Abstract
Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call the complexity approach space, the space of all functions in X = ]0, ∞ ]Y, where Y can be a more dimensional input space. The set X, which is a dcpo for the pointwise order, moreover carries the complexity approach structure. There is an associated selfmap Φ on the complexity approach space X such that the problem of solving the recurrence equation is reduced to finding a fixed point for Φ. We will prove a general fixed point theorem that relies on the presence of the limit operator of the complexity approach space X and on a given well founded relation on Y. Our fixed point theorem deals with monotone selfmaps Φ that need not be contractive. We formulate conditions describing a class of recursive algorithms that can be treated in this way.
Published Version
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