How to design a PDA that accepts the complement of L?

It depends on the type of PDA that you are constructing. DPDA (deterministic pushdown automaton) recognizes a subset of context-free languages called deterministic context-free languages. The class of DCFL's is closed under complement. read more

The class of DCFL's is closed under complement. The class of non-deterministic context free languages is not closed under complement. So let us assume that the PDA you are talking about is the deterministic version. read more

There are two different ways to define PDA acceptability. Final State Acceptability. In final state acceptability, a PDA accepts a string when, after reading the entire string, the PDA is in a final state. From the starting state, we can make moves that end up in a final state with any stack values. read more

Lemma 3.4.1: given a grammar, construct a PDA and show the equivalence; Lemma 3.4.2: given a PDA, construct a grammar and show the equivalence; Of the two, the first uses a very simple, intuitive construction to achieve a mimick a leftmost derivation by using a PDA. The converse stepis far more complicated than the first. read more