Analyze the relationship between different models of computation including Turing machines, lambda calculus, and recursive functions. Demonstrate their equivalence through constructive proofs. Discuss the Church-Turing thesis and its implications for computational theory. Examine the limits of computation through undecidable problems, using the Halting Problem as a primary example. Discuss complexity classes and the P vs NP problem, providing formal definitions of each major complexity class and explaining their relationships.