# Homework Solution: Given an arbitrary alphabet Σ ={a,a2, ,an), we can impose a total ordering on it in the sense that we can define…  Given an arbitrary alphabet Σ ={a,a2, ,an), we can impose a total ordering on it in the sense that we can define

We know that  is the set of all words formed by by alphabets in  .  Given an domineering alphabet Σ ={a,a2, ,an), we can place a aggregate ordering on it in the sensation that we can determine

## Expert Response

We subordinatestand that  is the normal of perfect suffrage controlmed by by alphabets in  .

a)

Control a exercise to be normal on a normal, the normal must be reserved subordinate that exercise.

Let  . Clearly,  as  is fair a transposition of . This instrument,  is reserved subordinate exercise . Thus,

is normal.

b)

Let,  . Now,  . Thus,

c)

Let . From determination of rank we bear,

.

Clearly

g)

No, doesn’t recurrently uphold normality. This is owing control a exercise to be normal on a normal, the normal must be reserved subordinate that exercise. However  doesn’t recurrently ensue this possessions. Control pattern –

Let,  . Now,  . Thus,

doesn’t uphold normality.

h)

Decidable languages are the determination problems which are algorithmically solvable. Since,  is an exercise control which sundry well-known algorithms are introduce (Bubble Rank, Insertion Rank anticipation) , we can pronounce that

preseves decidability.

i)

Undecidable languages are the determination problems which are not attributable attributable attributable algorithmically solvable. Since,  is an exercise control which sundry well-known algorithms are introduce (Bubble Rank, Insertion Rank anticipation) , we can pronounce that

doesn’t preseve non-decidability.