2,559 research outputs found
Loops under Strategies ... Continued
While there are many approaches for automatically proving termination of term
rewrite systems, up to now there exist only few techniques to disprove their
termination automatically. Almost all of these techniques try to find loops,
where the existence of a loop implies non-termination of the rewrite system.
However, most programming languages use specific evaluation strategies, whereas
loop detection techniques usually do not take strategies into account. So even
if a rewrite system has a loop, it may still be terminating under certain
strategies.
Therefore, our goal is to develop decision procedures which can determine
whether a given loop is also a loop under the respective evaluation strategy.
In earlier work, such procedures were presented for the strategies of
innermost, outermost, and context-sensitive evaluation. In the current paper,
we build upon this work and develop such decision procedures for important
strategies like leftmost-innermost, leftmost-outermost,
(max-)parallel-innermost, (max-)parallel-outermost, and forbidden patterns
(which generalize innermost, outermost, and context-sensitive strategies). In
this way, we obtain the first approach to disprove termination under these
strategies automatically.Comment: In Proceedings IWS 2010, arXiv:1012.533
Tiramisu: A Polyhedral Compiler for Expressing Fast and Portable Code
This paper introduces Tiramisu, a polyhedral framework designed to generate
high performance code for multiple platforms including multicores, GPUs, and
distributed machines. Tiramisu introduces a scheduling language with novel
extensions to explicitly manage the complexities that arise when targeting
these systems. The framework is designed for the areas of image processing,
stencils, linear algebra and deep learning. Tiramisu has two main features: it
relies on a flexible representation based on the polyhedral model and it has a
rich scheduling language allowing fine-grained control of optimizations.
Tiramisu uses a four-level intermediate representation that allows full
separation between the algorithms, loop transformations, data layouts, and
communication. This separation simplifies targeting multiple hardware
architectures with the same algorithm. We evaluate Tiramisu by writing a set of
image processing, deep learning, and linear algebra benchmarks and compare them
with state-of-the-art compilers and hand-tuned libraries. We show that Tiramisu
matches or outperforms existing compilers and libraries on different hardware
architectures, including multicore CPUs, GPUs, and distributed machines.Comment: arXiv admin note: substantial text overlap with arXiv:1803.0041
Sequential Implementation of Monte Carlo Tests with Uniformly Bounded Resampling Risk
This paper introduces an open-ended sequential algorithm for computing the
p-value of a test using Monte Carlo simulation. It guarantees that the
resampling risk, the probability of a different decision than the one based on
the theoretical p-value, is uniformly bounded by an arbitrarily small constant.
Previously suggested sequential or non-sequential algorithms, using a bounded
sample size, do not have this property. Although the algorithm is open-ended,
the expected number of steps is finite, except when the p-value is on the
threshold between rejecting and not rejecting. The algorithm is suitable as
standard for implementing tests that require (re-)sampling. It can also be used
in other situations: to check whether a test is conservative, iteratively to
implement double bootstrap tests, and to determine the sample size required for
a certain power.Comment: Major Revision 15 pages, 4 figure
The orbital structure of a tidally induced bar
Orbits are the key building blocks of any density distribution and their
study helps us understand the kinematical structure and the evolution of
galaxies. Here we investigate orbits in a tidally induced bar of a dwarf
galaxy, using an -body simulation of an initially disky dwarf galaxy
orbiting a Milky Way-like host. After the first pericenter passage, a tidally
induced bar forms in the stellar component of the dwarf. The bar evolution is
different than in isolated galaxies and our analysis focuses on the period
before it buckles. We study the orbits in terms of their dominant frequencies,
which we calculate in a Cartesian coordinate frame rotating with the bar. Apart
from the well-known x orbits we find many other types, mostly with boxy
shapes of various degree of elongation. Some of them are also near-periodic,
admitting frequency ratios of 4/3, 3/2 and 5/3. The box orbits have various
degrees of vertical thickness but only a relatively small fraction of those
have banana (i.e. smile/frown) or infinity-symbol shapes in the edge-on view.
In the very center we also find orbits known from the potential of triaxial
ellipsoids. The elongation of the orbits grows with distance from the center of
the bar in agreement with the variation of the shape of the density
distribution. Our classification of orbits leads to the conclusion that more
than of them have boxy shapes, while only have shapes of
classical x orbits.Comment: 15 pages, 15 figures, accepted for publication in Ap
Certification of nontermination proofs using strategies and nonlooping derivations
© 2014 Springer International Publishing Switzerland. The development of sophisticated termination criteria for term rewrite systems has led to powerful and complex tools that produce (non)termination proofs automatically. While many techniques to establish termination have already been formalized—thereby allowing to certify such proofs—this is not the case for nontermination. In particular, the proof checker CeTA was so far limited to (innermost) loops. In this paper we present an Isabelle/HOL formalization of an extended repertoire of nontermination techniques. First, we formalized techniques for nonlooping nontermination. Second, the available strategies include (an extended version of) forbidden patterns, which cover in particular outermost and context-sensitive rewriting. Finally, a mechanism to support partial nontermination proofs further extends the applicability of our proof checker
Decision Procedures for Loop Detection
The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems. We first show that dependency pairs are also suitable for disproving termination: loops can be detected more easily.
In a second step we analyze how to disprove innermost termination. Here, we present a novel procedure to decide whether a given loop is an innermost loop.
All results have been implemented in the termination prover AProVE
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