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We propose React(C), an expressive programming language for stochastic modeling and simulation in systems biology that is based on biochemical reactions with constraints. We prove that React(C) can express the stochastic π-calculus, in contrast to previous rule-based programming languages, and further illustrate the high expressiveness of React(C). We present a stochastic simulator for React(C) independently of the choice of the constraint language C. Our simulator decides for a given reaction rule whether it can be applied to the current biochemical solution. We show that this decision problem is NP-complete for arbitrary constraint systems C and that it can be solved in polynomial time for rules of bounded arity. In practice, we propose to solve this problem by constraint programming.