A unified view to string matching algorithms

Abstract

We present a unified view to sequential algorithms for many pattern matching problems, using a finite automaton built from the pattern which uses the text as input. We show the limitations of deterministic finite automata (DFA) and the advantages of using a bitwise simulation of non-deterministic finite automata (NFA). This approach gives very fast practical algorithms which have good complexity for small patterns on a RAM machine with word length O(log n), where n is the size of the text. For generalized string matching the time complexity is O(mn/log n) which for small patterns is linear. For approximate string matching we show that the two main known approaches to the problem are variations of the NFA simulation. For this case we present a different simulation technique which gives a running time of O(n) independently of the maximum number of errors allowed, k, for small patterns. This algorithm improves the best bit-wise or comparison based algorithms of running time O(kn) and can be used as a basic block for algorithms with good average case behavior. We also formalize previous bit-wise simulation of general NFAs achieving O(mn log log n/log n) time.