What is exponential space?

In computational complexity theory, EXPSPACE is the set of all decision problems solvable by a deterministic Turing machine in exponential space, i.e., in space, where is a polynomial function of . Some authors restrict. to be a linear function, but most authors instead call the resulting class ESPACE.

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.

Why is PSPACE in Npspace?

PSPACE is a strict superset of the set of context-sensitive languages. Because of Savitch’s theorem, NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a non-deterministic Turing machine without needing much more space (even though it may use much more time).

Is chess a PSPACE?

Some other generalized games, such as chess, checkers (draughts), and Go are EXPTIME-complete because a game between two perfect players can be very long, so they are unlikely to be in PSPACE. But they will become PSPACE-complete if a polynomial bound on the number of moves is enforced.

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.

What is meant by NP hard?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

Is PSPACE equal to Exptime?

That’s what the difference is: although both PSPACE and EXP are problems that can be solved in exponential time, PSPACE is restricted to polynomial space use, whereas EXP can use exponential space.

Is NL equal to PSPACE?

This statement is actually equivalent to P≠PSPACE (as a PSPACE complete problem in NL obviously implies P=PSPACE). Examine the equivalent statement, that P=PSPACE implies there exists a PSPACE complete problem in NL.

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].

Is NP equal to P?

NP-hard problems are those at least as hard as NP problems; i.e., all NP problems can be reduced (in polynomial time) to them. If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.

Is sat PSPACE?

SAT is in PSPACE That takes a lot of time, but not much space. Think of a truth-value assignment as a sequence of 0’s and 1’s, where 0 indicates false and 1 indicates true. If there are v variables, then there are v bits in the sequence.

What is NP algorithm?

NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems. Fast Facts.

When to reformulate EXPTIME to a space class?

More precisely, EXPTIME ≠ NEXPTIME if and only if there exist sparse languages in NP that are not in P. 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.

What’s the difference between a PSPACE and an EXP?

That’s what the difference is: although both PSPACE and EXP are problems that can be solved in exponential time, PSPACE is restricted to polynomial space use, whereas EXP can use exponential space. That already suggests that EXP ought to be more powerful. For example, suppose you’re trying to solve a problem about graphs.

Can a Turing machine reformulate the space class EXPTIME?

Which is an example of an EXPTIME class?

EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations. For example, the class 2-EXPTIME is defined similarly to EXPTIME but with a doubly exponential time bound .

What is exponential space?