What is the difference between EXPTIME and Expspace?
EXPTIME — Problems that can be solved in exponential amount of time. LOGSPACE — Problems that can be solved in logarithmic amount of space. PSPACE — Problems that can be solved in polynomial amount of space. EXPSPACE — Problems that can be solved in exponential amount of space.
Is NP hard in EXPTIME?
Because NP⊂2EXPTIME any 2EXPTIME-complete problem is NP-hard. However, by the time hierarchy theorem, we know that EXPTIME≠2EXPTIME, which means that no problem in EXPTIME is 2EXPTIME-complete.
What is polynomial time problem?
A polynomial-time algorithm is an algorithm whose execution time is either given by a polynomial on the size of the input, or can be bounded by such a polynomial. Problems that can be solved by a polynomial-time algorithm are called tractable problems. Sorting algorithms usually require either O(n log n) or O(n2) time.
Is the class of decision problem?
Explanation: NP problems are called as non-deterministic polynomial problems. They are a class of decision problems that can be solved using NP algorithms.
Why is PSPACE in EXPTIME?
EXPTIME can be reformulated as the space class APSPACE, the set of all problems that can be solved by an alternating Turing machine in polynomial space. This is one way to see that PSPACE ⊆ EXPTIME, since an alternating Turing machine is at least as powerful as a deterministic Turing machine.
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 chess an EXPTIME?
For many generalized games which may last for a number of moves exponential in the size of the board, the problem of determining if there is a win for the first player in a given position is EXPTIME-complete. Generalized chess, go (with Japanese ko rules), Quixo, and checkers are EXPTIME-complete.
What is polynomial time algorithm example?
Some examples of polynomial time algorithms: The selection sort sorting algorithm on n integers performs operations for some constant A. Thus it runs in time and is a polynomial time algorithm.
Is NP a PSPACE?
Since, PSPACE is closed under reductions and NP is contained in PSPACE, then we have that NP = PSPACE. The P versus NP problem is a major unsolved problem in computer science. This problem was introduced in 1971 by Stephen Cook [1]. It is considered by many to be the most important open problem in the field [2].
What is P problem example?
An example of a decision problem in P is: Given a list of n integers and an integer k, is there an integer in the list greater than k? Plainly the question can be answered in time linear to n by stepping through the list and checking whether an integer is greater than k.
What are P type problems?
P-Class. The class P consists of those problems that are solvable in polynomial time, i.e. these problems can be solved in time O(nk) in worst-case, where k is constant. These problems are called tractable, while others are called intractable or superpolynomial.