Sequenceor

Sequenceor is a term used in mathematics and computer science to denote an operator or function that takes a sequence as input and produces another sequence as output. In its broad sense, a sequenceor can be viewed as a rule or device that transforms, filters, augments, or otherwise reinterprets the elements of a sequence.

Formally, a sequenceor can be described as a unary sequence-to-sequence transformation F that maps sequences over a base domain D to sequences over a base codomain E (F: D* -> E*). In practice, sequenceors are implemented as functions, finite-state transducers, or streaming pipelines. They may be classified by properties such as determinism, locality (whether the output at position i depends only on a fixed window of input positions), and whether they preserve length, order, or certain structural aspects of the input sequence.

Examples of sequenceors include: a mapping that replaces each element with a function of itself and a fixed offset; an operator that removes consecutive duplicates; an operator that outputs the running sum of elements; a transformer that outputs the first element of each length-k window; and a projection that selects every nth element. More complex sequenceors can combine multiple steps, such as filtering followed by mapping.

Variants and implementation notes: sequenceors can be deterministic or nondeterministic, finite-state or context-sensitive, and suitable for streaming or batch processing. In practice, they appear in areas such as data processing, formal language theory, and algorithm design, where sequence-level transformations are common.

See also: sequence, operator, morphism, transducer, automaton, data stream processing.

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