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Sequential Sampling for Binary Sequences

Constrained binary sequences arise in problems of regulatory networks, social networks, and random permutations. Sampling from sets of sequences can sometimes be done with sequential methods. Sequential sampling methods break down the problem of feasibility to local computations as do Markov chains, but give independent, identically distributed outcomes that need a reweighting correction. We will show one example where most of the computational work can be done algebraically with a Groebner basis over a finite field before sampling, which we call the retrospective method, and another example where numerical methods are used intensively during sampling, which we call the prospective method.