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THOR: A tool for reasoning about shape and arithmetic
 In CAV, LNCS 5123
, 2008
"... tool based on separation logic that is capable of reasoning automatically about heapmanipulating programs. There are several such systems in development now. However, Thor is unique in that it provides not only shape analysis, but also arithmetic reasoning via a novel combination procedure. Also, c ..."
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Cited by 20 (4 self)
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tool based on separation logic that is capable of reasoning automatically about heapmanipulating programs. There are several such systems in development now. However, Thor is unique in that it provides not only shape analysis, but also arithmetic reasoning via a novel combination procedure. Also
Arithmetic Strengthening for Shape Analysis ⋆
"... Abstract. Shape analyses are often imprecise in their numerical reasoning, whereas numerical static analyses are often largely unaware of the shape of a program’s heap. In this paper we propose a lazy method of combining a shape analysis based on separation logic with an arbitrary arithmetic analysi ..."
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Cited by 47 (17 self)
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for the shape analysis. Our method is aimed at proving properties that require comprehensive reasoning about heaps together with more targeted arithmetic reasoning. Given a sufficient precondition, our technique can automatically prove memory safety of programs whose errorfree operation depends on a
Modular Automatic Assertion Checking with Separation Logic
, 2005
"... Separation logic is a program logic for reasoning about programs that manipulate pointer data structures. We describe a tool, Smallfoot, for checking certain lightweight separation logic specifications. The assertions describe the shapes of data structures rather than their detailed contents, and th ..."
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Cited by 163 (6 self)
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Separation logic is a program logic for reasoning about programs that manipulate pointer data structures. We describe a tool, Smallfoot, for checking certain lightweight separation logic specifications. The assertions describe the shapes of data structures rather than their detailed contents
Propositional Reasoning about Safety and Termination of HeapManipulating Programs
"... Abstract. This paper shows that it is possible to reason about the safety and termination of programs handling potentially cyclic, singlylinked lists using propositional reasoning even when the safety invariants and termination arguments depend on constraints over the lengths of lists. For this pur ..."
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. For this purpose, we propose the theory SLH of singlylinked lists with length, which is able to capture nontrivial interactions between shape and arithmetic. When using the theory of bitvector arithmetic as background theory, SLH is efficiently decidable via a reduction to SAT. We show the utility of SLH
Bacterial evolution: chromosome arithmetic and geometry
 Curr Biol
, 2002
"... Recent sequencing projects have characterized bacterial genomes that are organized onto elements of various sizes, shapes and numbers. Aside from its biological relevance and curiosity, this diversity calls into question the way that we define bacterial chromosomes. In the beginning, bacteria were s ..."
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Cited by 1 (0 self)
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simple. The two workhorses of bacterial genetics — Escherichia coli and Bacillus subtilis — were both shown to have circular genetic maps and chromosomes of about 4.5 million base pairs. Because these organisms were known to be rather distantly related, it was reasonable to assume that the shape
Local and global geometric methods for analysis, interrogation, reconstruction, modification and design of shape
 in Computer Graphics International, 2000. Proceedings. IEEE, 2000
"... This paper gives an overview of some recent methods useful for local and global shape analysis and for the design of solids. These methods include as new tools for global and local shape analysis the Spectra of the Laplace and the LaplaceBeltrami Operator and the Concept of stable Umbilical Points ..."
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Cited by 15 (7 self)
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i.e. stable singularities of the principal curvature line wire frame model of the solid’s boundary surface. Most material in this paper deals with the Medial Axis Transform as a tool for shape interrogation, reconstruction, modification and design. We show that it appears to be pos
Fitness landscapes for effects of shape on chemotaxis and other behaviors of bacteria
 J
, 1998
"... Data on the shapes of 218 genera of freefloating or freeswimming bacteria reveal groupings around spherical shapes and around rodlike shapes of axial ratio about 3. Motile genera are less likely to be spherical and have larger axial ratios than nonmotile genera. The effects of shape on seven pos ..."
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Cited by 4 (0 self)
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the largest effect (several hundredfold) is on temporal detection of stimulus gradients, and this explains why rodlike shapes and this mechanism of chemotaxis are common. The first bacteria to be observed were classified by their shapes It seems reasonable to assume that early organisms were spherical as a
Robust Geometric Computations for Vision and Robotics
 In DARPA Image Understanding Workshop
, 1989
"... A new technique, the hidden variable method, is described for the creation of robust geometric algorithms: algorithms which can be implemented with absolute reliability using rounded finite precision arithmetic. The specific application given here is an algorithm for computing arrangements of line s ..."
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Cited by 2 (1 self)
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with just N +6 bits of precision. Applications of this algorithm to problems in vision and robotics are discussed. 1 Introduction Shape, position, orientation, and velocity are all geometric properties, and reasoning about these properties is an important part of vision and robotics. As much as possible
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up
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