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The Journal of Supercomputing - This article presents a new algorithmic approach for computational convergence verification of the Collatz problem. The main contribution of the paper is the...  相似文献   

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The paper refers to the Collatz's conjecture. In the first part, we present some equivalent forms of this conjecture and a slight generalization of a former result from [1]. Then, we present the notion of “chain subtrees” in Collatz's tree followed by a characterization theorem and some subclass of numbers which are labels for some chain subtrees. Next, we define the notion of “fixed points” and using this, we give another conjecture similar to Collatz's conjecture. Some new infinite sets of numbers for which the Collatz's conjecture holds are given. Finally, we present some interesting results related to the number of “even” and “odd” branches in the Collatz's tree. Received: 15 September 1999 / 2 June 2000  相似文献   

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Erich Bukovics 《Computing》1970,5(3):185-188
Ohne Zusammenfassung  相似文献   

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Algorithms for producing a Collatz sequence are considered in the cases of the binary and ternary number systems. Advantages of this approach to the representation of such a sequence are considered. Logic circuits of iterative automata that implement the algorithms described are presented.  相似文献   

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冰雹猜想是一个风靡全球的趣味数学游戏。迄今为止,人们还未能得到这个猜想在数学上的严格证明。可以利用计算机强大的计算能力,根据冰雹猜想的计算规律,编写程序让计算机来证明冰雹猜想的正确性。程序的设计思想是先证明任意一个数的正确性,再证明某个数据区间内所有数据的正确性,通过程序的运行,对一定范围内的所有自然数进行验证,从而证明了冰雹猜想。  相似文献   

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We give partial results on the factorization conjecture on codes proposed by Schützenberger. We consider a family of finite maximal codes $C$ over the alphabet $A = \{a, b\}$ and we prove that the factorization conjecture holds for these codes. This family contains $(p,4)$ -codes, where a $(p,4)$ -code $C$ is a finite maximal code over $A$ such that each word in $C$ has at most four occurrences of $b$ and $a^p \in C$ , for a prime number $p$ . We also discuss the structure of these codes. The obtained results once again show relations between factorizations of finite maximal codes and factorizations of finite cyclic groups.  相似文献   

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In their study of algorithms for reasoning about intervals, Golumbic and Shamir conjectured that a certain class of interval inference problems is intractable (Golumbic and Shamir, J. ACM 40(1993)1108-1133). The conjecture is correct; this paper proves the NP-completeness of the interval satisfiability (ISAT) problem for the domain of relations known as 5.  相似文献   

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A proof of the Vose-Liepins conjecture   总被引:1,自引:0,他引:1  
A key result sufficient for the asymptotic stability of the mixing operator in infinite population genetic algorithms depended upon a conjecture. While empirical results supported the conjecture, no proof has been heretofore obtained. In this paper we supply a proof of the conjecture. In so doing, we obtain properties useful for the study of genetic algorithms.  相似文献   

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《软件》2016,(6):65-71
本文从3x+1问题的原始Collatz函数出发,放宽对原Collatz函数的限制条件,将确定的Collatz程序推广到非确定程序,得到扩展的Collatz模型。从一个特殊的角度描述3x+1问题,引入互逆操作的概念,建立自然数之间同等类型数的联系,发现扩展Collatz模型的存在环结构。通过选取大范围的自然数深度搜索遍历,得出扩展模型下存在一定的规律的环结构。  相似文献   

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Necessary and sufficient Liapunov-like conditions for both absolute stability and the Aizerman conjecture are established in the framework of stationary, continuous-time Lurie-Postnikov systems with multiple nonlinearities, thus providing theoretical solutions for these problems in the Liapunov sense. The solutions are based on the use of functional families instead of a single Liapunov function.Directly applicable results of the paper are new algebraic criteria for absolute stability. One of them is proved by using a new form of a tentative system Liapunov function. Also an estimate of the asymptotic stability domain is determined for all admissible nonlinearities.The results do not impose any requirement on the linear part of the system (such as its stability or controllability or observability).Three illustrative examples are worked out.  相似文献   

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This note provides counterexamples to the conjecture which is formulated in Fessas' correspondence [2].  相似文献   

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We give a short and elementary proof of the following stronger version of Duval's conjecture: let u be an unbordered word, and v a word of length |u|-1, such that v is not a prefix of u. Then uv contains an unbordered word of length at least |u|+1.  相似文献   

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A conjecture that the norm of Lyapunov mapping LA equals to its restriction to the symmetric set, S, i.e., ||LA|| =||LA|s|| was proposed in [1]. In this paper, a method for numerical testing is provided first. Then, some recent progress on this conjecture is presented.  相似文献   

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Stimulated by the work of Hartmanis and Berman [5], we study the question of the existence of a tally languageL inNP such thatL is inP if and only ifP = NP. The method used is applicable to questions regarding the comparison of a wide range of pairs of classes of formal languages specified by machines whose computational resources are bounded in time or space.This research was supported in part by the National Science Foundation under Grants MCS76-05744 and MCS77-11360.  相似文献   

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