A formal-linguistic approach for solving an entertaining task is offered in this paper. The well-known task of the Hanoi towers is discussed in relation to some concepts of formal languages and grammars. A context-fre...A formal-linguistic approach for solving an entertaining task is offered in this paper. The well-known task of the Hanoi towers is discussed in relation to some concepts of formal languages and grammars. A context-free grammar which generates an algorithm for solving this task is described. A deterministic pushdown automation which in its work imitates the work of monks in solving the task of the Hanoi towers is built.展开更多
We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k...We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.展开更多
大规模的用户口令集因可用于评估口令猜测算法的效率、检测现有用户口令保护机制的缺陷等,而广受系统安全研究领域的重视.然而,尽管可以通过一些渠道,譬如网站口令泄露、用户自愿征集或者个别网站出于研究目的的共享等,获取真实的大规...大规模的用户口令集因可用于评估口令猜测算法的效率、检测现有用户口令保护机制的缺陷等,而广受系统安全研究领域的重视.然而,尽管可以通过一些渠道,譬如网站口令泄露、用户自愿征集或者个别网站出于研究目的的共享等,获取真实的大规模用户明文口令对当前研究人员来说仍然非常困难.为应对上述问题,该文提出了一种基于样本的模拟口令集生成算法(Sample Perturbation Based Password Generation,SPPG).该算法利用较容易获得的小规模真实口令样本,通过学习生成概率模型,并产生大规模用户口令集合.为评估这一算法的效能,该文提出了一组模拟口令集质量的检测指标,包括真实口令覆盖率、Zipf分布拟合度等.最后,论文对比了SPPG算法与当前常见的用户口令猜测概率模型,包括概率上下文无关文法和多种马尔科夫模型,在生成用户口令集上的效能差异.结果显示,SPPG算法产生的模拟口令集在各指标下都有更好的表现.平均地,在真实口令覆盖率上,相对上下文无关文法和四阶马尔科夫模型分别提高了9.58%和72.79%,相对三阶和一阶马尔科夫模型分别提高了10.34倍和13.41倍,并且Zipf分布的拟合度保持在0.9及以上的水平.同时,其口令结构分布和特殊模式的使用也更符合真实用户生成口令的情况.展开更多
文摘A formal-linguistic approach for solving an entertaining task is offered in this paper. The well-known task of the Hanoi towers is discussed in relation to some concepts of formal languages and grammars. A context-free grammar which generates an algorithm for solving this task is described. A deterministic pushdown automation which in its work imitates the work of monks in solving the task of the Hanoi towers is built.
基金Supported by the 973 Projectthe PCSIRT Project+1 种基金the Doctoral Program Fund of the Ministry of Educationthe National Science Foundation of China
文摘We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.
文摘大规模的用户口令集因可用于评估口令猜测算法的效率、检测现有用户口令保护机制的缺陷等,而广受系统安全研究领域的重视.然而,尽管可以通过一些渠道,譬如网站口令泄露、用户自愿征集或者个别网站出于研究目的的共享等,获取真实的大规模用户明文口令对当前研究人员来说仍然非常困难.为应对上述问题,该文提出了一种基于样本的模拟口令集生成算法(Sample Perturbation Based Password Generation,SPPG).该算法利用较容易获得的小规模真实口令样本,通过学习生成概率模型,并产生大规模用户口令集合.为评估这一算法的效能,该文提出了一组模拟口令集质量的检测指标,包括真实口令覆盖率、Zipf分布拟合度等.最后,论文对比了SPPG算法与当前常见的用户口令猜测概率模型,包括概率上下文无关文法和多种马尔科夫模型,在生成用户口令集上的效能差异.结果显示,SPPG算法产生的模拟口令集在各指标下都有更好的表现.平均地,在真实口令覆盖率上,相对上下文无关文法和四阶马尔科夫模型分别提高了9.58%和72.79%,相对三阶和一阶马尔科夫模型分别提高了10.34倍和13.41倍,并且Zipf分布的拟合度保持在0.9及以上的水平.同时,其口令结构分布和特殊模式的使用也更符合真实用户生成口令的情况.
