This paper presents a new method to translate a regular expression into a nondeterministic finite automaton (an NFA for short). Let r be a regular expression and let M be a Thompson automaton for r. We first introduce a labeled Thompson automaton defined by assigning two types of expressions which denote prefixes and suffixes of words in L(r) to each state of M. Then we give new ϵ-free NFAs constructed from a labeled Thompson automaton. These NFAs are called a prefix equation automaton and a suffix equation automaton. We show that a suffix equation automaton is isomorphic to an equation automaton defined by Antimirov. Furthermore we give an NFA called a unified equation automaton by joining two NFAs. Thus the number of states of a unified equation automaton can be smaller than that of an equation automaton.

Recently, for more efficient filtering of XML data, YFilter system has been suggested to exploit the prefix commonalities that exist among path expressions. Sharing the prefix commonality gives the benefit of improving filtering performance through the tremendous reduction in filtering machine size. However, exploiting the postfix commonality can also be useful for an XML filtering situation. For example, when a stream of XML messages does not have any defined schema, or users cannot remember the defined schema exactly, users often use the partial matching path queries which begins with the descendant axis ("//"), e.g., '//science/article/title', '//entertainment/article/title', and '//title'. If so, the registered XPath queries are most likely to have the postfix commonality, e.g., the sample queries share the partial path expressions 'article/title' and 'title'. Therefore, in this paper, we introduce a bottom-up filtering approach exploiting the postfix commonality against the top-down approach of YFilter exploiting the prefix commonality. Some experimental results show that our method has better filtering performance when registered XPath queries mainly consist of the partial matching path queries with the postfix commonality.