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...
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...
This is the third edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book “Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. ...
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 ...
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...
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 ...
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....
complete. However, a fairly succinct argument demonstrates that this conjecture fails. Suppose we take the verifier for k-clique and define a new verifier which accepts only “padded” proofs of the form s, H where H is a clique and s is a ...
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...