FINITE AUTOMATA

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.

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).

• 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)*abba

0 21 3a b b

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.

• 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 {0,1} {0}

1 ---- {2}

2 ---- {3}