Question

Show that if P is a PDA, then there is a PDA P2 with only two stack symbols, such that L(P 2):

a) Equals L(P)
b) Is a proper subset of L(P)
c) Is a proper superset of L(P)
d) Has no relation to L(P)

Answer 1

To show that if P is a PDA, there is a PDA P2 with only two stack symbols. The process involves converting P to an equivalent deterministic PDA and modifying its transitions to use only two stack symbols.

Step-by-step explanation:

In order to show that if P is a PDA (Pushdown Automaton), then there is another PDA P2 with only two stack symbols, we first need to understand the concept of equivalence between PDAs.

A PDA P is said to be equivalent to a PDA Q if and only if both P and Q accept the same language. So, to show that there is a PDA P2 with only two stack symbols, we need to show that it accepts the same language as P.

Here is a step-by-step process to construct the PDA P2 using P:

1. Convert the PDA P into an equivalent deterministic PDA, say DP, using the subset construction algorithm.
2. Now, create a new PDA P2 with only two stack symbols, say 1 and z.
3. Modify the transitions of P2 as follows:

This process ensures that the resulting PDA P2 accepts the same language as the original PDA P, but with only two stack symbols - 1 and z.