State complexity of Kleene-star operations on regulat tree languages

The concatenation of trees can be defined either as a sequential or a parallel operation, and the corresponding iterated operation gives an extension of Kleene-star to tree languages. Since the sequential tree concatenation is not associative, we get two essentially different iterated sequential concatenation operations that we call the bottom-up star and top-down star operation, respectively. We establish that the worst-case state complexity of bottom-up star is (n + 3/2) · 2 n−1. The bound differs by an order of magnitude from the corresponding result for string languages. The state complexity of top-down star is similar as in the string case. We consider also the state complexity of the star of the concatenation of a regular tree language with the set of all trees

Nondeterministic State Complexity for Suffix-Free Regular Languages

We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case for a minimal nondeterministic finite-state automaton that accepts the language obtained from the operation. We consider basic operations (catenation, union, intersection, Kleene star, reversal and complementation) and establish matching upper and lower bounds for each operation. In the case of complementation the upper and lower bounds differ by an additive constant of two.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Computing User Reputation in a Social Network of Web 2.0

In the Web 2.0 era, people not only read web contents but create, upload, view, share and evaluate all contents on the web. This leads us to introduce a new type of social network based on user activity and content metadata. We notice that we can determine the quality of related contents using this new social network. Based on this observation, we introduce a user evaluation algorithm for user-generated video sharing website. First, we make a social network of users from video contents and related social activities such as subscription, uploading or favorite. We then use a modified PageRank algorithm to compute user reputation from the social network. We re-calculate the content scores using user reputations and compare the results with a standard BM25 result. We apply the proposed approach to YouTube and demonstrate that the user reputation is closely related to the number of subscriptions and the number of uploaded contents. Furthermore, we show that the new ranking results relied on the user reputation is better than the standard BM25 approach by experiments

State Complexity of Regular Tree Languages for Tree Matching

We study the state complexity of regular tree languages for tree matching problem. Given a tree t and a set of pattern trees L, we can decide whether or not there exists a subtree occurrence of trees in L from the tree t by considering the new language L′ which accepts all trees containing trees in L as subtrees. We consider the case when we are given a set of pattern trees as a regular tree language and investigate the state complexity. Based on the sequential and parallel tree concatenation, we define three types of tree languages for deciding the existence of different types of subtree occurrences. We also study the deterministic top-down state complexity of path-closed languages for the same problem.</jats:p