Is TQBF PSPACE-complete?
Theorem 4 TQBF is PSPACE-complete. Proof It is not too difficult to see that TQBF ∈ PSPACE, since in polynomial space we can try all settings of all the variables and keep track of whether the quantified expression is true.
What is PSPACE-complete problem?
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time.
Is PSPACE a Logspace?
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.
Why SAT is a special case of TQBF?
Notice that SAT is a special case of TQBF where all quantifiers must be ∃. But TQBF is much tougher than SAT. Theorem. The practical import of PSPACE-completeness is that TQBF is very time-consuming to solve for smaller lengths than SAT.
Is QBF NP-hard?
Similarly, φ is valid if, and only if, the formula ∀X1 ···∀Xn φ is true. Thus, SAT ≤L QBF and VAL ≤L QBF and so QBF is NP-hard and co-NP-hard. In fact, QBF is PSPACE-complete.
Can NP-complete problems be solved in polynomial time?
If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.
Is PSPACE harder than NP?
though you shouldn’t necessarily expect it to be as effective as SAT solvers have been for NP-complete problems, given that PSPACE-complete problems are believed to be harder than NP-complete problems.
What is Pspace hard?
A language B is PSPACE-complete if it is in PSPACE and it is PSPACE-hard, which means for all A ∈ PSPACE, , where. means that there is a polynomial-time many-one reduction from A to B.
What is the use of complexity classes?
Complexity classes are sets of related computational problems. They are defined in terms of the computational difficulty of solving the problems contained within them with respect to particular computational resources like time or memory.
Why is TQBF in PSPACE?
Formulas that lack quantifiers can be evaluated in space logarithmic in the number of variables. The initial QBF was fully quantified, so there are at least as many quantifiers as variables. Thus, this algorithm uses O(n + log n) = O(n) space. This makes the TQBF language part of the PSPACE complexity class.
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.