Since we are verifying NP-complete problems, we have to assume that the prover has access to the classical witness, otherwise there would be an efficient algorithm for NP, which is highly unlikely. Then, the first ingredient in the verification protocol is the construction of the quantum proofs...
A background equivalent to that provide by [G&J] is assumed, and, when appropriate, cross-references will be given to that book and the list of problems (NP-complete and harder) presented there. Readers who have results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time...
If an NP-hard problem can be solved by an algorithm of polynomial complexity, then all NP-complete problems can be so solved. The importance of these two classes comes from the following facts: 1. No NP-hard or NP-complete problem is known to be polynomially solvable. 2. The two ...
monotone [Math Processing Error]NP-complete problems) it might be computationally hard to verify that the parties form an “unqualified” subset. Next, in Definition 3.1 we give a uniform definition of secret-sharing for [Math Processing Error]NP. In Sect. 3.1 we give an alternative definition...
2.The satisfiability problem of conjunction normal form (abbreviate SAT problem) is an NP_complete problem.合取范式可满足性问题(简称SAT问题)是一个NP完全问题。 3.Knapsack problem is a typical NP complete problem.背包问题是一个典型的np完全问题。 4.DNA Computing of NP Complete Problem in Discrete...
32 Such problems lie in the complexity class NP, such that a solution can be verified in polynomial time, and are at least as hard as the most difficult problems in NP. A common way to determine NP-completeness is to map an already known NP-complete problem to the problem of interest....
That is, if we had a black box for an NP-hard problem, we could use it to solve all NP problems in polynomial time. Also, L is NP-complete if L is NP-hard and L ∈ NP. Informally, NP-complete problems are the hardest problems in NP, in the sense that an efficient algorithm ...
Although NP-complete problems are hard to solve efficiently, once solutions are found, they can be verified trivially. The challenge that the team at CNRS (the French National Centre for Scientific Research) and the University of Edinburgh focused on occupies a middle ground between the two: veri...
The security requirement guarantees that as long as the parties form an "unqualified" subset, they are unable to learn the secret. Note that the security requirement stated above is possibly hard to check efficiently: For some access structures in mNP (e.g., monotone NP-complete problems) it...
we study the task of verifying NP-complete problems, in particular whether a set of boolean constraints have a satisfying assignment to them or not, when an untrusted party provides some limited information about the solution of the problem. For this task, we show that we can achieve a quantu...