Define a two-headed finite automaton (2DFA) to be a deterministic finite automaton that has two read-only, bidirectional heads that start at the left-hand end of the input tape and can be independently controlled to move in either direction. The tape of a 2DFA is finite and is just large enough to contain the input plus two additional blank tape cells, one on the left-hand end and one on the right-hand end, that serve as delimiters. A 2DFA accepts its input by entering a special accept state. For example, a 2DFA can recognize the language {aⁿbⁿcⁿ| n ≥ 0}.

a. Let A_2DFA = {〈M, x〉| M is a 2DFA and M accepts x}. Show that A_2DFA is decidable.

b. Let E_2DFA = {〈M〉| M is a 2DFA and L(M) = ⌀}. Show that E2DFA is not decidable.