  Classical programming languages cannot model essential elements of complex
systems such as true random number generation. This paper develops a formal
programming language called the lambda-q calculus that addresses the
fundamental properties of complex systems. This formal language allows the
expression of quantumized algorithms, which are extensions of randomized
algorithms in that probabilities can be negative, and events can cancel out. An
illustration of the power of quantumized algorithms is the ability to
efficiently solve the satisfiability problem, something that many believe is
beyond the capability of classical computers. This paper proves that the
lambda-q calculus is not only capable of solving satisfiability but can also
simulate such complex systems as quantum computers. Since satisfiability is
believed to be beyond the capabilities of quantum computers, the lambda-q
calculus may be strictly stronger.
