3,300 research outputs found
The Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an
important key to understanding the loop behavior, proving its termination and
establishing iteration bounds. If no preconditions are provided, the decision
problem is known to be in coNP when variables range over the integers and in
PTIME for the rational numbers, or real numbers. Here we show that deciding
whether a linear-constraint loop with a precondition, specifically with
partially-specified input, has a linear ranking function is EXPSPACE-hard over
the integers, and PSPACE-hard over the rationals. The precise complexity of
these decision problems is yet unknown. The EXPSPACE lower bound is derived
from the reachability problem for Petri nets (equivalently, Vector Addition
Systems), and possibly indicates an even stronger lower bound (subject to open
problems in VAS theory). The lower bound for the rationals follows from a novel
simulation of Boolean programs. Lower bounds are also given for the problem of
deciding if a linear ranking-function supported by a particular form of
inductive invariant exists. For loops over integers, the problem is PSPACE-hard
for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of
natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers
of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State
Systems", for the opportunity to present an early draft of this wor
Termination Analysis by Learning Terminating Programs
We present a novel approach to termination analysis. In a first step, the
analysis uses a program as a black-box which exhibits only a finite set of
sample traces. Each sample trace is infinite but can be represented by a finite
lasso. The analysis can "learn" a program from a termination proof for the
lasso, a program that is terminating by construction. In a second step, the
analysis checks that the set of sample traces is representative in a sense that
we can make formal. An experimental evaluation indicates that the approach is a
potentially useful addition to the portfolio of existing approaches to
termination analysis
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
Synthesis for Polynomial Lasso Programs
We present a method for the synthesis of polynomial lasso programs. These
programs consist of a program stem, a set of transitions, and an exit
condition, all in the form of algebraic assertions (conjunctions of polynomial
equalities). Central to this approach is the discovery of non-linear
(algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's
template-based approach and prove a completeness criterion. We perform program
synthesis by generating a constraint whose solution is a synthesized program
together with a loop invariant that proves the program's correctness. This
constraint is non-linear and is passed to an SMT solver. Moreover, we can
enforce the termination of the synthesized program with the support of test
cases.Comment: Paper at VMCAI'14, including appendi
Testing for knowledge : maximising information obtained from fire tests by using machine learning techniques
A machine learning (ML) algorithm was applied to predict the onset of flashover in 1:5 scale Room Corner Test experiments with sandwich panels. Towards this end, a penalized logistic regression model was chosen to detect the relevant variables and consequently provided a tool that can be used to make predictions of unseen samples. The method indicates that a deeper understanding of the contributing factors leading to flashover can be achieved. Furthermore, it allows a more nuanced ranking than currently offered by the commonly used classification methods for reaction to fire tests. The proposed methodology shows a substantial value in terms of guidance for future large and intermediate scale testing. In particular, it is foreseen that the method will be extremely useful for assessing and understanding the behaviour of innovative materials and design solutions
Non-convex Global Minimization and False Discovery Rate Control for the TREX
The TREX is a recently introduced method for performing sparse
high-dimensional regression. Despite its statistical promise as an alternative
to the lasso, square-root lasso, and scaled lasso, the TREX is computationally
challenging in that it requires solving a non-convex optimization problem. This
paper shows a remarkable result: despite the non-convexity of the TREX problem,
there exists a polynomial-time algorithm that is guaranteed to find the global
minimum. This result adds the TREX to a very short list of non-convex
optimization problems that can be globally optimized (principal components
analysis being a famous example). After deriving and developing this new
approach, we demonstrate that (i) the ability of the preexisting TREX heuristic
to reach the global minimum is strongly dependent on the difficulty of the
underlying statistical problem, (ii) the new polynomial-time algorithm for TREX
permits a novel variable ranking and selection scheme, (iii) this scheme can be
incorporated into a rule that controls the false discovery rate (FDR) of
included features in the model. To achieve this last aim, we provide an
extension of the results of Barber & Candes (2015) to establish that the
knockoff filter framework can be applied to the TREX. This investigation thus
provides both a rare case study of a heuristic for non-convex optimization and
a novel way of exploiting non-convexity for statistical inference
- …