Prove that IS is in NP. If a language L polynomial-time reduces to IS, must L...
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...
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...
true or False with prove? (f) ___ NP =co-NP (g) The complement of any recursive language is recursive. h) The grader's problem is decidable. We say programs Pi and P are equivalent if they give the same output if given the same input. The problem is to decide whether two programs (in C++, Pascal, Java, or some other modern programming language) are equivalent. )Given any CF language L, there is always an unambiguous CF grammar which generates L 6)Given any...
(complexity) prove: if P=NP, then there's an algorithm with a polynomial running time for the following problem: input: a boolean formula φ output: a satisfying assignment of φ if φ satisfiable. if φ not satisfiable, a "no" will be returned. explanation: the algorithm accepts φ as an input (boolean formula). if φ doesn't have a satisfiable assignment, a "no" is returned. if φ does have a satisfiable assignment, one of the satisfying assignment is returned,. so we assign 0 or...
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
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...
Why P = NP is considered an open problem? P- Polynomial time solving NP- Non deterministic Polynomial time solving
If a deterministic polynomial algorithm is found for any NP-complete problem, then it must be the case that P + NP. O True False
Let language L consist of simple, undirected graphs that contain at least one cycle. Prove that L ∈ NP.
2. (a) Prove the transitive property for polynomial-time mapping reductions (b) Using the transitivity, show that if A Sp B and A is NP-Hard, then B is NP-Hard as well