43 research outputs found
Ranking Templates for Linear Loops
We present a new method for the constraint-based synthesis of termination
arguments for linear loop programs based on linear ranking templates. Linear
ranking templates are parametrized, well-founded relations such that an
assignment to the parameters gives rise to a ranking function. This approach
generalizes existing methods and enables us to use templates for many different
ranking functions with affine-linear components. We discuss templates for
multiphase, piecewise, and lexicographic ranking functions. Because these
ranking templates require both strict and non-strict inequalities, we use
Motzkin's Transposition Theorem instead of Farkas Lemma to transform the
generated -constraint into an -constraint.Comment: TACAS 201
Static analysis of energy consumption for LLVM IR programs
Energy models can be constructed by characterizing the energy consumed by
executing each instruction in a processor's instruction set. This can be used
to determine how much energy is required to execute a sequence of assembly
instructions, without the need to instrument or measure hardware.
However, statically analyzing low-level program structures is hard, and the
gap between the high-level program structure and the low-level energy models
needs to be bridged. We have developed techniques for performing a static
analysis on the intermediate compiler representations of a program.
Specifically, we target LLVM IR, a representation used by modern compilers,
including Clang. Using these techniques we can automatically infer an estimate
of the energy consumed when running a function under different platforms, using
different compilers.
One of the challenges in doing so is that of determining an energy cost of
executing LLVM IR program segments, for which we have developed two different
approaches. When this information is used in conjunction with our analysis, we
are able to infer energy formulae that characterize the energy consumption for
a particular program. This approach can be applied to any languages targeting
the LLVM toolchain, including C and XC or architectures such as ARM Cortex-M or
XMOS xCORE, with a focus towards embedded platforms. Our techniques are
validated on these platforms by comparing the static analysis results to the
physical measurements taken from the hardware. Static energy consumption
estimation enables energy-aware software development, without requiring
hardware knowledge
Badger: Complexity Analysis with Fuzzing and Symbolic Execution
Hybrid testing approaches that involve fuzz testing and symbolic execution
have shown promising results in achieving high code coverage, uncovering subtle
errors and vulnerabilities in a variety of software applications. In this paper
we describe Badger - a new hybrid approach for complexity analysis, with the
goal of discovering vulnerabilities which occur when the worst-case time or
space complexity of an application is significantly higher than the average
case. Badger uses fuzz testing to generate a diverse set of inputs that aim to
increase not only coverage but also a resource-related cost associated with
each path. Since fuzzing may fail to execute deep program paths due to its
limited knowledge about the conditions that influence these paths, we
complement the analysis with a symbolic execution, which is also customized to
search for paths that increase the resource-related cost. Symbolic execution is
particularly good at generating inputs that satisfy various program conditions
but by itself suffers from path explosion. Therefore, Badger uses fuzzing and
symbolic execution in tandem, to leverage their benefits and overcome their
weaknesses. We implemented our approach for the analysis of Java programs,
based on Kelinci and Symbolic PathFinder. We evaluated Badger on Java
applications, showing that our approach is significantly faster in generating
worst-case executions compared to fuzzing or symbolic execution on their own
A static cost analysis for a higher-order language
We develop a static complexity analysis for a higher-order functional
language with structural list recursion. The complexity of an expression is a
pair consisting of a cost and a potential. The former is defined to be the size
of the expression's evaluation derivation in a standard big-step operational
semantics. The latter is a measure of the "future" cost of using the value of
that expression. A translation function tr maps target expressions to
complexities. Our main result is the following Soundness Theorem: If t is a
term in the target language, then the cost component of tr(t) is an upper bound
on the cost of evaluating t. The proof of the Soundness Theorem is formalized
in Coq, providing certified upper bounds on the cost of any expression in the
target language.Comment: Final versio
On Multiphase-Linear Ranking Functions
Multiphase ranking functions () were proposed as a means
to prove the termination of a loop in which the computation progresses through
a number of "phases", and the progress of each phase is described by a
different linear ranking function. Our work provides new insights regarding
such functions for loops described by a conjunction of linear constraints
(single-path loops). We provide a complete polynomial-time solution to the
problem of existence and of synthesis of of bounded depth
(number of phases), when variables range over rational or real numbers; a
complete solution for the (harder) case that variables are integer, with a
matching lower-bound proof, showing that the problem is coNP-complete; and a
new theorem which bounds the number of iterations for loops with
. Surprisingly, the bound is linear, even when the
variables involved change in non-linear way. We also consider a type of
lexicographic ranking functions, , more expressive than types
of lexicographic functions for which complete solutions have been given so far.
We prove that for the above type of loops, lexicographic functions can be
reduced to , and thus the questions of complexity of
detection and synthesis, and of resulting iteration bounds, are also answered
for this class.Comment: typos correcte
A General Framework for Static Profiling of Parametric Resource Usage
Traditional static resource analyses estimate the total resource usage of a
program, without executing it. In this paper we present a novel resource
analysis whose aim is instead the static profiling of accumulated cost, i.e.,
to discover, for selected parts of the program, an estimate or bound of the
resource usage accumulated in each of those parts. Traditional resource
analyses are parametric in the sense that the results can be functions on input
data sizes. Our static profiling is also parametric, i.e., our accumulated cost
estimates are also parameterized by input data sizes. Our proposal is based on
the concept of cost centers and a program transformation that allows the static
inference of functions that return bounds on these accumulated costs depending
on input data sizes, for each cost center of interest. Such information is much
more useful to the software developer than the traditional resource usage
functions, as it allows identifying the parts of a program that should be
optimized, because of their greater impact on the total cost of program
executions. We also report on our implementation of the proposed technique
using the CiaoPP program analysis framework, and provide some experimental
results. This paper is under consideration for acceptance in TPLP.Comment: Paper presented at the 32nd International Conference on Logic
Programming (ICLP 2016), New York City, USA, 16-21 October 2016, 22 pages,
LaTe
Summary-based inference of quantitative bounds of live heap objects
This article presents a symbolic static analysis for computing parametric upper bounds of the number of simultaneously live objects of sequential Java-like programs. Inferring the peak amount of irreclaimable objects is the cornerstone for analyzing potential heap-memory consumption of stand-alone applications or libraries. The analysis builds method-level summaries quantifying the peak number of live objects and the number of escaping objects. Summaries are built by resorting to summaries of their callees. The usability, scalability and precision of the technique is validated by successfully predicting the object heap usage of a medium-size, real-life application which is significantly larger than other previously reported case-studies.Fil: Braberman, Victor Adrian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Garbervetsky, Diego David. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Hym, Samuel. Universite Lille 3; FranciaFil: Yovine, Sergio Fabian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin