arXiv subjects

Ke Xu

Publications and source records attributed to Ke Xu.

457 records · Page 26Linked to original sources

arXiv2002

The Algorithms of Updating Sequential Patterns

Because the data being mined in the temporal database will evolve with time, many researchers have focused on the incremental mining of frequent sequences in temporal database. In this paper, we propose an algorithm called IUS, using the frequent and negative border sequences in the original database for incremental sequence mining. To deal with the case where some data need to be updated from the original database, we present an algorithm called DUS to maintain sequential patterns in the updated database. We also define the negative border sequence threshold: Min_nbd_supp to control the number of sequences in the negative border.

cs.DB↗

arXiv2002

The Limits of Horn Logic Programs

Given a sequence $\{Π_n\}$ of Horn logic programs, the limit $Π$ of $\{Π_n\}$ is the set of the clauses such that every clause in $Π$ belongs to almost every $Π_n$ and every clause in infinitely many $Π_n$'s belongs to $Π$ also. The limit program $Π$ is still Horn but may be infinite. In this paper, we consider if the least Herbrand model of the limit of a given Horn logic program sequence $\{Π_n\}$ equals the limit of the least Herbrand models of each logic program $Π_n$. It is proved that this property is not true in general but holds if Horn logic programs satisfy an assumption which can be syntactically checked and be satisfied by a class of Horn logic programs. Thus, under this assumption we can approach the least Herbrand model of the limit $Π$ by the sequence of the least Herbrand models of each finite program $Π_n$. We also prove that if a finite Horn logic program satisfies this assumption, then the least Herbrand model of this program is recursive. Finally, by use of the concept of stability from dynamical systems, we prove that this assumption is exactly a sufficient condition to guarantee the stability of fixed points for Horn logic programs.

cs.LO↗

arXiv2002

A Logical Framework for Convergent Infinite Computations

Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is proposed by extending first order theories using Cauchy sequences, which has stronger expressive power than the first order logic. A class of fixed points characterizing the logical properties of the limits can be represented by means of infinite-length terms defined by Cauchy sequences. We will show that the limit of sequence of first order theories can be defined in terms of distance, similar to the $ε-N$ style definition of limits in real analysis. On the basis of infinitary terms, a computation model for convergent infinite computations is proposed. Finally, the interpretations of logic programs are extended by introducing real Herbrand models of logic programs and a sufficient condition for computing a real Herbrand model of Horn logic programs using convergent infinite computation is given.

cs.LO↗

arXiv2001

Intelligent Search of Correlated Alarms from Database containing Noise Data

Alarm correlation plays an important role in improving the service and reliability in modern telecommunications networks. Most previous research of alarm correlation didn't consider the effect of noise data in Database. This paper focuses on the method of discovering alarm correlation rules from database containing noise data. We firstly define two parameters Win_freq and Win_add as the measure of noise data and then present the Robust_search algorithm to solve the problem. At different size of Win_freq and Win_add, experiments with alarm data containing noise data show that the Robust_search Algorithm can discover the more rules with the bigger size of Win_add. We also experimentally compare two different interestingness measures of confidence and correlation.

cs.NI↗

arXiv2000

The SAT Phase Transition

Phase transition is an important feature of SAT problem. For random k-SAT model, it is proved that as r (ratio of clauses to variables) increases, the structure of solutions will undergo a sudden change like satisfiability phase transition when r reaches a threshold point. This phenomenon shows that the satisfying truth assignments suddenly shift from being relatively different from each other to being very similar to each other.

cs.AI↗

arXiv2000

An Average Analysis of Backtracking on Random Constraint Satisfaction Problems

In this paper we propose a random CSP model, called Model GB, which is a natural generalization of standard Model B. It is proved that Model GB in which each constraint is easy to satisfy exhibits non-trivial behaviour (not trivially satisfiable or unsatisfiable) as the number of variables approaches infinity. A detailed analysis to obtain an asymptotic estimate (good to 1+o(1)) of the average number of nodes in a search tree used by the backtracking algorithm on Model GB is also presented. It is shown that the average number of nodes required for finding all solutions or proving that no solution exists grows exponentially with the number of variables. So this model might be an interesting distribution for studying the nature of hard instances and evaluating the performance of CSP algorithms. In addition, we further investigate the behaviour of the average number of nodes as r (the ratio of constraints to variables) varies. The results indicate that as r increases, random CSP instances get easier and easier to solve, and the base for the average number of nodes that is exponential in r tends to 1 as r approaches infinity. Therefore, although the average number of nodes used by the backtracking algorithm on random CSP is exponential, many CSP instances will be very easy to solve when r is sufficiently large.

cs.CC↗

arXiv2000

Exact Phase Transitions in Random Constraint Satisfaction Problems

In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satisfiable to a region where almost all problems are unsatisfiable do exist for Model RB as the number of variables approaches infinity. Moreover, the critical values at which the phase transitions occur are also known exactly. By relating the hardness of Model RB to Model B, it is shown that there exist a lot of hard instances in Model RB.

cs.AI↗