C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. Submitted.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... corresponding to face number i is determined by projecting the five dimensional polytope defined by (5) and (6) onto the plane (u i ; v i ) Several algorithms can be used to perform this projection, including Fourier s method [15] the convex hull and extreme point approaches of Lassez and Lassez [26, 25], and the Gaussian elimination and contour tracking techniques of Ponce et al. 46] For faces with a bounded number of edges, all of these algorithms run in constant time, and they can be used to construct sub faces that can be passed as input to the rest of the algorithm. Enumerating Locator ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

.... corresponding to face number i is determined by projecting the fivedimensional polytope defined by (3) and (4) onto the plane (u i ; v i ) Several algorithms can be used to perform this projection, including Fourier s method [7] the convex hull and extreme point approaches of Lassez and Lassez [9], and the Gaussian elimination and contour tracking techniques of Ponce et al. 17] For faces with a bounded number of edges, all of these algorithms run in constant time, and they can be used to construct sub faces that can be passed as input to the rest of the algorithm. 3.2 Enumerating ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, eds., Symbolic and Numerical Computation for Artificial Intelligence, pp. 103--122. Academic Press, 1992.

....LCIP is decidable and the CIA terminates in at most l 1 steps. Proposition 1 states that in order to check for the decidability of the LCIP problem it is su#cient to solve a finite number of linear programs (polynomial time) plus one Fourier Motzkin elimination problem (worst case exponential [12]) However, there is no way of detecting if the algorithm terminates in an infinite number of iterations, which happens for l = #. The following propositions are special cases under which l is guaranteed to be finite. Proposition 2 If A is nilpotent of index l, # 1 (# max d l #D l MC l ....

....necessary. In this case, the conditions of Proposition 1 are met for l = 2. 5 CIP for LDTS with Ellipsoidal Constraints Although for the classes of linear systems in Propositions 2 and 3 the LCIP is decidable, the computational complexity of exactly solving the problem is worst case exponential [12]. Because of this, in this section we specialize the implementation of the CIA to the case where the sets F , U and D are ellipsoids. Notice that given a LDTS, if F and U are convex so are W and g(x) Hence the CIP is suitable for convex optimization algorithms, such as convex programming (CP) ....

C. Lassez and J. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In Symbolic and Numeric Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....whether the five dimensional polytope defined by these constraints and the face bounds inequalities and i 0 is empty. When this polytope is not empty, the subset of each face that may participate in an equilibrium configuration is efficiently determined using polytope projection techniques [11, 16, 15, 31] (see [45, 44] for details) The second step of our algorithm uses distance constraints to reduce the enumeration of the pin positions that may yield equilibrium grasps to the scan line conversion of circular shells (see [4, 5, 47, 48] for related approaches to fixture planning for ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....(3) For each such position, enumerate the pin lengths that immobilize the object and compute the remaining grasp parameters. 4) Compute the corresponding coefficients i and check that they are positive. The first step of the algorithm uses linear programming and polytope projection techniques [14, 23, 22, 39] to prune gripper configurations that cannot achieve equilibrium. The second step uses distance constraints to reduce the enumeration of the pin positions that may yield equilibrium grasps to the scan line conversion of circular shells (see [4, 5, 53, 54] for related approaches to fixture planning ....

....configuration. The subset corresponding to face number i is determined by projecting the polytope defined onto the plane (u i ; v i ) Several algorithms can be used to perform this projection, including Fourier s method [14] the convex hull and extreme point approaches of Lassez and Lassez [23, 22], and the Gaussian elimination and contour tracking techniques of Ponce et al. 39] For faces with a bounded number of edges, all of these algorithms run in constant time, and they can be used to construct subsets of the original faces that are then passed as input to the rest of the algorithm. ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....the convex set is represented by means of linear restrictions, it is not a good idea to enumerate all the extreme points and then to calculate the marginalization. Direct algorithms to carry out the marginalization of a convex set given by linear restrictions are available and much more efficient [22]. The direct algorithm calculates all the extreme points of the marginalized set and not of the original convex set. 3 An Axiomatic View of Propagation Algorithms In this section, we briefly describe the Shafer and Shenoy axiomatic framework for local computation [34, 36] A valuation is a ....

....#I , instead of the original convex set H . This makes marginalization much more efficient because the number of extreme points of the marginalized set is much more smaller. An example of this type of algorithms can be obtained by applying the quantifier elimination technique by Lassez and Lassez [22]. 4.1 Constraints Propagation In this section we describe some procedures of propagating general knowledge based on the application of local rules. In general, in all these procedures it is not possible to propagate every type of restrictions, but only some particular types, usually bounds in ....

C. Lassez and J.L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B.R. Donald et al., editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--119. Academic Press, London, 1992.

.... such as linear inequalities over reals, this framework may be computationally unmanageable: the quantifier elimination may result in a constraint exponential in the size of the original conjunction, although for many sub families more efficient algorithms were developed (e.g. GK, JMSY92, HLL90, LL91] A more flexible first order logic structure that allows the entire linear constraints over reals while controlling computational complexity was described in [BJM93, BK95] 4.2 C 3 Constraint Families and Canonical Forms In C 3 we concentrate on linear constraint over reals, which are ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. Technical Report RC16779, IBM T.J. Watson Research Center, 1991.

....on the Fourier variable elimination techique. It also contains a discussion on how the essential technique of Fourier can be adapted to perform projection in other domains such as linear integer constraints and the boolean domain. We finish here by mentioning the non Fourier algorithms of [123, 158]. In some circumstances, especially when the matrix representing the constraints is dense, the algorithm of [123] can be far more efficient. It is, however, believed that typical CLP programs produce sparse matrices. The algorithm of [158] has the advantageous property that it can produce an ....

....here by mentioning the non Fourier algorithms of [123, 158] In some circumstances, especially when the matrix representing the constraints is dense, the algorithm of [123] can be far more efficient. It is, however, believed that typical CLP programs produce sparse matrices. The algorithm of [158] has the advantageous property that it can produce an approximation of the projection if the size of the 29 Obtained, for example, by multiplying c by 1=m and c 0 by ( Gamma1=m 0 ) where m and m 0 are the coefficients of x in c and c 0 respectively, and then adding the resulting ....

C. Lassez & J-L. Lassez, Quantifier Elimination for Conjunctions of Linear Constraints via a Convex Hull Algorithm, in: Symbolic and Numeric Computation for Artificial Intelligence, B. Donald, D. Kapur and J.L. Mundy (Eds), Academic Press, to appear. Also, IBM Research Report RC16779, T.J. Watson Research Center, 1991.

.... different methods have been proposed for performing quantifier elimination in OF(R) 1, 22, 24] and the process can be automated using symbolic tools [9] the quantifier elimination procedure is in general hard, both in theory and in practice, since the solvability may be doubly exponential [14]. For the theory Lin(R) a somewhat more efficient implementation can be derived using techniques from linear algebra and linear programming. The next section shows how quantifier elimination in the theory Lin(R) can be performed more efficiently for the formula (1) used in the controlled ....

....added to ensure that the set is a polytope. Although the extreme points method is better than Fourier elimination, because it eliminates the costly intermediate steps, the computation of the extreme points is still costly and also generates a lot of redundant constraints. A more efficient method [14] uses a generalized linear programming formulation and an on line convex hull construction to obtain an incremental inner approximation of the set defined by OE l . The method considerably reduces the number of constraints defining the resulting set. 3.2 Intersection, Emptiness and Redundancy ....

C. Lassez and J.-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In Symbolic and Numeric Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....information requires about 1 Gamma 10 of the total time required by simple workstation compilers that do no array data dependence analysis of any kind. Our techniques are based on an extension of Fourier variable elimination to integers. Many other researchers in the constraints field [Duf74, LL92, Imb93, JMSY93] have stated that direct application of Fourier s technique is impractical because of the number of redundant constraints generated. We have not experienced any significant problems with Fourier elimination generating redundant constraints, even though we have not implemented ....

....2; 3; 5g and the u j s are f1; 1; 3; 7g, Williams method produces 23156852670000 clauses, while ours produces 12. It is almost certainly possible to improve Williams method while using the same approach as Williams, but we know of no description of such an improvement. Jean Louis Lassez [LHM89, LL92, HLL92] gives an alternative to Fourier variable elimination for elimination of existentially quantified variables. However, his methods work over real variables, are optimized for dense constraints (constraints with few zero coefficients) and are inefficient when the final problem contains more ....

[Article contains additional citation context not shown here]

Catherine Lassez and Jean-Louis Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In Bruce Donald, Deepak Kapur, and Joseph Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence. Academic Press, 1992.

....The main problem we face during the variable elimination process in linear inequation systems, is the size of the output. It is doubly exponential. Variable elimination in inequation systems has been extensively investigated. Among these investigations one can cite the C. and JL. Lassez method [LaLa91], which globally eliminates in one single operation the set of unwanted variables. It is based on 1 Supported by ACCLAIM Project. semantic properties of projection and of convex hull. It makes it possible to obtain approximations. Nevertheless, so far, mainly methods derived from Fourier s ....

....is to use a general method of redundancy removing [Telg81, KLTZ83, LHMA89, ImVH92a] As for the second cause, which is structural, it cannot be suppressed. Other methods are necessary for remedying this inconvenience. Numerous methods have been proposed, including one already cited and set out in [LaLa91] which is particularly interesting as it creates a minimal representation of the final system and does not use intermediary systems. 2.3 Some results Let S be the linear inequation system fa 1 x b 1 ; anx b ng. It is known (Farkas [Shri86, p87 90] that the inequation cx d is a ....

C. Lassez and JL. Lassez. "Quantifier Elimination for Conjunctions of Linear Constraints via a Convex Hull Algorithm". To Appear 1991.

.... corresponding to face number i is determined by projecting the five dimensional polytope defined by (5) and (6) onto the plane (u i ; v i ) Several algorithms can be used to perform this projection, including Fourier s method [15] the convex hull and extreme point approaches of Lassez and Lassez [26, 25], and the Gaussian elimination and contour tracking techniques of Ponce et al. 46] For faces with a bounded number of edges, all of these algorithms run in constant time, and they can be used to construct sub faces that can be passed as input to the rest of the algorithm. Enumerating Locator ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....the convex set is represented by means of linear restrictions, it is not a good idea to enumerate all the extreme points and then to calculate the marginalization. Direct algorithms to carry out the marginalization of a convex set given by linear restrictions are available and much more efficient [34]. The direct algorithm calculates all the extreme points of the marginalized set and not of the original convex set. The weak union operation is much more difficult. If H 1 and H 2 are convex sets defined on U I and U J and we want to calculate H 1 fiH 2 this can be carried out with the following ....

....#I , instead of the original convex set H. This makes marginalization much more efficient because the number of extreme points of the marginalized set is much more smaller. An example of this type of algorithms can be obtained by applying the quantifier elimination technique by Lassez and Lassez [34]. Here we give a modification of Manas and Nedoma s vertex enumeration algorithm [41, 42] to carry out marginalization. In its original formulation, this algorithm starts with an extreme point of the convex set and its corresponding simplex tableau, and then visits all the other extreme points by ....

C. Lassez and J.L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B.R. Donald et al., editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--119. Academic Press, London, 1992.

....configuration. The subset corresponding to face number i is determined by projecting the polytope defined onto the plane (u i ; v i ) Several algorithms can be used to perform this projection, including Fourier s method [9] the convex hull and extreme point approaches of Lassez and Lassez [13, 12], and the Gaussian elimination and contour tracking techniques of Ponce et al. 26] For faces with a bounded number of edges, all of these algorithms run in constant time, and they can be used to construct subsets of the original faces that are then passed as input to the rest of the algorithm. ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....and nonsubsumption in CQLs with linear arithmetic constraints. We adapt indexing strategies from spatial databases for efficiently indexing facts in such a CQL: such indexing is crucial for performance in the presence of large databases. Based on a recent algorithm by Lassez and Lassez ([LL]) for quantifier elimination, we present an incremental version of the algorithm to check for subsumption in CQLs with linear arithmetic constraints. 1 Introduction Recently, there have been attempts ( KKR90, Rev90, Cho90, BNW91] among others) to increase the expressive power of database query ....

....the computation of constraint facts with checking for subsumption in the bottom up evaluation of a CQL program. This algorithm tries to minimize the wasted effort by early detection of when a newly computed constraint fact is subsumed. It is based on a recent algorithm by Lassez and Lassez [LL] for quantifier (variable) elimination for systems of linear constraints. The algorithm in [LL] computes successive approximations using linear programming techniques and an on line convex hull construction algorithm. Further, the algorithm can provide an upper bound or lower bound approximation ....

[Article contains additional citation context not shown here]

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. Submitted.

.... corresponding to face number i is determined by projecting the fivedimensional polytope defined by (3) and (4) onto the plane (u i ; v i ) Several algorithms can be used to perform this projection, including Fourier s method [7] the convex hull and extreme point approaches of Lassez and Lassez [9], and the Gaussian elimination and contour tracking techniques of Ponce et al. 17] For faces with a bounded number of edges, all of these algorithms run in constant time, and they can be used to construct sub faces that can be passed as input to the rest of the algorithm. 3.2 Enumerating ....

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In B. Donald, D. Kapur, and J. Mundy, eds., Symbolic and Numerical Computation for Artificial Intelligence, pp. 103--122. Academic Press, 1992.

....be preferable if they would not appear in the final result when displayed. So far, two methods have been explored. One using Fourier s Algorithm, 70, 31, 32, 117, 67, 122, 120, 103, 104, 102] based on a one at a time variable elimination, the other based on a simplex method and or optimizations [121]. The number of constraints in the final result can be exponential compared to the number of constraints in the initial result. Moreover, in the first method, this number can grow significantly before decreasing to the final result. We propose developing a preprocessing which makes it possible to ....

....in [151] Linear constraint solving over numeric domains has been investigated in various CLP systems such as PROLOG III [140] CLP(R) 106] CHIP [84] etc. Linear constraints simplification is mainly based on the method of Fourier [70] Various modification and improvements have been made[31, 32, 117, 67, 122, 120, 103, 104, 102, 121], based on a one at a time variable elimination, and on a simplex method and or optimizations. Non linear (algebraic) constraints solving has been studied extensively in mathematics during last 200 years under the name elimination theory , and recently in computer algebra. During last three ....

C. Lassez and J.L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull. Technical report, IBM T.J. Watson Center, P.O. Box 704, Yorktown Heights, NY 10598, U.S.A., 1991.

....we face during the variable elimination process in linear inequation systems, is the size of the output. It is doubly exponential. Variable elimination in inequation systems has been extensively investigated. Among these investigations one can cite the C. and JL. Lassez 2 Chapter 1 method [18], which globally eliminates in one single operation the set of unwanted variables. It is based on semantic properties of projection and of convex hull. It makes it possible to obtain approximations. Nevertheless, so far, mainly methods derived from Fourier s elimination [8] are used in CLP ....

....the first cause is to use a general method of redundancy removing [20, 16, 19, 11] As for the second cause, which is structural, it cannot be suppressed. Other methods are necessary for remedying this inconvenience. Numerous methods have been proposed, including one already cited and set out in [18] which is particularly interesting as it creates a minimal representation of the final system and does not use intermediary systems. Fourier s Elimination: Which to Choose 5 1.3.3 Some results Let S be the linear inequation system fa 1 x b 1 ; anx b ng. It is known (Farkas [21, ....

C. Lassez and JL. Lassez. Quantifier Elimination for Conjunctions of Linear Constraints via a Convex Hull Algorithm. To Appear 1991.

....to two finger grasping of curved objects by using algebraic cell decomposition and global optimization methods. In [45] Ponce and Faverjon have proposed a totally different computational approach to three finger grasp planning, relying on variable elimination (or equivalently, polytope projection [12, 16, 25, 26]) to characterize the regions of the grasp configuration space that yield force closure, and using linear optimization within these regions to compute maximal independent grasps. We generalize this approach to three dimensional four finger grasping in this paper. From an algorithmic viewpoint, the ....

....constructing Q as the dual of the convex hull of the projected vertices. The cost of the computation is dominated by the construction of D, which takes time O(n b d 2 c ) 5, 3] Other algorithms based on convex hull and extreme point computation have also been proposed by Lassez and Lassez [26, 25]. While each approach is effective within certain domains (e.g. projection through many dimensions or with dense or redundant polytopes) there has yet to emerge an algorithm which performs well for all types of inputs. In this section we present two projection algorithms which have proven to be ....

[Article contains additional citation context not shown here]

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In D. Kapur B. Donald and J. Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence, pages 103--122. Academic Press, 1992.

....variables to project on, the projector first combines the defining equations for these variables with all the slack equations. Then a projection algorithm computes the actual projection. Since the projection space is assumed to be small, we use a projection algorithm called the Convex Hull Method [14], which is based on a geometric approach. For small projection spaces, it is much faster than other projection algorithms based on algebraic manipulation. It uses the Simplex algorithm repeatedly to compute the convex hull of the projected constraints. 4.2.5 Quadratic Optimization The algorithm ....

C. Lassez and J.-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. Research Report RC 16779, IBM T.J. Watson Research Center, 1991. To appear, Symbolic and Numerical Computation---Towards Integration, Kapur and Mundy editors, Academic Press.

....efficiency [Jaffar and Lassez, 1987] In the CLP class of languages [Jaffar and Lassez, 1987, Lassez, 1990] it is possible to compute over universes other than that of Herbrand. The user can more easily express his problem and can expect a quicker computation of the solution or its approximation [Lassez and Lassez, 1991, Lassez and McAloon, 1991, for example] The notion of derivation sequence is similar to our bc resolution. It is more restrictive in the sense that it applies only to Horn clauses, but in another sense it is less restrictive because not limited to Herbrand terms, as in bc resolution. The ....

Lassez and Lassez, 1991 Lassez, C. and Lassez, J.-L. (1991). Quantifier elimination for conjunctions of linear constraints via a convex hull. Technical report, IBM Research Division, T.J. Watson Research Center.

....information requires about 1 Gamma 10 of the total time required by simple workstation compilers that do no array data dependence analysis of any kind. Our techniques are based on an extension of Fourier variable elimination to integers. Many other researchers in the constraints field [Duf74, LL92, Imb93, JMSY93] have stated that direct application of Fourier s technique may be impractical because of the number of redundant constraints generated. We have not experienced any significant problems with Fourier elimination generating redundant constraints, even though we have not implemented ....

....3; 5g and the u j s are f1; 1; 3; 7g, Williams method produces 23156852670000 clauses, while ours produces 12. It is almost certainly possible to improve Williams method while using the same approach as Williams, but we know of no description of such an improvement. Jean Louis Lassez [LHM89, LL92, HLL92] gives an alternative to Fourier variable elimination for elimination of existentially quantified variables. However, his methods work over real variables, are optimized for dense constraints (constraints with few zero coefficients) and are inefficient when the final problem contains more ....

[Article contains additional citation context not shown here]

Catherine Lassez and Jean-Louis Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. In Bruce Donald, Deepak Kapur, and Joseph Mundy, editors, Symbolic and Numerical Computation for Artificial Intelligence. Academic Press, 1992.

....[49, 25, 2] 8. 2 Domain Specific Constraint Solvers Multi way, local propagation solvers may be used either individually or in concert with domainspecific solvers, such as linear constraint solvers [17] non linear constraint solvers [10, 50, 51, 16, 8] and linear equality and inequality solvers [29, 32, 31, 30, 19, 28]. Domain specific algorithms are capable of satisfying more expressive constraints within their domain of knowledge, but they have the drawbacks cited in Section 2 including less coverage, less efficiency, and less usability relative to local propagation techniques. Some systems, such as ThingLab ....

Catherine Lassez and Jean-Louis Lassez. Quantifier Elimination for Conjunctions of Linear Constraints via a Convex Hull Algorithm. Tech. Rept. Research Report RC 16779, IBM, 1991.

....the reduced formula is no longer equivalent to the original one ( overestimation ) This may be an interesting way of synthesizing inductive assertions of programs with no need for generalization heuristics (cf . 8, 20] The technique bears also some resemblance to the geometrical approach of [13, 14] which treats linear constraint problems by computing a convex hull approximation in a projection space. Acknowledgements. This work was partly done while I was visiting Prof. Maluszynski s group LOGPRO at Linkoping University. I would like to thank Ron van der Meyden for directing me to the ....

Lassez, C. and Lassez, J.L. (1991). Quantifier Elimination for Conjunction of Linear Constraints via a Convex Hull Algorithm, IBM Research Report, T.J. Watson Research Center, New York.

No context found.

C. Lassez and J-L. Lassez. Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm. Submitted.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC