66,331 research outputs found
A Simple and Scalable Static Analysis for Bound Analysis and Amortized Complexity Analysis
We present the first scalable bound analysis that achieves amortized
complexity analysis. In contrast to earlier work, our bound analysis is not
based on general purpose reasoners such as abstract interpreters, software
model checkers or computer algebra tools. Rather, we derive bounds directly
from abstract program models, which we obtain from programs by comparatively
simple invariant generation and symbolic execution techniques. As a result, we
obtain an analysis that is more predictable and more scalable than earlier
approaches. Our experiments demonstrate that our analysis is fast and at the
same time able to compute bounds for challenging loops in a large real-world
benchmark. Technically, our approach is based on lossy vector addition systems
(VASS). Our bound analysis first computes a lexicographic ranking function that
proves the termination of a VASS, and then derives a bound from this ranking
function. Our methodology achieves amortized analysis based on a new insight
how lexicographic ranking functions can be used for bound analysis
Combining k-Induction with Continuously-Refined Invariants
Bounded model checking (BMC) is a well-known and successful technique for
finding bugs in software. k-induction is an approach to extend BMC-based
approaches from falsification to verification. Automatically generated
auxiliary invariants can be used to strengthen the induction hypothesis. We
improve this approach and further increase effectiveness and efficiency in the
following way: we start with light-weight invariants and refine these
invariants continuously during the analysis. We present and evaluate an
implementation of our approach in the open-source verification-framework
CPAchecker. Our experiments show that combining k-induction with
continuously-refined invariants significantly increases effectiveness and
efficiency, and outperforms all existing implementations of k-induction-based
software verification in terms of successful verification results.Comment: 12 pages, 5 figures, 2 tables, 2 algorithm
Lepton Flavour Violating top decays at the LHC
We consider lepton flavour violating decays of the top quark, mediated by
four-fermion operators. We compile constraints on a complete set of
SU(3)*U(1)-invariant operators, arising from their loop contributions to rare
decays and from HERA's single top search. The bounds on e-mu flavour change are
more restrictive than l-tau; nonetheless the top could decay to a jet with a branching ratio of order . We estimate that the
currently available LHC data (20 inverse-fb at 8 TeV) could be sensitive to
+ jet) , and extrapolate that 100
inverse-fb at 13 TeV could reach a sensitivity of .Comment: 10 pages + Appendice
Invariant Generation for Multi-Path Loops with Polynomial Assignments
Program analysis requires the generation of program properties expressing
conditions to hold at intermediate program locations. When it comes to programs
with loops, these properties are typically expressed as loop invariants. In
this paper we study a class of multi-path program loops with numeric variables,
in particular nested loops with conditionals, where assignments to program
variables are polynomial expressions over program variables. We call this class
of loops extended P-solvable and introduce an algorithm for generating all
polynomial invariants of such loops. By an iterative procedure employing
Gr\"obner basis computation, our approach computes the polynomial ideal of the
polynomial invariants of each program path and combines these ideals
sequentially until a fixed point is reached. This fixed point represents the
polynomial ideal of all polynomial invariants of the given extended P-solvable
loop. We prove termination of our method and show that the maximal number of
iterations for reaching the fixed point depends linearly on the number of
program variables and the number of inner loops. In particular, for a loop with
m program variables and r conditional branches we prove an upper bound of m*r
iterations. We implemented our approach in the Aligator software package.
Furthermore, we evaluated it on 18 programs with polynomial arithmetic and
compared it to existing methods in invariant generation. The results show the
efficiency of our approach
Succinct Representations for Abstract Interpretation
Abstract interpretation techniques can be made more precise by distinguishing
paths inside loops, at the expense of possibly exponential complexity.
SMT-solving techniques and sparse representations of paths and sets of paths
avoid this pitfall. We improve previously proposed techniques for guided static
analysis and the generation of disjunctive invariants by combining them with
techniques for succinct representations of paths and symbolic representations
for transitions based on static single assignment. Because of the
non-monotonicity of the results of abstract interpretation with widening
operators, it is difficult to conclude that some abstraction is more precise
than another based on theoretical local precision results. We thus conducted
extensive comparisons between our new techniques and previous ones, on a
variety of open-source packages.Comment: Static analysis symposium (SAS), Deauville : France (2012
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