AC演算法是Alfred V.Aho（《編譯原理》（龍書）的作者），和Margaret J.Corasick於1974年提出（與KMP演算法同年）的一個經典的多模式匹配演算法，可以保證對於給定的長度為n的文字，和模式集合P{p1,p2,...pm}，在O(n)時間複雜度內，找到文字中的所有目標模式，而與模式集合的規模m無關.
  AC演算法從某種程度上可以說是KMP演算法在多模式環境下的擴充套件。

KMP 演算法簡述

  對於模式串而言，其字首，有可能也是模式串中的非字首的子串，而且這裡找的是最大字首，非字首可能包含多個字首。
  在KMP演算法中有個陣列，叫做字首陣列，也有的叫next陣列，發現不匹配，下一步模式(pattern)串匹配目標(target)串的模式串的位置，它記錄著字串匹配過程中失配情況下，模式串可以向前跳幾個字元，當然它描述的也是子串的對稱程度，程度越高，值越大，當然之前可能出現再匹配的機會就更大。

示例1

示例2

示例2中，a g c t a g c，包含兩個字首。對於t，其next一定小於其前面c的next。

AC自動機演算法

  AC are determined by three functions:goto function ,failure function,output function

Keyword Tree

A keyword tree (or a trie ) for a set of patterns P

1. each edge of K is labeled by a char acter
2. any two edges out of a node have diferent labels
   Define the label of a node v as the concatenation of edge labels on the path from the root to v , and denote it by L(v)
3. for each p∈P there’s a node v with L(v)=P , and
4. the label L(v) of any leaf v equals some p∈P

A keyword tree for P={he，she，his，hers}

goto function

States: nodes of the keyword tree
initial state: 0 = the root
the goto function g(q;a)gives the state entered from current state q by matching target char a

1. if edge (q;v)is labeled by a, then g(q;a)=v;
2. g(0;a)=0 for each a that does not label an edge out of the root the automaton stays at the initial state while scanning non-matching characters
3. Otherwise g(q;a)=∅;

failure function

the failure function f(q) for q≠0 gives the state entered at a mismatch
f(q) is the node labeled by the longest proper suffix w of L(q) s.t.w is a prefix of some pattern,a fail transition does not miss any potential occurrences

f(q) is always defined, since L(0)=ϵ is a prefix of any pattern

Dashed arrows are fail transitions

output function

the output function out(q) gives the set of patterns recognized when entering state q