Which of the following could be false? A. A is polynomial time reducible to B. B. Given a decider for B which runs in polynomial time, it is possible to decide A in polynomial time. C. Given a decider for A which runs in polynomial time, it is possible to decide B in polynomial time. D. Given a decider for B which runs in...
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...
Indicate whether each of the following statements are correct. JUSTIFICATION NEEDED. (A) Suppose both problems and are in NP. If problem is polynomial time reducible to , and is NP-complete, then so is . (B) Suppose both problems and are in NP. If problem is polynomial time reducible to , and is NP-complete, then so is .
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...
Explain, or define, briefly but completely: a. If you are told that a language L is finite, what category(ies) is the language in? Why? b. State – carefully, completely -- the Church-Turing Thesis c. If you have an NDFA for L, how do you construct an NFA for L*? Describe in general but perhaps also illustrate with an example. d. If L = a*b*(ab)* what is PREFIX(L) = {x: x is a prefix of some string in L}? e. Define:...
Prove that IS is in NP. If a language L polynomial-time reduces to IS, must L be in NP? Prove your answer.
EXP is the class of languages decidable in exponential time (i.e. in 2" steps for some k) Much like the relationship between P and time can be decided in exponential time (i.e., NP EXP), but it is an open question if all problems decidable in exponential time are verifiable in polynomial time (i.e., EXP NP), though this is not expected to be true. Formally, the EXP class can be defined similarly to how we define P: NP, all languages that...
4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm to find a longest path in a directed graph.
4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm to find a longest path in a directed graph. Answer:
4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then show that there is a polynomial time algorithm to find a longest path in a directed graph.