30,339 research outputs found
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
Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: general solution and main properties
We analyze the non-Markovian dynamics of a quantum system subject to
spontaneous collapse in space. After having proved, under suitable conditions,
the separation of the center-of-mass and relative motions, we focus our
analysis on the time evolution of the center of mass of an isolated system
(free particle case). We compute the explicit expression of the Green's
function, for a generic Gaussian noise, and analyze in detail the case of an
exponential correlation function. We study the time evolution of average
quantities, such as the mean position, momentum and energy. We eventually
specialize to the case of Gaussian wave functions, and prove that all basic
facts about collapse models, which are known to be true in the white noise
case, hold also in the more general case of non-Markovian dynamics.Comment: 37 pages, LaTeX. Title changed. Other minor correction
Formalizing Termination Proofs under Polynomial Quasi-interpretations
Usual termination proofs for a functional program require to check all the
possible reduction paths. Due to an exponential gap between the height and size
of such the reduction tree, no naive formalization of termination proofs yields
a connection to the polynomial complexity of the given program. We solve this
problem employing the notion of minimal function graph, a set of pairs of a
term and its normal form, which is defined as the least fixed point of a
monotone operator. We show that termination proofs for programs reducing under
lexicographic path orders (LPOs for short) and polynomially quasi-interpretable
can be optimally performed in a weak fragment of Peano arithmetic. This yields
an alternative proof of the fact that every function computed by an
LPO-terminating, polynomially quasi-interpretable program is computable in
polynomial space. The formalization is indeed optimal since every
polynomial-space computable function can be computed by such a program. The
crucial observation is that inductive definitions of minimal function graphs
under LPO-terminating programs can be approximated with transfinite induction
along LPOs.Comment: In Proceedings FICS 2015, arXiv:1509.0282
A Constrained Path Monte Carlo Method for Fermion Ground States
We describe and discuss a recently proposed quantum Monte Carlo algorithm to
compute the ground-state properties of various systems of interacting fermions.
In this method, the ground state is projected from an initial wave function by
a branching random walk in an over-complete basis of Slater determinants. By
constraining the determinants according to a trial wave function
, we remove the exponential decay of signal-to-noise ratio
characteristic of the sign problem. The method is variational and is exact if
is exact. We illustrate the method by describing in detail its
implementation for the two-dimensional one-band Hubbard model. We show results
for lattice sizes up to and for various electron fillings and
interaction strengths. Besides highly accurate estimates of the ground-state
energy, we find that the method also yields reliable estimates of other
ground-state observables, such as superconducting pairing correlation
functions. We conclude by discussing possible extensions of the algorithm.Comment: 29 pages, RevTex, 3 figures included; submitted to Phys. Rev.
Synthesis of sup-interpretations: a survey
In this paper, we survey the complexity of distinct methods that allow the
programmer to synthesize a sup-interpretation, a function providing an upper-
bound on the size of the output values computed by a program. It consists in a
static space analysis tool without consideration of the time consumption.
Although clearly related, sup-interpretation is independent from termination
since it only provides an upper bound on the terminating computations. First,
we study some undecidable properties of sup-interpretations from a theoretical
point of view. Next, we fix term rewriting systems as our computational model
and we show that a sup-interpretation can be obtained through the use of a
well-known termination technique, the polynomial interpretations. The drawback
is that such a method only applies to total functions (strongly normalizing
programs). To overcome this problem we also study sup-interpretations through
the notion of quasi-interpretation. Quasi-interpretations also suffer from a
drawback that lies in the subterm property. This property drastically restricts
the shape of the considered functions. Again we overcome this problem by
introducing a new notion of interpretations mainly based on the dependency
pairs method. We study the decidability and complexity of the
sup-interpretation synthesis problem for all these three tools over sets of
polynomials. Finally, we take benefit of some previous works on termination and
runtime complexity to infer sup-interpretations.Comment: (2012
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