What is QSAT problem?

The QSAT problem (satisfiability of quantified propositional formulas) is a well-known PSPACE-complete problem [19], it is defined as follows: Given the fully quantified formula ⁎ associated with a Boolean formula φ ( x 1 , … , x n ) in conjunctive normal form, determine whether or not ⁎ is satisfiable.

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 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 does QBF stand for?

QBF

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.

Is QBF NP complete?

∃X1 ···∃Xn φ is true. 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.

What is reduction in DAA?

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first.