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Automatic Symmetry Detection for Model Checking Using Computational Group Theory [chapter]

A. F. Donaldson, A. Miller
2005 Lecture Notes in Computer Science  
This group can then be used for symmetry reduction during model checking using existing quotient-based methods.  ...  We present an automatic technique for the detection of structural symmetry in a model directly from its Promela specification.  ...  Acknowledgments The authors would like to thank Simon Gay, Warwick Harvey and Colva Roney-Dougal for their useful comments on this work.  ... 
doi:10.1007/11526841_32 fatcat:vytl422rrfcapc3v5paairw7d4

A Computational Group Theoretic Symmetry Reduction Package for the Spin Model Checker [chapter]

Alastair F. Donaldson, Alice Miller
2006 Lecture Notes in Computer Science  
We present TopSPIN, a fully automatic symmetry reduction package for the SPIN model checker.  ...  TopSPIN uses the GAP computational algebra system to effectively detect state space symmetry from the associated Promela specification, and to choose an efficient symmetry reduction strategy by classifying  ...  TopSPIN uses GAP to compute, from the set of valid generators, the largest group G ≤ Aut(SCD) which can be safely used for symmetry-reduced model checking.  ... 
doi:10.1007/11784180_29 fatcat:v6bpcc4rfve5tia2uv7o3vxhea

Computational Symmetry [chapter]

Yanxi Liu
2014 Computer Vision  
The introduction of computers poses challenging tasks for machine representation and reasoning about symmetry and group theory.  ...  We demonstrate, through three concrete applications, the power, the difficulties and feasibility of using symmetry and group theory on computers.  ...  It is the goal of this research to construct a computational model for periodic pattern perception and analysis based on the theory of crystallographic groups.  ... 
doi:10.1007/978-0-387-31439-6_640 fatcat:jqjxxpnszngu3azp2p67w566p4

Exact and Approximate Strategies for Symmetry Reduction in Model Checking [chapter]

Alastair F. Donaldson, Alice Miller
2006 Lecture Notes in Computer Science  
We show how computational group theoretic techniques can be used to analyse the structure of a symmetry group so that an appropriate symmetry reduction strategy can be chosen, and we describe a symmetry  ...  reduction package for the SPIN model checker which interfaces with the computational algebra system GAP.  ...  TopSPIN uses GAP to compute, from the set of valid generators, the largest group G ≤ Aut(SCD) which can be safely used for symmetry-reduced model checking.  ... 
doi:10.1007/11813040_36 fatcat:ofosrj2a45da5eu4yorhz2egoq

Automatic Symmetry Detection for Promela

Alastair F. Donaldson, Alice Miller
2008 Journal of automated reasoning  
We extend our approach to Promela and introduce a tool, SymmExtractor, for automatically detecting symmetries of Promela specifications.  ...  We show how we can detect symmetry in specifications defined in Promela-lite by constructing a directed, coloured bipartite digraph called a static channel diagram, and applying computational group theoretic  ...  Acknowledgements We would like to thank Simon Gay for his advice concerning the type theoretic aspects of this work, and the anonymous referees for their valuable suggestions towards improving this paper  ... 
doi:10.1007/s10817-008-9107-4 fatcat:cpj74do3dzgffj735pm7xz6yea

Replication and Abstraction: Symmetry in Automated Formal Verification

Thomas Wahl, Alastair Donaldson
2010 Symmetry  
This article surveys fundamental and applied aspects of symmetry in system models, and of symmetry reduction methods used to counter state explosion in model checking, an automated formal verification  ...  Theorem 5 ([19]) Let M be a Kripke structure symmetric with respect to a group G. The quotient Kripke structureM , derived from the orbit relation, is bisimilar to M .  ...  The authors would like to thank David Parker for his comments on symmetry reduction in PRISM.  ... 
doi:10.3390/sym2020799 fatcat:q4mcwtywq5bgla4e5u4dfu6iii

Constraint-based automatic symmetry detection

Shao Jie Zhang, Jun Sun, Chengnian Sun, Yang Liu, Junwei Ma, Jin Song Dong
2013 2013 28th IEEE/ACM International Conference on Automated Software Engineering (ASE)  
We present an automatic approach to detecting symmetry relations for general concurrent models.  ...  To the best of our knowledge, our method is the first approach that can automatically detect both process and data symmetries as demonstrated via a number of systems.  ...  Acknowledgements We thank the anonymous reviewers for their invaluable comments.  ... 
doi:10.1109/ase.2013.6693062 dblp:conf/kbse/Zhang0SLMD13 fatcat:qkmutrv5q5anvpf2i55cyr7lwa

A template-based approach for the generation of abstractable and reducible models of featured networks

A. Miller, M. Calder, A.F. Donaldson
2007 Computer Networks  
Due to the open symmetry of our Promela specifications, this group of permutations can be used directly for symmetry reduced model checking.  ...  detection and reduction in the context of model checking featured networks.  ...  Acknowledgements The first and third authors would like to thank the Glasgow University John Robertson Bequest and the Carnegie Trust for funding this research.  ... 
doi:10.1016/j.comnet.2006.08.009 fatcat:itzdvz4zi5b5fadufojscwjkl4

Accurate detection of symmetries in 3D shapes

Aurélien Martinet, Cyril Soler, Nicolas Holzschuch, François X. Sillion
2006 ACM Transactions on Graphics  
The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its subparts  ...  We propose an automatic method for finding symmetries of 3D shapes, that is, isometric transforms which leave a shape globally unchanged.  ...  This method is based on a graph representation of a solid model and uses graph theory.  ... 
doi:10.1145/1138450.1138462 fatcat:fi3jqpkx3rbgdhno4kvui764pq

Regular Symmetry Patterns [chapter]

Anthony W. Lin, Truong Khanh Nguyen, Philipp Rümmer, Jun Sun
2015 Lecture Notes in Computer Science  
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking.  ...  Gries's coffee can problem), our technique automatically synthesises a safety-preserving finite approximant, which can then be verified for safety solely using a finite-state model checker.  ...  We thank Marty Weissman for a fruitful discussion.  ... 
doi:10.1007/978-3-662-49122-5_22 fatcat:bgkkbmyrdvanbbndngjymjkvhu

A computational model for periodic pattern perception based on frieze and wallpaper groups

Yanxi Liu, R.T. Collins, Y. Tsin
2004 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups.  ...  We also extend this computational model for near-periodic patterns using geometric AIC.  ...  ACKNOWLEDGMENTS This work is supported in part by the US National Science Foundation grants IIS-0099597, IIS-0208965, and ONR N00014-00-1-0915.  ... 
doi:10.1109/tpami.2004.1262332 pmid:15376882 fatcat:3xhaufaheveaxdoy4gfsz67kvu

Periodic Pattern Analysis under Affine Distortions Using Wallpaper Groups [chapter]

Yanxi Liu, Robert T. Collins
2000 Lecture Notes in Computer Science  
In this paper, the mathematical theory of wallpaper groups is used to construct a computational tool for symmetry analysis of periodic patterns.  ...  Starting with a novel peak detection algorithm based on regions of dominance", an input periodic pattern can be automatically classi ed into one of the 17 wallpaper groups.  ...  Our work, initially inspired by 7 , appears to be the rst to use the theory of frieze and wallpaper groups for automated analysis of periodic patterns, although there exist owcharts and computer programs  ... 
doi:10.1007/10722492_18 fatcat:kjztdgg66vgynomblnxwxoj7xq

Gossiping Girls Are All Alike [chapter]

Theo C. Ruys, Pim Kars
2012 Lecture Notes in Computer Science  
The highly symmetric nature of the problem is exploited using plain promela, topspin (an extension to Spin for symmetry reduction), and by connecting Spin to bliss (a tool to compute canonical representations  ...  The model checker Spin is used to compare the consequences of the various modelling choices.  ...  Acknowledgements We would like to thank Arend Rensink for providing us with the groove models of the gossiping girls problem and with his assistance in running groove.  ... 
doi:10.1007/978-3-642-31759-0_10 fatcat:gnfn224zhzh5bopt4b6eqj2yii

Generic SBDD Using Computational Group Theory [chapter]

Ian P. Gent, Warwick Harvey, Tom Kelsey, Steve Linton
2003 Lecture Notes in Computer Science  
It can be used for any symmetry group arising in a constraint program.  ...  We introduce a novel approach for symmetry breaking by dominance detection (SBDD).  ...  Acknowledgements We are very grateful for their helpful comments and other assistance to Iain McDonald, Karen Petrie, Barbara Smith and Toby Walsh.  ... 
doi:10.1007/978-3-540-45193-8_23 fatcat:kfzhkl2p4fb2hke2gtcxchcthm

Computational Symmetry in Computer Vision and Computer Graphics

Yanxi Liu
2008 Foundations and Trends in Computer Graphics and Vision  
Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences.  ...  The recent resurging interests in computational symmetry for computer vision and computer graphics applications have shown promising results.  ...  Thanks also go to Jingchen Liu, Kyle Brocklehurst, and Seungkyu Lee for collecting citations on symmetry related papers, and Jingchen Liu for creating Figure 1  ... 
doi:10.1561/0600000008 fatcat:t4x5zq3n5jcjnktzlft63eblnm
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