The Factor Automaton

The amount of information processed by computers grows very dramatically. Now every application should contain an information searching engine. Let us deal with exact substring matching for one pattern-text pair. There are a lot of pattern matching algorithms with the same function but each of them is optimal in different field. Standard algorithms (Aho-Corasick or Boyer-Moore) sequentially compare given pattern with a text to be searched in. These algorithms are relatively slow but they need not any precomputed data structures and have small memory complexity. Time complexity is typically from O(n-r-m) to 0(n*m) where n is the size of the searching text and m is the size of the pattern. The space complexity is equal to the size of the text and the pattern. Algorithms in this category are useful for applications with small texts or in applications which source text changes too often. Another category of searching algorithms prefer preprocessing the base text and extremely fast searching in special data structures. The most useful data structure is directed acyclic word graph sometimes called DAWG. In this case the searching engine is a finite automaton with the same structure as DAWG has. The space complexity is also 0(n) but implementation of this automaton is approximately 4 times larger than algorithms in previous category. The main benefit is the fastest possible searching speed. The time complexity is linear with respect to the size of the pattern, not depending on the size of the searched text. However, the source text must be preprocessed. The preprocessing is an operation with the time and space complexity linear with respect to the size of the text. Any change of the source text causes a new reinitialization of the data structure (or structure of the finite automaton). It seems the cost of this reinitialization is too high but recently the