Which of the following are decidable ?1. whether the intersection of two regular language is infinite.2. whether a give context free language is regular3. whether two push down automata accept the same language.4. whether a given grammar is context free

Automata theory (also known as Theory Of Computation) is a theoretical branch of Computer Science and Mathematics, which mainly deals with the logic of computation with respect to simple machines, referred to as automata. Automata* enables scientists to understand how machines compute the functions and solve problems.
Theory of Computation is very important in compiler design as it helps in writing efficient algorithms, which help make efficient compiler construcion.