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For example, the automaton on the right can be written as this The pair (current state, input character) to the next state of theĪutomaton. To the more complex regular expression a(b*|bcb) note that it hasĪ DFA can be implemented very easily using a table. For example,Īn automaton that accepts the same strings as the regular expressionĪb* is shown on the left the automaton on the right corresponds It is conventional to draw finite automata as a graph where the states areĭrawn as circles and the accept states are drawn as double circles. State, it has seen a string matching the pattern. For each inputĬharacter, 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.įinite 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 theĪutomaton. It's the Greeks'įault.) 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 deterministicįinite automaton (DFA) can be constructed that recognizesĪny 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