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The complexity of counting solutions to generalised satisfiability problems modulo k
 CoRR
, 2008
"... Generalised Satisfiability Problems (or Boolean Constraint Satisfaction Problems), introduced by Schaefer in 1978, are a general class of problem which allow the systematic study of the complexity of satisfiability problems with different types of constraints. In 1979, Valiant introduced the complex ..."
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Cited by 4 (1 self)
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the complexity class parity P, the problem of counting the number of solutions to NP problems modulo two. Others have since considered the question of counting modulo other integers. We give a dichotomy theorem for the complexity of counting the number of solutions to Generalised Satisfiability Problems modulo
TimeSpace Tradeoffs for Counting NP Solutions Modulo Integers
 In Proceedings of the 22nd IEEE Conference on Computational Complexity
, 2007
"... We prove the first timespace tradeoffs for counting the number of solutions to an NP problem modulo small integers, and also improve upon known timespace tradeoffs for Sat. Let m> 0 be an integer, and define MODmSat to be the problem of determining if a given Boolean formula has exactly km sat ..."
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Cited by 15 (5 self)
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We prove the first timespace tradeoffs for counting the number of solutions to an NP problem modulo small integers, and also improve upon known timespace tradeoffs for Sat. Let m> 0 be an integer, and define MODmSat to be the problem of determining if a given Boolean formula has exactly km
Pfaffian point process for the Gaussian real generalised eigenvalue problem
, 2011
"... The generalised eigenvalues for a pair of N × N matrices (X1, X2) are defined as the solutions of the equation det(X1 − λX2) = 0, or equivalently, for X2 invertible, as the eigenvalues of X−12 X1. We consider Gaussian real matrices X1, X2, for which the generalised eigenvalues have the rotational i ..."
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Cited by 10 (8 self)
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The generalised eigenvalues for a pair of N × N matrices (X1, X2) are defined as the solutions of the equation det(X1 − λX2) = 0, or equivalently, for X2 invertible, as the eigenvalues of X−12 X1. We consider Gaussian real matrices X1, X2, for which the generalised eigenvalues have the rotational
Integral projection models for species with complex demography.
 American Naturalist
, 2006
"... abstract: Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation (e.g., body size). The integral projection model (IPM) avoids discrete classes and po ..."
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Cited by 42 (6 self)
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individuals as a discrete stage inevitably creates some degree of error. Increasing the number of stages to minimize this problem leads to higher sampling error because fewer data are available on each stage. "Optimal" stage boundaries Integral Models for Complex Demography 411 and elasticities
A new algorithm for optimal constraint satisfaction and its implications
 Alexander D. Scott) Mathematical Institute, University of Oxford
, 2004
"... We present a novel method for exactly solving (in fact, counting solutions to) general constraint satisfaction optimization with at most two variables per constraint (e.g. MAX2CSP and MIN2CSP), which gives the first exponential improvement over the trivial algorithm; more precisely, it is a cons ..."
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Cited by 38 (1 self)
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(n)], for any k(n) ∈ o ( √ n / log n). Further extensions of our technique yield connections between the complexity of some (polynomial time) high dimensional geometry problems and that of some general NPhard problems. For example, if there are sufficiently faster algorithms for computing the diameter of n
A new algorithm for optimal 2constraint satisfaction and its implications
 Theoretical Computer Science
, 2005
"... Abstract. We present a novel method for exactly solving (in fact, counting solutions to) general constraint satisfaction optimization with at most two variables per constraint (e.g. MAX2CSP and MIN2CSP), which gives the first exponential improvement over the trivial algorithm. More precisely, th ..."
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Cited by 40 (6 self)
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)approximation with roughly the same runtime, modulo polynomial factors. Our construction shows that improvement in the runtime exponent of either kclique solution (even when k = 3) or matrix multiplication over GF(2) would improve the runtime exponent for solving 2CSP optimization. Our approach also yields connections
Publ. Mat. 48 (2004), 127{137 COUNTING FIXED POINTS OF A FINITELY GENERATED SUBGROUP OF A[C]
"... Given a nitely generated subgroup G of the group of ane transformations acting on the complex line C, we are interested in the quotient Fix(G)=G. The purpose of this note is to establish when this quotient is nite and in this case its cardinality. We give an application to the qualitative study of ..."
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Given a nitely generated subgroup G of the group of ane transformations acting on the complex line C, we are interested in the quotient Fix(G)=G. The purpose of this note is to establish when this quotient is nite and in this case its cardinality. We give an application to the qualitative study
new algorithm to compute fusion coecients By
"... This is a proceedings article reviewing a recent combinatorial construction of the bsu(n)k WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion coecients dierent from the KacWalton formula. The discussion ..."
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This is a proceedings article reviewing a recent combinatorial construction of the bsu(n)k WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion coecients dierent from the KacWalton formula
Results 1  10
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161