Automatic Abstraction in SMT-Based Unbounded Software Model Checking

Software model checkers based on under-approximations and SMT solvers are very successful at verifying safety (i.e. reachability) properties. They combine two key ideas -- (a) "concreteness": a counterexample in an under-approximation is a counterexample in the original program as well, and (b) "generalization": a proof of safety of an under-approximation, produced by an SMT solver, are generalizable to proofs of safety of the original program. In this paper, we present a combination of "automatic abstraction" with the under-approximation-driven framework. We explore two iterative approaches for obtaining and refining abstractions -- "proof based" and "counterexample based" -- and show how they can be combined into a unified algorithm. To the best of our knowledge, this is the first application of Proof-Based Abstraction, primarily used to verify hardware, to Software Verification. We have implemented a prototype of the framework using Z3, and evaluate it on many benchmarks from the Software Verification Competition. We show experimentally that our combination is quite effective on hard instances.Comment: Extended version of a paper in the proceedings of CAV 201

On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents

Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In particular we show that the replacement, in FSS analyses, of the correlation length by its asymptotic scaling form can lead to apparently good scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page

The Astrophysical Multipurpose Software Environment

We present the open source Astrophysical Multi-purpose Software Environment (AMUSE, www.amusecode.org), a component library for performing astrophysical simulations involving different physical domains and scales. It couples existing codes within a Python framework based on a communication layer using MPI. The interfaces are standardized for each domain and their implementation based on MPI guarantees that the whole framework is well-suited for distributed computation. It includes facilities for unit handling and data storage. Currently it includes codes for gravitational dynamics, stellar evolution, hydrodynamics and radiative transfer. Within each domain the interfaces to the codes are as similar as possible. We describe the design and implementation of AMUSE, as well as the main components and community codes currently supported and we discuss the code interactions facilitated by the framework. Additionally, we demonstrate how AMUSE can be used to resolve complex astrophysical problems by presenting example applications.Comment: 23 pages, 25 figures, accepted for A&

Statistics of lowest excitations in two dimensional Gaussian spin glasses

A detailed investigation of lowest excitations in two-dimensional Gaussian spin glasses is presented. We show the existence of a new zero-temperature exponent lambda describing the relative number of finite-volume excitations with respect to large-scale ones. This exponent yields the standard thermal exponent of droplet theory theta through the relation, theta=d(lambda-1). Our work provides a new way to measure the thermal exponent theta without any assumption about the procedure to generate typical low-lying excitations. We find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal exponent obtained in domain-wall theory showing that MacMillan excitations are not typical.Comment: 4 pages, 3 figures, (v2) revised version, (v3) corrected typo

Phase Transition in the Three-Dimensional ±J\pm J Ising Spin Glass

We have studied the three-dimensional Ising spin glass with a $\pm J$ distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, $T_c$, with ordering below $T_c$. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, $\nu$, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that $T_c = 0$ or that $T_c$ is finite but with no order below $T_c$. However, from our data, these possibilities seem less likely.Comment: Postscript file compressed using uufiles. The postscript file is also available by anonymous ftp at ftp://chopin.ucsc.edu/pub/sg3d.p

A simple abstraction of arrays and maps by program translation

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm

Energetics and geometry of excitations in random systems

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk perturbations. The numerical data support the assumptions of compact droplets and a single exponent for droplet energy scaling. Analytic calculations show how strong corrections to power laws can result when samples and droplets are averaged over. Such corrections can explain apparent discrepancies in several previous numerical results for spin glasses.Comment: 4 pages, eps files include

General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems

Reconsidering the variational procedure for uniaxial systems modeled by continuous free energy functionals, we derive new general conditions for thermodynamic extrema. The utility of these conditions is briefly illustrated on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let