Question

Let L1 = {ω|ω begins with a 1 and ends with a 0}, L2 = {ω|ω has length at least 3 and its third symbol is a 0}, and L3 = {ω| every odd position of ω is a 1} where L1, L2, and L3 are all languages over the alphabet {0, 1}. Draw finite automata (may be NFA) for L1, L2, and L3 and for each of the following (note: L means complement of L):

Let L w begins with a 1 and ends with a 0), L2 wIw has length at least 3 and its third symbol is a 0), and L3 wl every odd position of w is a 11 where L1, L2, and Ls are all languages over the alphabet f0,1) Draw finite automata (may be NFA) for L1, L2, and La and for each of the following (note: L means complement of L): (a) L (b) LiUL2 (c) L L2 (d) L L1 (e) L (f) (L2 u L3)

Answer 1

し1-1c1ω begins with a 1 and ends with a 0)(ω@begins with a 1 and ends with a 0} Solution q0 q1 q2 q3 0.1

L2-olo has length atleast 3 and its third symbol is a 0) 0.1 0,1 q0 q3 q4 0.1

L3 (ol every odd position of o is a 1) 0.1 0.1

a)L1 ,(COMPLEMENT OF L) q0 q1 q2 0 q3 1.0

b)L1 UL2

Solution q0 q1 q2 q3 0.1 0.1 0,1 q4 0.1