787 research outputs found
Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum
Motivated by the concept of shape invariance in supersymmetric quantum
mechanics, we obtain potentials whose spectrum consists of two shifted sets of
equally spaced energy levels. These potentials are similar to the
Calogero-Sutherland model except the singular term always falls
in the transition region and there is a delta-function
singularity at x=0.Comment: Latex, 12 pages, Figures available from Authors, To appear in Physics
Letters A. Please send requests for figures to [email protected] or
[email protected]
Interprocedural Data Flow Analysis in Soot using Value Contexts
An interprocedural analysis is precise if it is flow sensitive and fully
context-sensitive even in the presence of recursion. Many methods of
interprocedural analysis sacrifice precision for scalability while some are
precise but limited to only a certain class of problems.
Soot currently supports interprocedural analysis of Java programs using graph
reachability. However, this approach is restricted to IFDS/IDE problems, and is
not suitable for general data flow frameworks such as heap reference analysis
and points-to analysis which have non-distributive flow functions.
We describe a general-purpose interprocedural analysis framework for Soot
using data flow values for context-sensitivity. This framework is not
restricted to problems with distributive flow functions, although the lattice
must be finite. It combines the key ideas of the tabulation method of the
functional approach and the technique of value-based termination of call string
construction.
The efficiency and precision of interprocedural analyses is heavily affected
by the precision of the underlying call graph. This is especially important for
object-oriented languages like Java where virtual method invocations cause an
explosion of spurious call edges if the call graph is constructed naively. We
have instantiated our framework with a flow and context-sensitive points-to
analysis in Soot, which enables the construction of call graphs that are far
more precise than those constructed by Soot's SPARK engine.Comment: SOAP 2013 Final Versio
Non-Central Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance
It is shown that the operator methods of supersymmetric quantum mechanics and
the concept of shape invariance can profitably be used to derive properties of
spherical harmonics in a simple way. The same operator techniques can also be
applied to several problems with non-central vector and scalar potentials. As
examples, we analyze the bound state spectra of an electron in a Coulomb plus
an Aharonov-Bohm field and/or in the magnetic field of a Dirac monopole.Comment: Latex, 12 pages. To appear in American Journal of Physic
Methods for Generating Quasi-Exactly Solvable Potentials
We describe three different methods for generating quasi-exactly solvable
potentials, for which a finite number of eigenstates are analytically known.
The three methods are respectively based on (i) a polynomial ansatz for wave
functions; (ii) point canonical transformations; (iii) supersymmetric quantum
mechanics. The methods are rather general and give considerably richer results
than those available in the current literature.Comment: 12 pages, LaTe
Generalized Points-to Graphs: A New Abstraction of Memory in the Presence of Pointers
Flow- and context-sensitive points-to analysis is difficult to scale; for
top-down approaches, the problem centers on repeated analysis of the same
procedure; for bottom-up approaches, the abstractions used to represent
procedure summaries have not scaled while preserving precision.
We propose a novel abstraction called the Generalized Points-to Graph (GPG)
which views points-to relations as memory updates and generalizes them using
the counts of indirection levels leaving the unknown pointees implicit. This
allows us to construct GPGs as compact representations of bottom-up procedure
summaries in terms of memory updates and control flow between them. Their
compactness is ensured by the following optimizations: strength reduction
reduces the indirection levels, redundancy elimination removes redundant memory
updates and minimizes control flow (without over-approximating data dependence
between memory updates), and call inlining enhances the opportunities of these
optimizations. We devise novel operations and data flow analyses for these
optimizations.
Our quest for scalability of points-to analysis leads to the following
insight: The real killer of scalability in program analysis is not the amount
of data but the amount of control flow that it may be subjected to in search of
precision. The effectiveness of GPGs lies in the fact that they discard as much
control flow as possible without losing precision (i.e., by preserving data
dependence without over-approximation). This is the reason why the GPGs are
very small even for main procedures that contain the effect of the entire
program. This allows our implementation to scale to 158kLoC for C programs
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