Linear Ramified Higher Type Recursion and Parallel Complexity
PTCS '01 Proceedings of the International Seminar on Proof Theory in Computer Science
Applicative Control and Computational Complexity
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Separating NC along the δ axis
Theoretical Computer Science - Implicit computational complexity
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
A characterization of NCk by first order functional programs
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A characterization of alternating log time by first order functional programs
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Towards an implicit characterization of NCk
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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We show that a boolean valued function is in NC iff it is defined by ramified schematic recurrence over trees. This machine-independent characterization uses no initial functions other than basic tree operations, and no bounding conditions on the recurrence.Aside from its technical interest, our result evidences the foundational nature of NC, thereby illustrating the merits of implicit (i.e. machine independent) computational complexity theory.