Asymptotic Resource Usage Bounds

When describing the resource usage of a program, it is usual to talk in asymptotic terms, such as the well-known “big O” notation, whereby we focus on the behaviour of the program for large input data and make a rough approximation by considering as equivalent programs whose resource usage grows at the same rate. Motivated by the existence of non-asymptotic resource usage analyzers, in this paper, we develop a novel transformation from a non-asymptotic cost function (which can be produced by multiple resource analyzers) into its asymptotic form. Our transformation aims at producing tight asymptotic forms which do not contain redundant subexpressions (i.e., expressions asymptotically subsumed by others). Interestingly, we integrate our transformation at the heart of a cost analyzer to generate asymptotic upper bounds without having to first compute their non-asymptotic counterparts. Our experimental results show that, while non-asymptotic cost functions become very complex, their a...

• Type: Conference
• Year: 2009
• Where: APLAS
• Authors: Elvira Albert, Diego Alonso, Puri Arenas, Samir Genaim, German Puebla
• Keywords: APLAS 2009, Asymptotic Forms, Non-asymptotic Cost Functions, Programming Languages, Resource Usage