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An algebra and a logic for \(NC^ 1\). (English) Zbl 0717.68032
This paper, which appeared in an earlier version K. Compton and C. Laflamme [A logic and an Algebra for \(NC^ 1\) in: Proc. 3rd Annual Conference on Logic in Computer Science, (1988; Washington (IEEE Computer Society Press)], presents an algebra and a logic characterizing the complexity class \(NC^ 1\). In the algebraic characterization a recursion scheme called upward tree recursion is applied to a class of simple functions. In the logical characterization, first-order logic is augmented by an operator for defining relations by primitive recursion provided that every structure has a relation giving the binary representations of integers.
Reviewer: E.Heinrich

MSC:
68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
03D15 Complexity of computation (including implicit computational complexity)
03C99 Model theory
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