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Exploiting Sparsity in Polyhedral Analysis
 Static Analysis Symposium, volume 3672 of LNCS
, 2005
"... Abstract. The intrinsic cost of polyhedra has lead to research on more tractable subclasses of linear inequalities. Rather than committing to the precision of such a subclass, this paper presents a projection algorithm that works directly on any sparse system of inequalities and which sacrifices p ..."
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Cited by 17 (11 self)
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Abstract. The intrinsic cost of polyhedra has lead to research on more tractable subclasses of linear inequalities. Rather than committing to the precision of such a subclass, this paper presents a projection algorithm that works directly on any sparse system of inequalities and which sacrifices precision only when necessary. The algorithm is based on a novel combination of the FourierMotzkin algorithm (for exact projection) and Simplex (for approximate projection). By reformulating the convex hull operation in terms of projection, conversion to the frame representation is avoided altogether. Experimental results conducted on logic programs demonstrate that the resulting analysis is efficient and precise. 1
Transfer Function Synthesis without Quantifier Elimination
"... Abstract. Recently it has been shown how transfer functions for linear template constraints can be derived for bitvector programs by operating over propositional Boolean formulae. The drawback of this method is that it relies on existential quantifier elimination, which induces a computational bott ..."
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Cited by 11 (3 self)
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Abstract. Recently it has been shown how transfer functions for linear template constraints can be derived for bitvector programs by operating over propositional Boolean formulae. The drawback of this method is that it relies on existential quantifier elimination, which induces a computational bottleneck. The contribution of this paper is a novel method for synthesising transfer functions that does not rely on quantifier elimination. We demonstrate the practicality of the method for generating transfer functions for both intervals and octagons. 1
Automatic abstraction for intervals using boolean formulae
 IN: SAS 2010. LNCS
, 2010
"... Traditionally, transfer functions have been manually designed for each operation in a program. Recently, however, there has been growing interest in computing transfer functions, motivated by the desire to reason about sequences of operations that constitute basic blocks. This paper focuses on deri ..."
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Cited by 10 (5 self)
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Traditionally, transfer functions have been manually designed for each operation in a program. Recently, however, there has been growing interest in computing transfer functions, motivated by the desire to reason about sequences of operations that constitute basic blocks. This paper focuses on deriving transfer functions for intervals — possibly the most widely used numeric domain — and shows how they can be computed from Boolean formulae which are derived through bitblasting. This approach is entirely automatic, avoids complicated elimination algorithms, and provides a systematic way of handling wraparounds (integer overflows and underflows) which arise in machine arithmetic.
Closure Algorithms for Domains with Two Variables per Inequality
, 2009
"... Abstract. Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Such domains often restrict their attention of TVPI constraints which are systems of constraints where each constrai ..."
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Cited by 3 (2 self)
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Abstract. Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Such domains often restrict their attention of TVPI constraints which are systems of constraints where each constraint involves, at most, two variables. This technical report addresses the problem of deriving an incremental version of the closure operation. In this operation, a new constraint is added to a system that is already closed, and the computational problem is how to efficiently close the augmented system. 1
Ranking Links on the Web: Search and Surf Engines
"... Abstract. The main algorithms at the heart of search engines have focused on ranking and classifying sites. This is appropriate when we know what we are looking for and want it directly. Alternatively, we surf, in which case ranking and classifying links becomes the focus. We address this problem us ..."
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Abstract. The main algorithms at the heart of search engines have focused on ranking and classifying sites. This is appropriate when we know what we are looking for and want it directly. Alternatively, we surf, in which case ranking and classifying links becomes the focus. We address this problem using a latent semantic analysis of the web. This technique allows us to rate, suppress or create links giving us a version of the web suitable for surfing. Furthermore, we show on benchmark examples that the performance of search algorithms such as PageRank is substantially improved as they work on an appropriately weighted graph.
SUM OF SQUARES CERTIFICATES FOR CONTAINMENT OF HPOLYTOPES IN VPOLYTOPES
"... Abstract. Given an Hpolytope P and a Vpolytope Q, the decision problem whether P is contained in Q is coNPcomplete. This hardness remains if P is restricted to be a standard cube and Q is restricted to be the affine image of a cross polytope. While this hardness classification by Freund and Orli ..."
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Abstract. Given an Hpolytope P and a Vpolytope Q, the decision problem whether P is contained in Q is coNPcomplete. This hardness remains if P is restricted to be a standard cube and Q is restricted to be the affine image of a cross polytope. While this hardness classification by Freund and Orlin dates back to 1985, for general dimension there seems to be only limited progress on that problem so far. Based on a formulation of the problem in terms of a bilinear feasibility problem, we study sum of squares certificates to decide the containment problem. These certificates can be computed by a semidefinite hierarchy. As a main result, we show that under mild and explicitly known preconditions the semidefinite hierarchy converges in finitely many steps. In particular, if P is contained in a large Vpolytope Q (in a welldefined sense), then containment is certified by the first step of the hierarchy. 1.