Design a PDA that accepts the language \(\{a^nb^n : n > 0\}\). Test your transition function’s completeness by ensuring that it correctly accepts or rejects each of the following strings: \[ ab, aabb, aa, b, ba, aab, baa, \epsilon \] Write the transition function as a 6-column table with columns, including state, tape, and stack inputs and state, advance, and stack string outputs.
Give a sketch of a proof that all regular languages are context-free by describing how to construct a PDA that accepts the same language as a given NFA.