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in automata, a*(a+b)* is equivalent to (i).a*+b* (ii).(ab)* (iii).a*b* (iv).none of these
sourav
on 2012-06-09 09:30:00i>. a* + b*
Deepanwita
on 2012-06-09 09:30:00the {star} is the Kleene star. the character replicated any number of times including null; the plus signifies OR. Now. expression in question is the character a repeated n-times followed by either a or b m-times. for example all the strings are all accepted aa aaa aaabb aaabba ababa bbb etc. Option1 means the string of a and b where a is repeated n-times or b is repeated m-times. but not both. so aa aaa bbbb b a are all accepted, but aba is not. Option2 is the string where ab is replicated n-times. for example ab abab ababab etc. Option3 is the string of a,b where a is replicated n-times followed by b m-times. here after a 'b' no 'a' can come. for example aabbb aa bb abbb etc, but aba is not accepted. So. in conclusion the given expression is equivalent to (a + b)*. and hence the answer to the question is option-iv. I have used m,n to indicate real positive integer numbers;