# Correcting a space-efficient simulation algorithm

## Authors

Rob van Glabbeek and Bas Ploeger

NICTA

UNSW

Eindhoven University of Technology

## Abstract

Although there are many efficient algorithms for calculating the simulation preorder on finite Kripke structures, only two have been proposed of which the space complexity is of the same order as the size of the output of the algorithm. Of these, the one with the best time complexity exploits the representation of the simulation problem as a generalised coarsest partition problem. It is based on a fixed-point operator for obtaining a generalised coarsest partition as the limit of a sequence of partition pairs. We show that this fixed-point theory is flawed, and that the algorithm is incorrect. Although we do not see how the fixed-point operator can be repaired, we correct the algorithm without affecting its space and time complexity.

## BibTeX Entry

@inproceedings{vanGlabbeek_Ploeger_08,
publisher = {Springer},
booktitle = {Proceedings of the 20th International Conference on Computer Aided Verification},
month = jul,
issn = {0302-9743},
paperurl = {https://trustworthy.systems/publications/nicta_full_text/156.pdf},
year = {2008},
editor = {{A. Gupta \& S. Malik}},
keywords = {concurrency, verification, algorithms, time and space complexity, simulation preorder, kripke
structures, generalised coarsest partition problem.},
title = {Correcting a Space-Efficient Simulation Algorithm},
pages = {517--529},
author = {van Glabbeek, Robert and Ploeger, Bas},
address = {Princeton, USA}
}

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