On the constructive orbit problem

Donaldson, A. and Miller, A. (2009) On the constructive orbit problem. Annals of Mathematics and Artificial Intelligence, 57(1), pp. 1-35. (doi:10.1007/s10472-009-9171-4)

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Publisher's URL: http://www.springerlink.com/content/f1417440502897l6/


Symmetry reduction techniques aim to combat the state-space explosion problem for model checking by restricting search to representative states from equivalence classes with respect to a group of symmetries. The standard approach to representative computation involves converting a state to its minimal image under a permutation group G, before storing the state. This is known as the Constructive orbit problem (COP), and is NP hard. It may be possible to solve the COP efficiently if G is known to have certain structural properties: in particular if G is isomorphic to a full symmetry group, or G is a disjoint/wreath product of subgroups. We extend existing results on solving the COP efficiently for fully symmetric groups, and investigate the problem of automatically classifying an arbitrary permutation group as a disjoint/wreath product of subgroups. We also present an approximate COP strategy based on local search, and some computational group-theoretic optimisations to improve the basic approach of solving the COP by symmetry group enumeration. Experimental results using the \topspin\ symmetry reduction package, which interfaces with the computational group-theoretic system GAP, illustrate the effectiveness of our techniques.

Item Type:Articles
Additional Information:From the issue entitled "Special Issue Title: Symmetry and Search / Guest Edited by Ian Gent and Tom Kelsey"
Glasgow Author(s) Enlighten ID:Miller, Dr Alice
Authors: Donaldson, A., and Miller, A.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Annals of Mathematics and Artificial Intelligence
Journal Abbr.:Ann. math. artif. intell.
ISSN (Online):1573-7470|

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