Finite state automata for string matching

If pos = String.size(text) then Array.sub(accept,state) *) fun search1(pos: int, state: int): bool = * returning whether it accepts the rest of the string. *) fun next_state(pos: int, state: int): dest =Д®lse let val char = Char.ord(String.sub(text, pos)) inД®nd (* Walk the DFA down the string 'text' from position 'pos', * state 'state' and the next character is text. | Error (* if no next state *) type DFA = : DFA, text: string): bool = let (* Give the next state of the DFA, assuming that it is in State of state (* Edge destination is another state *) Type state = int (* Note: 0 is the start state *) datatype dest = Implementing pattern matching for regular expressions using For example, the automaton on the right can be written as this The pair (current state, input character) to the next state of theДЄutomaton. To the more complex regular expression a(b*|bcb) note that it hasДЄ DFA can be implemented very easily using a table. For example,ДЄn automaton that accepts the same strings as the regular expressionДЄb* is shown on the left the automaton on the right corresponds It is conventional to draw finite automata as a graph where the states areДrawn as circles and the accept states are drawn as double circles. State, it has seen a string matching the pattern. For each inputД¬haracter, it follows the single outgoing edge from the current state Start state and scans the text from left to right. Node labeled with a particular character. Is a distinguished start state and some number of accept states.ДЇinite automaton, there is at most one outgoing edge from any given The edges of the graph are labeled with characters, and there Graph in which the vertices (nodes) are the states of theДЄutomaton. It's the Greeks'ДЇault.) A DFA, also known as a finite state machine, is a finite Is the singular, 'automata' is the plural. Length of the string! (For those who care about language: It turns out that for any regular expression, a deterministicДЇinite automaton (DFA) can be constructed that recognizesДЄny string that the regular expression describes in time linear in the Patterns we saw earlier, they can be efficiently searched for in a larger They are particularly useful because, like the simple string Regular expressions provide an expressive language for describing Recitation 26: Regular expressions and finite automata CS 312 Recitation 26

Finite state automata for string matching