6,814 research outputs found
On Quasi-Interpretations, Blind Abstractions and Implicit Complexity
Quasi-interpretations are a technique to guarantee complexity bounds on
first-order functional programs: with termination orderings they give in
particular a sufficient condition for a program to be executable in polynomial
time, called here the P-criterion. We study properties of the programs
satisfying the P-criterion, in order to better understand its intensional
expressive power. Given a program on binary lists, its blind abstraction is the
nondeterministic program obtained by replacing lists by their lengths (natural
numbers). A program is blindly polynomial if its blind abstraction terminates
in polynomial time. We show that all programs satisfying a variant of the
P-criterion are in fact blindly polynomial. Then we give two extensions of the
P-criterion: one by relaxing the termination ordering condition, and the other
one (the bounded value property) giving a necessary and sufficient condition
for a program to be polynomial time executable, with memoisation.Comment: 18 page
Compositional uniformity, domain patterning and the mechanism underlying nano-chessboard arrays
We propose that systems exhibiting compositional patterning at the nanoscale,
so far assumed to be due to some kind of ordered phase segregation, can be
understood instead in terms of coherent, single phase ordering of minority
motifs, caused by some constrained drive for uniformity. The essential features
of this type of arrangements can be reproduced using a superspace construction
typical of uniformity-driven orderings, which only requires the knowledge of
the modulation vectors observed in the diffraction patterns. The idea is
discussed in terms of a simple two dimensional lattice-gas model that simulates
a binary system in which the dilution of the minority component is favored.
This simple model already exhibits a hierarchy of arrangements similar to the
experimentally observed nano-chessboard and nano-diamond patterns, which are
described as occupational modulated structures with two independent modulation
wave vectors and simple step-like occupation modulation functions.Comment: Preprint. 11 pages, 11 figure
On the Model of Computation of Place/Transition Petri Nets
In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game", one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. More precisely, we introduce the new notion of decorated processes of Petri nets and we show that they induce on nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net N can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification
Process versus Unfolding Semantics for Place/Transition Petri Nets
In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification
Blazes: Coordination Analysis for Distributed Programs
Distributed consistency is perhaps the most discussed topic in distributed
systems today. Coordination protocols can ensure consistency, but in practice
they cause undesirable performance unless used judiciously. Scalable
distributed architectures avoid coordination whenever possible, but
under-coordinated systems can exhibit behavioral anomalies under fault, which
are often extremely difficult to debug. This raises significant challenges for
distributed system architects and developers. In this paper we present Blazes,
a cross-platform program analysis framework that (a) identifies program
locations that require coordination to ensure consistent executions, and (b)
automatically synthesizes application-specific coordination code that can
significantly outperform general-purpose techniques. We present two case
studies, one using annotated programs in the Twitter Storm system, and another
using the Bloom declarative language.Comment: Updated to include additional materials from the original technical
report: derivation rules, output stream label
A combinatorial analysis of Severi degrees
Based on results by Brugall\'e and Mikhalkin, Fomin and Mikhalkin give
formulas for computing classical Severi degrees using long-edge
graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version
of a special function associated to long-edge graphs appeared in
Fomin-Mikhalkin's formula, and conjectured it to be linear. They have since
proved their conjecture. At the same time, motivated by their conjecture, we
consider a special multivariate function associated to long-edge graphs that
generalizes their function. The main result of this paper is that the
multivariate function we define is always linear. A special case of our result
gives an independent proof of Block-Colley-Kennedy's conjecture.
The first application of our linearity result is that by applying it to
classical Severi degrees, we recover quadraticity of and a
bound for the threshold of polynomiality of Next, in
joint work with Osserman, we apply the linearity result to a special family of
toric surfaces and obtain universal polynomial results having connections to
the G\"ottsche-Yau-Zaslow formula. As a result, we provide combinatorial
formulas for the two unidentified power series and appearing
in the G\"ottsche-Yau-Zaslow formula.
The proof of our linearity result is completely combinatorial. We define
-graphs which generalize long-edge graphs, and a closely related family
of combinatorial objects we call -words. By introducing height
functions and a concept of irreducibility, we describe ways to decompose
certain families of -words into irreducible words, which leads to
the desired results.Comment: 38 pages, 1 figure, 1 table. Major revision: generalized main results
in previous version. The old results only applies to classical Severi
degrees. The current version also applies to Severi degrees coming from
special families of toric surface
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
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