Finite Automata

Finite automata are recognizers A recoganizer for a language L is a program that takes as input a string x and answers “yes” if x is a sentence of L and “no ” otherwise. Finite automata can be : Nondeterministic finite automata (NFA) no restrictions on the labels of their edges. A symbol can label several edges out of the same state, and , the empty string, is a possible label. Deterministic finite automata (DFA) for each state, and for each symbol of its input alphabet exactly one edge with that symbol leaving that state. 2

Nondeterministic Finite Automata A nondeterministic finite automaton (NFA) consists of: A finite set of states S. A set of input symbols Σ (the input alphabet). empty string, is never a member of Σ. A transition function that maps state-symbol pairs to sets of states. A state S0 that is distinguished as the start state (or initial state). A set of states F, that is distinguished as the accepting states (or final states).

which recognizes the language (a/b)*abb An NFA can be represented diagrammatically by a labelled directed graph transition graph (transition diagram). nodes represents states and the labelled edges represent the transition function Eg for NFA- which recognizes the language (a/b)*abb a 2 1 3 b start The language defined (or accepted) by an NFA is the set of strings labeling some path from the start to an accepting state.

Transition table for NFA of regular expression (a/b)*abb The transitions of an NFA can be represented in tabular form called transition table Transition table for NFA of regular expression (a/b)*abb In transition table ,there is a row for each state, and a column for each input symbol and є The entry for row i and symbol a is the set of possible next states that can be reached from state i on input a. state Input symbol a b {0,1} {0} 1 ---- {2} 2 ---- {3}