Regular expression matching plays an important role in network security. Regular expression matching is achieved by NFA and DFA. DFA is suitable for high-speed IDS due to its efficiency. However, the combined compilation of multiple rules containing “.*” may blow up in state and storage space. In this paper, we give an explanation to this problem from the prospective of information theory, and propose a multidimensional mathematical model focusing on the most serious state explosion. We divide redundant states into zero-dimensional ones and one-dimensional ones. The former are compressed by dimension, and the later are dynamically built. Theory proof illustrates that the space complexity of the model reaches the theoretical lower bound. Then we propose the multi-dimensional finite automata (MFA) based on the model. Experimental results show that, MFA reduces greatly the construction time, memory and matching time, compared with several typical state-of-the-arts DFA improved algorithms.