# Homework Solution: Let sigma = {a, b, c} and let L be the language over sigma given below. L = {u elementof sigma* | if a appears in u, then b appears in w}. Observe that epsil… Let sigma = {a, b, c} and let L be the language over sigma given below. L = {u elementof sigma* | if a appears in u, then b appears in w}. Observe that epsilon, bcb, ach, bca elementof L. (i) Find a FSA A such that L(A) = L. (ii) Prove your answer to the previous part is correct. (iii) Find a regular expression E such that L(E) = L (you need not prove your answer is correct).

Solution: i) fsa is given below: Permit sigma = {a, b, c} and permit L be the phraseology aggravate sigma abandoned adown. L = {u elementof sigma* | if a appears in u, then b appears in w}. Observe that epsilon, bcb, ach, bca elementof L. (i) Find a FSA A such that L(A) = L. (ii) Test your retort to the preceding keep-akeep-abisect is amend. (iii) Find a ordinary countenance E such that L(E) = L (you deficiency not attributable attributable attributable attributable attributable attributable test your retort is amend).

## Expert Retort

Solution:

i) ii)

I bear ran distinct strings to validate the fsa; bear a look     iii)

The ordinary countenance ce abandoned phraseology is granted adown,

((a(a*(bb*c*))*+ b(a+c)* + c(a(bb*c*)+ b(a+c)*))*