Question

6. (a) Use Thompson's construction to convert the above regular expression 1(0/1) *101 into an NFA (7 points) (b) Convert the NFA of part (&) into a DFA using the subset construction (points)

Answer 1

1 (0/1) 101 a) NFA fox given Regular Expression by wing Tompson's Construction. Automata u to mata finite NFA Non Deterministic & moves method use Thompson's construction to construct NFA. NFA for 1 (0/1) 101. JE to start state (or) initial state input symbols (C): 0, 1 2 final state.

using the subset b) Conversion of NFA to of Construction. Algorithm. subset construction Algorithm :- Initially &-closure (so) is the only state in p- states and it is connected, I unmarked state T in while there is an D-states : do begin mark Ti for each input symbol a do begin U = E-closure (move (7,al); if u is in Dostates then addu as an unmarked state in D-states; otran [r, a] =U end end

E-closur(s) : set of Nf states reachable from NFA states on 'E' transition alone. E-closure(t); - set of NFA states reachable from NFA state s in I on & Transistion alone move CT, a) - set of NFA state to which there is a transistion on input symbol 'a' from same NFA state s in T. 9. initial state. A = E-closure (20) = {20 122 123 124, 287 E-closure (move (4,0)) = f 4 E-closure (more (A,()) = {2,} = 8 E-closure (more (8,0)) = 2 2 2 1 23, 24, 25} = c. E-clasure (move (6.1)) = { 22, 22, 24, 26 ) = 0 E-closun (move (6.0)) = { 22, 23, 24, 25} = 0 E-closure (move (0,1)) = { 22, 23, 24, 25}=0 & -closure (move (0,0) = 1 1 22, 23, 24, 26 izzi 3-F &- closure (move (6, 1) = 2 22, 23, 24, 252 = 0

E-closure (move CEO : 24 s-closure (move (6, 1)) = {2, 23, 24, 26128, 28, 29, 21) Transistion Table DFA from NEA o Poil o 2011 block. block

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