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…

    1, Let Σ = {a,b,c) and let L be the language over Σ given below. し= { u, E Σ* l if a appears in u, then b appears in w} Observe that ε, bcb, ach, bca E 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).
    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).

    Expert Answer

     
    Solution: i) fsa is given below:

    1, Permit Σ = {a,b,c) and permit L be the phraseology aggravate Σ abandoned adown. し= { u, E Σ* l if a appears in u, then b appears in w} Observe that ε, bcb, ach, bca E 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).

    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)

    fsa is abandoned adown:

    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)*))*