Lucassen's Theorem is a result in the field of theoretical computer science, specifically concerning the complexity of certain decision problems. It provides a framework for understanding the relationship between randomized algorithms and deterministic algorithms, showing that if a problem can be solved efficiently with randomness, it can also be solved efficiently without it under certain conditions. The theorem is particularly significant in the study of complexity classes, as it helps to clarify the boundaries between P (problems solvable in polynomial time) and BPP (problems solvable in polynomial time with bounded error using randomness). This insight contributes to ongoing discussions about the power and limitations of different computational models.