Invertible Polynomial Representation for Private Set Operations.
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Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this paper we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove that in this framework every recursive definition of a graph polynomial can be converted into a subset expansion formula.
Tutte polynomial
Chromatic polynomial
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Abstract Interpretation
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Lattice (music)
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Gröbner basis
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Representation
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Journal Article Graph Polynomials: From Recursive Definitions to Subset Expansion Formulas Get access B. Godlin, B. Godlin Department of Computer Science, Technion–Israel Institute of Technology, 32000 Haifa, Israel.E-mail: bgodlin@cs.technion.ac.il; emika@cs.technion.ac.il; janos@cs.technion.ac.il Search for other works by this author on: Oxford Academic Google Scholar E. Katz, E. Katz Department of Computer Science, Technion–Israel Institute of Technology, 32000 Haifa, Israel.E-mail: bgodlin@cs.technion.ac.il; emika@cs.technion.ac.il; janos@cs.technion.ac.il Search for other works by this author on: Oxford Academic Google Scholar J. A. Makowsky J. A. Makowsky Department of Computer Science, Technion–Israel Institute of Technology, 32000 Haifa, Israel.E-mail: bgodlin@cs.technion.ac.il; emika@cs.technion.ac.il; janos@cs.technion.ac.il Search for other works by this author on: Oxford Academic Google Scholar Journal of Logic and Computation, Volume 22, Issue 2, April 2012, Pages 237–265, https://doi.org/10.1093/logcom/exq006 Published: 15 February 2010 Article history Received: 01 December 2008 Published: 15 February 2010
Tutte polynomial
Chromatic polynomial
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Characterization
Theory of computation
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