CS402 Theory of Automata Assignment No 2 fall 11 November 2011

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CS 402_2nd Assignment Solution

Question # 1:
Using the FA’s corresponding to r1 and r2, Build an FA corresponding to

a) r1+ r2 (Union of r1 and r2).
b) r1r2 (Concatenation of r1 and r2).
c) r1* (Closure of r1).



Solution:
r1+ r2 (Union of r1 and r2).


New States Old States
A B
Z1-  (x1,x1) (x2,x2)  Z2 (x3,x1)  Z3
Z2  (x2,x2) (x3.x2)  Z4 (x4,x3)  Z5
Z3  (x3,x1) (x3,x2)  Z4 (x3,x1)  Z3
Z4  (x3,x2) (x3,x2)  Z4 (x3,x3)  Z6
Z5+  (x4,x3) (x4,x2)  Z7 (x4,x1)  Z8
Z6+  (x3,x3) (x3,x2)  Z4 (x3,x1)  Z3
Z7+  (x4,x2) (x4,x2)  Z7 (x4,x3)  Z5
Z8+  (x4,x1) (x4,x2)  Z7 (x4,x1)  Z8















a




a Z2

+Z7



-Z1 b a
a
a



Z4 b
+x5 a

a


b b
Z3 a




b +Z6
b

+Z8




b





r1r2 (Concatenation of r1 and r2).

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