Abstract: Regular expression matching technology based on finite automaton(FA)has been widely used in the network and information field. A new method was proposed to construct the smaller nondeterministic FA(NFA) of regular expressions， namely， grouping regular expression based on closure(GREC). The GREC method was constructed based on the principle that all kinds of homomorphism computing of regular expression were closure and the hierarchy and recursiveness of closure operation were in regular set. The regular expression was cut into pieces， and then the NFA was constructed for each slice. Finally the stack to the restructuring of the NFA of each slice was used to obtain the final NFA. It can be concluded that NFA can be quickly constructed by the proposed GREC method， which has higher space efficiency compared with traditional Thompson structured approach when the regular expression is too complex in hierarchical structure or contains too many closure operations.

Key words: regular expression, finite automaton, closure, homomorphism computing, construction algorithm