Question

Problem 4 Draw a DFA and an NFA for the following languages where $\sum$ = {a,b}.

(a) L={(ab)ⁿ; n $\geq$ 0}

(b) L={aⁿ(bb); n $\geq$ 1}

Answer 1

NEA- Non-Defcomunistic finite Automata. * In NFA by reading an input we can reach more than one state. * There is rule an N.F-A that every deput state should have transition with every input symbol. Formal Definition in N.F.A is a fire tople Automata, (Q, E, qof, s). @ : Finste set of states (20,77) -- finite set of input symbols (a,b) 20 Initial state final state si transition function (@x<>220 DfAir Deterministic Finele Automata. where (FCQ) F : In DFA by reading an input Symbol we only. exactly adnost one state reach to wil) * Every state must have transition with every input symbol in D.F.A.

Formal Definition * D.F.A is also represented by Ituple (Q, E, 90,4,5) where Q - Finite set of states E-) Finite set of input symbols Transition function (& QX&ta Initial state 20 > Final state a) L= {cab)"; n20 >> Le{ ¢, ab, abab, a babab, 21 N.F.A b Q = {20,2,3, E-{a,b], 20-20%,ffroy D-F.A b a Q={20,2,3@y, E={a, by, o={20, F={ Roj

b) = { a n (bb); nzig 2)Le {abb, aabb, aaa bb, .....9 N.F.Ai- 23 Q={20,21,22,23%, £= {a,b], 20 ={80%, F = {23 Def-Air az b ) Job Q-{20,21,92,93,0}, {= { a, by, 20={20%,F= {23%