4,077 research outputs found
Proving Non-Termination via Loop Acceleration
We present the first approach to prove non-termination of integer programs
that is based on loop acceleration. If our technique cannot show
non-termination of a loop, it tries to accelerate it instead in order to find
paths to other non-terminating loops automatically. The prerequisites for our
novel loop acceleration technique generalize a simple yet effective
non-termination criterion. Thus, we can use the same program transformations to
facilitate both non-termination proving and loop acceleration. In particular,
we present a novel invariant inference technique that is tailored to our
approach. An extensive evaluation of our fully automated tool LoAT shows that
it is competitive with the state of the art
Loop Quasi-Invariant Chunk Motion by peeling with statement composition
Several techniques for analysis and transformations are used in compilers.
Among them, the peeling of loops for hoisting quasi-invariants can be used to
optimize generated code, or simply ease developers' lives. In this paper, we
introduce a new concept of dependency analysis borrowed from the field of
Implicit Computational Complexity (ICC), allowing to work with composed
statements called Chunks to detect more quasi-invariants. Based on an
optimization idea given on a WHILE language, we provide a transformation method
- reusing ICC concepts and techniques - to compilers. This new analysis
computes an invariance degree for each statement or chunks of statements by
building a new kind of dependency graph, finds the maximum or worst dependency
graph for loops, and recognizes if an entire block is Quasi-Invariant or not.
This block could be an inner loop, and in that case the computational
complexity of the overall program can be decreased. We already implemented a
proof of concept on a toy C parser 1 analysing and transforming the AST
representation. In this paper, we introduce the theory around this concept and
present a prototype analysis pass implemented on LLVM. In a very near future,
we will implement the corresponding transformation and provide benchmarks
comparisons.Comment: In Proceedings DICE-FOPARA 2017, arXiv:1704.0516
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Variational method for locating invariant tori
We formulate a variational fictitious-time flow which drives an initial guess
torus to a torus invariant under given dynamics. The method is general and
applies in principle to continuous time flows and discrete time maps in
arbitrary dimension, and to both Hamiltonian and dissipative systems.Comment: 10 page
Recurrence with affine level mappings is P-time decidable for CLP(R)
In this paper we introduce a class of constraint logic programs such that
their termination can be proved by using affine level mappings. We show that
membership to this class is decidable in polynomial time.Comment: To appear in Theory and Practice of Logic Programming (TPLP
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
Generalized Global Symmetries
A -form global symmetry is a global symmetry for which the charged
operators are of space-time dimension ; e.g. Wilson lines, surface defects,
etc., and the charged excitations have spatial dimensions; e.g. strings,
membranes, etc. Many of the properties of ordinary global symmetries (=0)
apply here. They lead to Ward identities and hence to selection rules on
amplitudes. Such global symmetries can be coupled to classical background
fields and they can be gauged by summing over these classical fields. These
generalized global symmetries can be spontaneously broken (either completely or
to a subgroup). They can also have 't Hooft anomalies, which prevent us from
gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies
can also lead to anomaly inflow on various defects and exotic Symmetry
Protected Topological phases. Our analysis of these symmetries gives a new
unified perspective of many known phenomena and uncovers new results.Comment: 49 pages plus appendices. v2: references adde
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