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Random Mapping Statistics
 IN ADVANCES IN CRYPTOLOGY
, 1990
"... Random mappings from a finite set into itself are either a heuristic or an exact model for a variety of applications in random number generation, computational number theory, cryptography, and the analysis of algorithms at large. This paper introduces a general framework in which the analysis of ..."
Abstract

Cited by 78 (6 self)
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Random mappings from a finite set into itself are either a heuristic or an exact model for a variety of applications in random number generation, computational number theory, cryptography, and the analysis of algorithms at large. This paper introduces a general framework in which the analysis of about twenty characteristic parameters of random mappings is carried out: These parameters are studied systematically through the use of generating functions and singularity analysis. In particular, an open problem of Knuth is solved, namely that of finding the expected diameter of a random mapping. The same approach is applicable to a larger class of discrete combinatorial models and possibilities of automated analysis using symbolic manipulation systems ("computer algebra") are also briefly discussed.
LambdaUpsilonOmega  The 1989 Cookbook
, 1989
"... LambdaUpsilonOmega ( \Upsilon\Omega ) is a research tool designed to assist the average case analysis of some well defined classes of algorithms and data structures. This cookbook consists of an informal introduction to the system together with eighteen examples of programmes that are automatica ..."
Abstract

Cited by 15 (6 self)
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LambdaUpsilonOmega ( \Upsilon\Omega ) is a research tool designed to assist the average case analysis of some well defined classes of algorithms and data structures. This cookbook consists of an informal introduction to the system together with eighteen examples of programmes that are automatically analyzed. Amongst the applications treated here, we find: addition chains, quantitative concurrency analysis of simple systems, symbolic manipulation algorithms such as formal differentiation, simplification and rewriting systems, as well as combinatorial models including various tree and permutation statistics and functional graphs with applications to integer factorisation.