Recursion Schemata for Slowly Growing Depth Circuit Classes

Kuroda, Satoru

doi:10.1007/s00037-004-0184-4

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As above, we use the mutual version of these recursion schemes, with the same tiering discipline. Note that, unlike previous characterizations of sub-polynomial complexity classes [3,4,10], our tropical composition and recursion schemes are only syntactical refinements of the usual composition and primitive recursion schemes -removing the syntactical sugar yields indeed the classical schemes.…”

Section: Tropical Recursionmentioning

confidence: 90%

“…Later on, Bellantoni and Cook's purely syntactical approach proved also useful for characterizing other complexity classes. Leivant and Marion [14,13] used a predicative version of the safe recursion scheme to characterize alternating complexity classes, while Bloch [3], Bonfante et al [4] and Kuroda [10], gave characterizations of small, polylogtime, parallel complexity classes. An important feature of these results is that they use, either explicitly or not, a tree-recursion on the input.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Pointers in Recursion: Exploring the Tropics

Naurois

2019

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tiering is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras. *

show abstract

Section: Tropical Recursionmentioning

confidence: 90%