PDA membership

Question

Answer 1

This is actually a decidability problem and hence can be redefined as :

Given a string and a PDA , whether a string belongs to language accepted by the PDA ..

                                        (or simply)

Membership property of CFL class of languages

So this property is decidable as we can membership algorithms for CFLs like CYK algo , LL(1) parsing algo and LR(1) parsing algorithms.

So since there is an algorithm to check the membership (acceptance) of string given a PDA or CFL , hence the problem is decidable..And this problem is depicted by language L as mentioned..Hence L is decidable and hence recursive as "recursive" and "decidable" are used synonymously..

Hence D) is the correct answer..