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  1. Plain Bases for Classes of Primitive Recursive Functions.Stefano Mazzanti - 2002 - Mathematical Logic Quarterly 48 (1):93-104.
    A basis for a set C of functions on natural numbers is a set F of functions such that C is the closure with respect to substitution of the projection functions and the functions in F. This paper introduces three new bases, comprehending only common functions, for the Grzegorczyk classes ℰ_n with n ≥ 3. Such results are then applied in order to show that ℰ_{n+1} = K_n for n ≥ 2, where {K_n}n∈ℕ is the Axt hierarchy.
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  • Control structures in programs and computational complexity.Karl-Heinz Niggl - 2005 - Annals of Pure and Applied Logic 133 (1-3):247-273.
    A key problem in implicit complexity is to analyse the impact on program run times of nesting control structures, such as recursion in all finite types in functional languages or for-do statements in imperative languages.Three types of programs are studied. One type of program can only use ground type recursion. Another is concerned with imperative programs: ordinary loop programs and stack programs. Programs of the third type can use higher type recursion on notation as in functional programming languages.The present approach (...)
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