String Matching Chapter 32 Highlights Charles Tappert Seidenberg School of CSIS, Pace University.
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Transcript of String Matching Chapter 32 Highlights Charles Tappert Seidenberg School of CSIS, Pace University.
String MatchingChapter 32 Highlights
Charles TappertSeidenberg School of CSIS, Pace
University
String Matching Problemin this chapter
Problem: Find all valid shifts s with which a given pattern P occurs in a given text T
This problem occurs in text editing, DNA sequence searches, and Internet search engines
Example:
String Matching AlgorithmsPreprocessing & Matching
Times
Notation and Terminology
(Sigma-star) = set of all finite-length strings of alphabet sigma (eta is empty string)
String w is a prefix of string x, denoted w [ x, if x = wy for some string y
String w is a suffix of string x, denoted w ] x, if x = yw for some string y
Example: ab [ abcca and cca ] abcca
Problem Re-statement
in notation/terminology
Denote a k-char prefix P[1..k] of pattern P by Pk
Similarly, denote a k-char prefix of text T by Tk
Matching problem: Given n = T.length and m = P.length, find all shifts s in range 0<=s<=n-m such that P ] Ts+m
Naïve String Match Algorithm
sliding “template” pattern match
Problem 1-1 How many template comparisons are made? How many were matches and how many non-matches? How many computation units are used?
Problem 1-2 How many computation units are used?
Naïve String Match Algorithm
sliding “template” pattern match
Finite Automata Algorithm
Efficient – examine each text char only once
Finite Automata Algorithm
Example: simple two-state finite automaton:
Transition function (delta)
State transition diagram
Finite Automata Algorithm
Final-state function
Final-state function (phi)
Finite Automata Algorithm
Construct the automaton
Suffix function (small sigma)
Finite Automata Algorithm
Construct the automaton
Example:
State m
P = a b a b a c a
Finite Automata AlgorithmCritical transition function
(delta)
Transition function (delta) obtained from Suffix function (small sigma)
Finite Automata AlgorithmMatching operation
Transition function (delta)
Finite Automata AlgorithmCompute transition function
Transition function (delta)
Finite Automata Algorithm
Problem 3-1 Problem 3-2
