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Rigorous specification early in the software development process can greatly reduce the cost of later development and maintenance, as well as provide an explicit means to manage risk and identify and meet safety requirements. Sequence-based software specification is a collection of techniques for implementing rigorous, practical software specification. The primary result of this research is the sequence enumeration method of specification writing. Straightforward, systematic enumeration of all sequences to produce an arguably complete, consistent, and traceably correct specification is made practical by controlling the growth of the process.