Can safe recursion be interpreted in light logic (2000) [6 citations — 1 self]
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Abstract:
We introduce a subalgebra BC of Bellantoni and Cook's safe-recursion function algebra BC. Functions of the subalgebra have safe arguments that are non-contractible (i.e nonduplicable). We propose a denition of safe and normal variables in Light Ane Logic (LAL), and show that BC is the largest subalgebra that is interpretable in LAL, relative to that de nition. Though BC itself is not PTIME complete, there are extensions of it (by additional schemes for dening functions with safe arguments) that are, and are still interpretable in LAL and so preserve PTIME closure. We focus on one such which is BC augmented by a de nition-by-cases construct and a restricted form of denition-by-recursion scheme over safe arguments. As a corollary we obtain a new proof of the PTIME completeness of LAL. 1
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