Given a programming language operating on stacks, we introduce a syntactical measure mu such that, a natural number mu(P) is assigned to each program P. The measure considers how the presence of loops defined over size-increasing (and/or non-size-increasing) subprograms influences the complexity of the program itself. We prove that a generic function f computed by a stack program with mu-measure n has length bound b in E^(n+2) (the n + 2-th Grzegorczyk class), that is |f( w)| <= b(| w|). Thus, we have a syntactical characterization of the functions belonging to the Grzegorczyk hierarchy; this result represents an improvement with respect to previous similar results.

On the complexity of programs with nested loops

Emanuele Covino;Giovanni Pani
2019

Abstract

Given a programming language operating on stacks, we introduce a syntactical measure mu such that, a natural number mu(P) is assigned to each program P. The measure considers how the presence of loops defined over size-increasing (and/or non-size-increasing) subprograms influences the complexity of the program itself. We prove that a generic function f computed by a stack program with mu-measure n has length bound b in E^(n+2) (the n + 2-th Grzegorczyk class), that is |f( w)| <= b(| w|). Thus, we have a syntactical characterization of the functions belonging to the Grzegorczyk hierarchy; this result represents an improvement with respect to previous similar results.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/237038
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