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Parallel FourierMotzkin Elimination
"... FourierMotzkin elimination is a computationally expensive but powerful method to solve a system of linear inequalities for real and integer solution spaces. Because it yields an explicit representation of the solution set, in contrast to other methods such as Simplex, one may, in some cases, take ..."
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Cited by 1 (0 self)
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FourierMotzkin elimination is a computationally expensive but powerful method to solve a system of linear inequalities for real and integer solution spaces. Because it yields an explicit representation of the solution set, in contrast to other methods such as Simplex, one may, in some cases, take
COMBINATORIAL PROPERTIES OF FOURIERMOTZKIN ELIMINATION ∗
"... Abstract. FourierMotzkin elimination is a classical method for solving linear inequalities in which one variable is eliminated in each iteration. This method is considered here as a matrix operation and properties of this operation are established. In particular, the focus is on situations where th ..."
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Cited by 3 (1 self)
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Abstract. FourierMotzkin elimination is a classical method for solving linear inequalities in which one variable is eliminated in each iteration. This method is considered here as a matrix operation and properties of this operation are established. In particular, the focus is on situations where
Implementation of FourierMotzkin Elimination
, 1994
"... Every transformation of a perfectly nested loop consisting of a combination of loop interchanging, loop skewing and loop reversal can be modeled by a linear transformation represented by a unimodular matrix. This modeling offers more flexibility than the traditional stepwise application of loop tra ..."
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Cited by 19 (1 self)
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Every transformation of a perfectly nested loop consisting of a combination of loop interchanging, loop skewing and loop reversal can be modeled by a linear transformation represented by a unimodular matrix. This modeling offers more flexibility than the traditional stepwise application of loop transformations because we can directly construct a unimodular matrix for a particular goal. In this paper, we present implementation issues arising when this framework is incorporated in a compiler. 1 Introduction Inherent to the application of program transformations in an optimizing or restructuring compiler is the socalled `phase ordering problem', i.e. the problem of finding an effective order in which particular transformations must be applied. This problem is still an important research topic [WS90]. An important step forwards in solving the phase ordering problem has been accomplished by the observation that any combination of the iterationlevel loop transformations loop interchangin...
Analog performance space exploration by FourierMotzkin elimination with application to hierarchical sizing
 in Proc. of ICCAD
, 2004
"... Analog performance space exploration identifies the range of feasible performance values of a given circuit topology. It is an extremely challenging task of great importance to topology selection and hierarchical sizing. In this paper, a novel technique for the efficient simulationbased exploration ..."
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Cited by 8 (1 self)
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Analog performance space exploration identifies the range of feasible performance values of a given circuit topology. It is an extremely challenging task of great importance to topology selection and hierarchical sizing. In this paper, a novel technique for the efficient simulationbased exploration of highdimensional performance spaces is presented. To this end, fundamental circuit design knowledge is described by constraint functions. Based on a linearization of the latter and of the circuit performance functions, a description of the feasible performance range in the form of a polytope is derived. Moreover, the approach is integrated into a hierarchical sizing method, where it propagates topological and technological constraints bottomup. Practical application results demonstrate the efficiency and usefulness of the new method. 1.
TROPICAL FOURIERMOTZKIN ELIMINATION, WITH AN APPLICATION TO REALTIME VERIFICATION
, 2014
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Modified FourierMotzkin Elimination Algorithm for Reducing Systems of Linear Inequalities with Unconstrained Parameters ABSTRACT
"... The need for eliminating redundancies in systems of linear inequalities arises in many applications. In linear programming (LP), one seeks a solution that optimizes a given linear objective function subject to a set of linear constraints, sometimes posed as linear inequalities. Linear inequalities a ..."
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of computations, and hence improve computation times in applications. Current techniques for eliminating redundant inequalities are not viable in higher dimensions [7]. As an alternative we propose a modified version of the FourierMotzkin Elimination
A Note on Preprocessing via FourierMotzkin Elimination in TwoStage Stochastic Programming
, 1996
"... Preprocessing in twostage stochastic programming is considered from the viewpoint ..."
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Preprocessing in twostage stochastic programming is considered from the viewpoint
Projection: A Unified Approach to SemiInfinite Linear Programs and Duality in Convex Programming
, 2014
"... FourierMotzkin elimination is a projection algorithm for solving finite linear programs. We extend FourierMotzkin elimination to semiinfinite linear programs which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations ..."
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FourierMotzkin elimination is a projection algorithm for solving finite linear programs. We extend FourierMotzkin elimination to semiinfinite linear programs which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations
On Solving Presburger and Linear Arithmetic with SAT
 In Proc. of Formal Methods in ComputerAided Design (FMCAD 2002), LNCS
, 2002
"... We show a reduction to propositional logic from quantifierfree Presburger arithmetic, and disjunctive linear arithmetic, based on FourierMotzkin elimination. While the complexity of this procedure is not better than competing techniques, it has practical advantages in solving verification problems ..."
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Cited by 25 (2 self)
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We show a reduction to propositional logic from quantifierfree Presburger arithmetic, and disjunctive linear arithmetic, based on FourierMotzkin elimination. While the complexity of this procedure is not better than competing techniques, it has practical advantages in solving verification
An Extension of the DavisPutnam Procedure and its Application to Preprocessing in SMT
 In SMT
, 2009
"... Abstract. We present a decision procedure for SMT(LRA) that works by eliminating Boolean and rational variables. The algorithm we propose (DPFM) is based on a combination of the DavisPutnam procedure and the FourierMotzkin elimination. We report on preliminary experiments where DPFM is not directl ..."
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Cited by 2 (1 self)
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Abstract. We present a decision procedure for SMT(LRA) that works by eliminating Boolean and rational variables. The algorithm we propose (DPFM) is based on a combination of the DavisPutnam procedure and the FourierMotzkin elimination. We report on preliminary experiments where DPFM
Results 1  10
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