Conscriptions are a model of sequential computations with assumption/commitment specifications in which assumptions can refer to final states, not just to initial states. We show that they instantiate existing algebras for iteration and infinite computations. We use these algebras to derive an approximation order for conscriptions and one for extended conscriptions, which additionally represent aborting executions. We give a new computation model which generalises extended conscriptions and apply the algebraic techniques for a unified treatment.
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