toc-reg

Question

 {a^mbⁿc^p|m+n+p>=10} Reg or not ?

Answer 1

Given :

L =  { a^mbⁿc^p | m + n + p >= 10 } 

Lets think about language L' as : {  a^mbⁿc^p | m + n + p < 10 }

Now this is clearly a finite language as there will be finite number of such <m,n,p> triplets..

Now let L'' = { a* b* c* }

Now clearly L = L'' - L'

Now as L'' and L' both are regular , hence L is also regular [ Also follows from closure property of regular languages]

Hence the given language is regular language..