gateforum test series

Question

Given a finite automata M, is it the minimum state FA accepting L(M)

is this problem decidable, if yes then why?

Comments

yes it is decidable, 

An algorithm like that:

check if two states are equal or not , if you find any two states are equal then it says yes else no.

If you can find the Algorithm for any problem to solve then TM can also solve that problem.

Answer 1

All the properties of Regular Languages and Finite Automata are decidable and algorithms possible.

Your question falls in the category of membership problem of regular languages, which is decidable.