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)

Abstract

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"
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Miller, Professor 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: 1012-2443
• ISSN (Online): 1573-7470|