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The Complexity of Resolution with Generalized Symmetry Rules

Stefan Szeider
2005 Theory of Computing Systems  
Abstract We generalize Krishnamurthy's well-studied symmetry rule for resolution systems by considering homomorphisms instead of symmetries; symmetries are injective maps of literals which preserve complements  ...  Finally, we obtain an exponential lower bound for the resolution system enhanced by the local homomorphism rule.  ...  This yields immediately an exponential separation of dynamic rules from their "static" variants. The complexities of resolution systems with dynamic rules remain open.  ... 
doi:10.1007/s00224-004-1192-0 fatcat:dqmy6qrixnb7tnyszw7qaugqsm

The Complexity of Resolution with Generalized Symmetry Rules [chapter]

Stefan Szeider
2003 Lecture Notes in Computer Science  
S. (2005) 'The complexity of resolution with generalized symmetry rules.', Theory of computing systems., 38 (2). pp. 171-188. Further information on publisher's website: http://dx.  ...  Abstract We generalize Krishnamurthy's well-studied symmetry rule for resolution systems by considering homomorphisms instead of symmetries; symmetries are injective maps of literals which preserve complements  ...  This yields immediately an exponential separation of dynamic rules from their "static" variants. The complexities of resolution systems with dynamic rules remain open.  ... 
doi:10.1007/3-540-36494-3_42 fatcat:mrhkxexihbdszczec4dcqefvqm

On the Complexity of Extending Ground Resolution with Symmetry Rules

Thierry Boy de la Tour, Stéphane Demri
1995 International Joint Conference on Artificial Intelligence  
One important issue of automated theorem proving is the complexity of the inference rules used in theorem provers.  ...  But this general rule can be simplified by restricting it to what we call 5symmetries, yielding the well-known symmetry rule.  ...  Hence representation matrices are not only useful for proving complexity results, as done above, but also for implementing extensions of resolution with the symmetry rule.  ... 
dblp:conf/ijcai/TourD95 fatcat:3hnrdyerijf6paztys5k4fdw2i

Page 627 of The Journal of Chemical Physics Vol. 21, Issue 4 [page]

1953 The Journal of Chemical Physics  
Since the LSC for reactions involving nonlinear complexes will in general be of a rather low symmetry," it is evident that the orbital electronic correlation rules do not play as im- portant a role in  ...  for point groups of lower symmetry by resolution from point groups of higher symmetry are independent of the path of the resolution; the correlating species of the LSC obtained by the direct resolution  ... 

Local Symmetries in Propositional Logic [chapter]

Noriko H. Arai, Alasdair Urquhart
2000 Lecture Notes in Computer Science  
Examples are exhibited in which resolution with the global symmetry rule has an exponential speed-up with respect to the cutting plane refutation system.  ...  In the context of resolution, the rule enables the shortening of refutations by using symmetries present in an initial set of clauses. These symmetries can be local or global.  ...  The symmetry rule can also be generalized in another direction.  ... 
doi:10.1007/10722086_3 fatcat:daicfvl26fazxidevd7eqojkvy

The symmetry rule in propositional logic

Alasdair Urquhart
1999 Discrete Applied Mathematics  
The addition of the symmetry rule to the resolution system sometimes allows considerable shortening in the length of refutations.  ...  We prove exponential lower bounds on the size of resolution refutations using two forms of a global symmetry rule.  ...  Acknowledgements The author gratefully acknowledges the support of the National Sciences and Engineering Research Council of Canada.  ... 
doi:10.1016/s0166-218x(99)00039-6 fatcat:kdogbbz7wjhfhgykzstqxsicei

Crystallography online by the Bilbao Crystallographic Server

Gemma De La Flor Martin, Emre Tasci, Luis Elcoro, Samuel Vidal, Gotzon Madariaga, Juan Manuel Perez-Mato, Mois I. Aroyo
2017 Acta Crystallographica Section A: Foundations and Advances  
Recently, due to the interest in the study of materials with diperiodic symmetry (layer and multilayer), new databases and tools have been developed to study this type of systems.  ...  In this section one can find very useful programs to calculate the selection rules of these processes and the polarization selection rules for different configurations of the scattering experiment.  ...  Recently, due to the interest in the study of materials with diperiodic symmetry (layer and multilayer), new databases and tools have been developed to study this type of systems.  ... 
doi:10.1107/s2053273317094359 fatcat:arnj5jad4jgvhozpnlgl235w74

Non-chiral fusion rules, structure constants of D_m minimal models [article]

A. Rida, T. Sami (SUBATECH, Ecole des Mines de Nantes, France.)
1999 arXiv   pre-print
Through this approach we emphasize the role played by some discrete symmetries in the classification of minimal models.  ...  Using these rules we solve the bootstrap equations and therefore determine the structure constants of these models.  ...  The Z 2 symmetry structure of the fusion rules in the real basis is manifested by the complex Z 3 symmetry in the new complex basis (52).  ... 
arXiv:hep-th/9910070v1 fatcat:j6ofxu5xujdytiexgqeuaeuy6y

A cognitive view of biological process

B GOODWIN
1978 Journal of Social and Biological Systems  
Such generative processes appear to have the property of proceeding from symmetry to asymmetry, which involves an increase in complexity; but then a new symmetry is generated which resolves the complexity  ...  Knowledge comes through the resolution of complication into greater and greater simplicity and the art of resolution is the art of life.  ... 
doi:10.1016/s0140-1750(78)80001-3 fatcat:rqix26dylbfl7pu3bwfked7inu

Page 661 of The Journal of Chemical Physics Vol. 29, Issue 3 [page]

1958 The Journal of Chemical Physics  
SELECTION RULES FOR OCTAHEDRAL COMPLEXES One of the main purposes of this section is to illu- strate a general method for obtaining the irredicuible representations to which functions belong which appear  ...  A general method for finding the irreducible repre- sentations in the expansion of V,, will be illustrated for octabedral complexes.  ... 

Complex Filters Applied to Fingerprint Images Detecting Prominent Symmetry Points Used for Alignment [chapter]

Kenneth Nilsson, Josef Bigun
2002 Lecture Notes in Computer Science  
Complex filters, applied to the orientation field in multiple resolution scales, are used to detect the symmetry and the type of symmetry. Experimental results are reported.  ...  For the alignment of two fingerprints position of certain landmarks are needed. These should be automatically extracted with low misidentification rate.  ...  Acknowledgment This work has been possible by support from the Swedish national SSF-program VISIT.  ... 
doi:10.1007/3-540-47917-1_5 fatcat:hkfbj25anrhonjihfbjrbnitla

Growing and Evolving Soft Robots

John Rieffel, Davis Knox, Schuyler Smith, Barry Trimmer
2014 Artificial Life  
In the second, the material properties of a simulated soft body coevolve alongside locomotive gaits, with body shape and muscle placement fixed.  ...  In the first, muscle placement and firing patterns are coevolved for a fixed body shape with fixed material properties.  ...  Acknowledgments This work was supported in part by the US Defense Advanced Research Project Agency under Grant W911SR08-C-0012 (ChemBots) and by the US National Science Foundation IOS-7045912 to Barry  ... 
doi:10.1162/artl_a_00101 pmid:23373976 fatcat:syie25goi5b63nf2kevjpax2pu

Page 299 of Applied Physics. A and B Vol. B48, Issue 4 [page]

1989 Applied Physics. A and B  
Equally impor- tant features are the complexity of the vibro-rotational spectra and the fairly large permanent components of the electric dipole moment along the quasi-symmetry axis (||) and orthogonal  ...  The main reason for its success as a laser source is the excellent overlap of the strong absorbing C—O stretch mode with the CO, laser emission generally used as a pump source.  ... 

Page 9691 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
Recall that, if Ye is the category of complex varieties (reduced, separated scheme of finite type over C), the Grothendieck ring of complex varieties Ko(%c) is simply the ring generated by symbols [X]  ...  It is shown there that the resultant of p and q with respect to s gives the implicit equation 2004m: 1 4079 of the rational ruled surface; however, the parametric equation P(s,t) of the rational ruled  ... 

Structure of theNeisseria meningitidisOuter Membrane PilQ Secretin Complex at 12 Å Resolution

Richard F. Collins, Stephan A. Frye, Ashraf Kitmitto, Robert C. Ford, Tone Tønjum, Jeremy P. Derrick
2004 Journal of Biological Chemistry  
Three-dimensional structure of PilQ at 12 Å resolution. A, surface-rendered side, top, and bottom views of the PilQ complex with C4 symmetry applied.  ...  Analysis of the complex using selforientation and by examination of two-dimensional crystals indicates a strong C4 rotational symmetry, with a much weaker C12 rotational symmetry, consistent with PilQ  ... 
doi:10.1074/jbc.m405971200 pmid:15254043 fatcat:ipif4lulpvc6rkapccyn7hr3by
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