相关论文: NP problem in quantum algorithm

The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…

Quantifier elimination (QE) is an important problem that has numerous applications. Unfortunately, QE is computationally very hard. Earlier we introduced a generalization of QE called $\mathit{partial}$ QE (or PQE for short). PQE allows to…

It is shown that any two clauses in an instance of 3SAT sharing the same terminal which is positive in one clause and negated in the other can imply a new clause composed of the remaining terms from both clauses. Clauses can also imply…

We present various analytic and number theoretic results concerning the #SAT problem as reflected when reduced into a #PART problem. As an application we propose a heuristic to probabilistically estimate the solution of #SAT problems.

A polynomial algorithm is obtained for the NP-complete linear ordering problem.

In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…

Stephen Cook posited SAT is NP-Complete in 1971. If SAT is NP-Complete then, as is generally accepted, any polynomial solution of it must also present a polynomial solution of all NP decision problems. It is here argued, however, that NP is…

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…

This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…

We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp…

This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical"…

In this paper with two equivalent representations of the information contained by a SAT formula, the reason why string generated by succinct SAT formula can be greatly compressed is firstly presented based on Kolmogorov complexity theory.…

It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential…

In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…

We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show it is…

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…

The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we investigate a descriptor approach based on lattice properties. This paper proposes a new way to…

Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…

Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…