اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSolvability of HornSAT and CNFSAT
70
0
0.0
(
0
)
تأليف
Koji Kobayashi
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This article describes the solvability of HornSAT and CNFSAT. Unsatisfiable HornCNF have partially ordered set that is made by causation of each clauses. In this partially ordered set, Truth value assignment that is false in each clauses become simply connected space. Therefore, if we reduce CNFSAT to HornSAT, we must make such partially ordered set in HornSAT. But CNFSAT have correlations of each clauses, the partially ordered set is not in polynomial size. Therefore, we cannot reduce CNFSAT to HornSAT in polynomial size.
قيم البحث
اقرأ أيضاً
This article describes about the difference of resolution structure and size between HornSAT and CNFSAT. We can compute HornSAT by using clauses causality. Therefore we can compute proof diagram by using Log space reduction. But we must compute CNFSA
T by using clauses correlation. Therefore we cannot compute proof diagram by using Log space reduction, and reduction of CNFSAT is not P-Complete.
This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $mathrm{sp}(A)$ of c
lasses of bounded operators $A = {a_{ij}}_{i,j in mathbb{N}} in mathcal{B}(l^2(mathbb{N}))$, given the matrix elements ${a_{ij}}_{i,j in mathbb{N}}$, that are sharp in the sense that they achieve the boundary of what a digital computer can achieve. Similarly, for a Schrodinger operator $H = -Delta+V$, determine the existence of algorithms that can compute the spectrum $mathrm{sp}(H)$ given point samples of the potential function $V$. In order to solve these problems, we establish the Solvability Complexity Index (SCI) hierarchy and provide a collection of new algorithms that allow for problems that were previously out of reach. The SCI is the smallest number of limits needed in the computation, yielding a classification hierarchy for all types of problems in computational mathematics that determines the boundaries of what computers can achieve in scientific computing. In addition, the SCI hierarchy provides classifications of computational problems that can be used in computer-assisted proofs. The SCI hierarchy captures many key computational issues in the history of mathematics including the insolvability of the quintic, Smales problem on the existence of iterative generally convergent algorithm for polynomial root finding, the computational spectral problem, inverse problems, optimisation etc.
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a viewing graph. Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration depends on t
he structure of this graph. We study characterizations of solvable viewing graphs and present several new results that can be applied to determine which pairs of views may be used to recover all camera parameters. We also discuss strategies for verifying the solvability of a graph computationally.
We address the question whether the condition on a fusion category being solvable or not is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple
Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the $S$-matrix of the Drinfeld center and show that this invariant does determine the solvability of a fusion category provided it is group-theoretical.
The paper is devoted to the further study of the remarkable classes of orthogonal polynomials recently discovered by Bender and Dunne. We show that these polynomials can be generated by solutions of arbitrary quasi - exactly solvable problems of quan
tum mechanichs both one-dimensional and multi-dimensional. A general and model-independent method for building and studying Bender-Dunne polynomials is proposed. The method enables one to compute the weight functions for the polynomials and shows that they are the orthogonal polynomials in a discrete variable $E_k$ which takes its values in the set of exactly computable energy levels of the corresponding quasi-exactly solvable model. It is also demonstrated that in an important particular case, the Bender-Dunne polynomials exactly coincide with orthogonal polynomials appearing in Lanczos tridiagonalization procedure.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
