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Asymptotic Enumeration of Predicate-Junction Flowgraphs

Published online by Cambridge University Press:  12 September 2008

C. Cooper
C. Cooper
Affiliation:
School of Mathematical Sciences, University of North London, London N7 8DB, UK
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Abstract

We consider unlabelled flowgraphs for a model of binary logic without the constraints of structured programming. The number of such flowgraphs is asymptotic to (3.4n)n/2, where n is the number of nodes in the flowgraph. This is to be compared with bounds of between (8.8)n/2 and of (9.8)n/2 for unlabelled structured flowgraphs of the Böhm and Jacopini type. Of the space of flowgraphs we study, 41% are prime, that is contain no proper sub-flowgraphs. The main obstructions to primality being the Dijkstra-structures, which are based on If_Then_Else and Do_While constructs.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 3 , September 1996 , pp. 215 - 226
Copyright
Copyright © Cambridge University Press 1996

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