# 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: Allow sigma = {a, b, c} and allow L be the phraseology aggravate sigma fond 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) Argue your vindication to the anterior multiply is improve. (iii) Find a periodical countenance E such that L(E) = L (you demand referable argue your vindication is improve).

## Expert Vindication

Solution:

i) ii)

I keep ran various strings to validate the fsa; keep a look     iii)

The periodical countenance restraint fond phraseology is supposing adown,

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