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Primitive recursion in the abstract. (English) Zbl 1435.68064
Summary: Recurrence can be used as a function definition schema for any nontrivial free algebra, yielding the same computational complexity in all cases. We show that primitive-recursive computing is in fact independent of free algebras altogether, and can be characterized by a generic programming principle, namely the control of iteration by the depletion of finite components of the underlying structure.
MSC:
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
03C13 Model theory of finite structures
03D75 Abstract and axiomatic computability and recursion theory
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