Related papers: Exploring P versus NP
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
In this paper, we make a preliminary interpretation of Cook's theorem presented in [1]. This interpretation reveals cognitive biases in the proof of Cook's theorem that arise from the attempt of constructing a formula in CNF to represent a…
Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…
We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
There has been a great of work on characterizing the complexity of the satisfiability and validity problem for modal logics. In particular, Ladner showed that the validity problem for all logics between K, T, and S4 is {\sl…
We show that for every polynomial q* there exist polynomial-size, constant-query, non-adaptive PCPs for NP which are perfect zero knowledge against (adaptive) adversaries making at most q* queries to the proof. In addition, we construct…
The reviewed paper describes an analog device that empirically solves small instances of the NP-complete Subset Sum Problem (SSP). The authors claim that this device can solve the SSP in polynomial time using polynomial space, in principle,…
The method for analyzing algorithmic runtime complexity using decision trees is discussed using the sorting algorithm. This method is then extended to optimal algorithms which may find all cliques of size q in network N, or simply the first…
This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial…
It is proved in this paper that to every underdetermined linear system $Ax=b$ there corresponds a constant $p(A,b)>0$ such that every solution to the $l_p$-norm minimization problem also solves the $l_0$-norm minimization problem whenever…
We prove that it is NP-complete to decide whether a given string can be factored into palindromes that are each unique in the factorization.
The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.
We prove that persuasion is an NP-complete problem.
The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we…
For all $k \geq 1$, we show that deciding whether a graph is $k$-planar is NP-complete, extending the well-known fact that deciding 1-planarity is NP-complete. Furthermore, we show that the gap version of this decision problem is…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
We study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…
This paper provides a further refinement to the previous response by introducing new structures and algorithms for counting VMPs of common \emph{Edge Requirement} (ER) and hence for counting the perfect matchings.
We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.