Related papers: P not equal to NP
A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations. The implications of the introduction of this class are considered.…
Let gamma be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in gamma is in Logspace or complete for the class CSP(gamma)_NP under…
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…
A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
We show that for any rational p \in [1,\infty) except p = 1, 2, unless P = NP, there is no polynomial-time algorithm for approximating the matrix p-norm to arbitrary relative precision. We also show that for any rational p\in [1,\infty)…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
By using of analytical multi-logic expresses in conjunction with non-deterministic Turing machine the proposition was proved that algorithm of deterministic Turing counter machine of polynomial time complexity can be decreased to the…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…
The Matrix Torsion Problem (MTP) is: given a square matrix M with rational entries, decide whether two distinct powers of M are equal. It has been shown by Cassaigne and the author that the MTP reduces to the Matrix Power Problem (MPP) in…
We build a class of polynomial problems with not polynomial certificates. The parameter concerning which are defined efficiency of corresponding algorithms is the number $n$ of elements of the set has used at construction of combinatory…
We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup…
We introduce an NP-complete graph decision problem, the "Multi-stage graph Simple Path" (abbr. MSP) problem, which focuses on determining the existence of specific "global paths" in a graph $G$. We show that the MSP problem can be solved in…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
On example of tasks of class NP the questions concerning accuracy of work of already existing and possible in the future algorithms for the solution of tasks on discrete structures are considered.
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we…