基于多维有限自动机的DFA改进算法

Improved DFA algorithm based on multi-dimensional finite automata

多个正则表达式规则编译成一个DFA（deterministerfiniteautomata）时，会产生状态爆炸、存储急剧增加的现象。针对最严重的状态爆炸问题，从信息论的角度给出了解释，并提出多维数学模型，将冗余状态分为0维状态和1维状态，通过前者按照维度压缩，后者动态构建的方法将空间复杂度降到理论下界，并在此基础上提出多维有限白动机（MFA，multi—dimensionalfiniteautomata）。实验表明，MFA构造时间比XFA略少，比DFA、STT冗余压缩算法和Hybrid．FA降低了2～3个数量级；存储空间比XFA略高，比DFA、STT冗余压缩算法、mDFA、Hybrid-FA降低了1-2个数量级；匹配时间比DFA、Hybrid．FA略多，但是比XFA略少，比sTT冗余压缩算法和mDFA降低了1-2个数量级。

Compiling multiple regular expression signatures into a combined DFA can blowup in state and storage space. Explanations from the prospective of information theory and multi-dimensional mathematical model were proposed fo- cusing on the most serious state explosion. Redundancy states were divided into zero-dimensional ones and one-dimensional ones. The former were compressed by dimension, and the later were dynamically built. The space com- plexity of the model came to the theoretical lower bound by the above methods. Then the multi-dimensional finite auto- mata （MFA） was proposed with the model. Experiments show that, the construction time taken by MFA is slightly less than XFA and is 2-3 orders of magnitude lower than DFA, STT redundancy compression algorithms and Hybrid-FA; the memory space of MFA is slightly higher than XFA, but is 1-2 orders of magnitude lower than DFA, STT redundancy compression algorithms, mDFA and Hybrid-FA; in the aspect of matching time, MFA ranks after DFA and Hybrid-FA, but ranks before XFA, and it achieves 1-2 orders of magnitude lower than that of STT redundancy compression algo- rithms and mDFA.