اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAligator.jl - A Julia Package for Loop Invariant Generation
170
0
0.0
(
0
)
نشر من قبل
Andreas Humenberger
تاريخ النشر
2018
مجال البحث
الهندسة المعلوماتية
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Aligator.jl is written in the programming language Julia and is open-source. Aligator.jl transforms program loops into a system of algebraic recurrences and implements techniques from symbolic computation to solve recurrences, derive closed form solutions of loop variables and infer the ideal of polynomial invariants by variable elimination based on Grobner basis computation.
قيم البحث
اقرأ أيضاً
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python framework. There a
re libraries for Julia that cover the majority of scientific and engineering computations demands. The aim of this paper is to combine the usage of the Julia framework for numerical computations and for symbolic computations in mathematical modeling problems. The main functional domains determining various variants of the application of computer algebra systems are described. In each of these domains, generic representatives of computer algebra systems in Julia are distinguished. The conclusion is that it is possible (and even convenient) to use computer algebra systems within the Julia framework.
Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed open sourc
e software, which is available in many programming languages. In this paper, we present a tutorial of the GaussianProcesses.jl package that has been developed for the Julia programming language. GaussianProcesses.jl utilises the inherent computational benefits of the Julia language, including multiple dispatch and just-in-time compilation, to produce a fast, flexible and user-friendly Gaussian processes package. The package provides many mean and kernel functions with supporting inference tools to fit exact Gaussian process models, as well as a range of alternative likelihood functions to handle non-Gaussian data (e.g. binary classification models) and sparse approximations for scalable Gaussian processes. The package makes efficient use of existing Julia packages to provide users with a range of optimization and plotting tools.
Analyzing and reasoning about safety properties of software systems becomes an especially challenging task for programs with complex flow and, in particular, with loops or recursion. For such programs one needs additional information, for example in
the form of loop invariants, expressing properties to hold at intermediate program points. In this paper we study program loops with non-trivial arithmetic, implementing addition and multiplication among numeric program variables. We present a new approach for automatically generating all polynomial invariants of a class of such programs. Our approach turns programs into linear ordinary recurrence equations and computes closed form solutions of these equations. These closed forms express the most precise inductive property, and hence invariant. We apply Grobner basis computation to obtain a basis of the polynomial invariant ideal, yielding thus a finite representation of all polynomial invariants. Our work significantly extends the class of so-called P-solvable loops by handling multiplication with the loop counter variable. We implemented our method in the Mathematica package Aligator and showcase the practical use of our approach.
Background. It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic models. Auth
ors have improved the method of stochastic models construction for the class of one-step processes and illustrated by models of population dynamics. Population dynamics was chosen for study because its deterministic models were sufficiently well explored that allows to compare the results with already known ones. Purpose. To optimize the models creation as much as possible some routine operations should be automated. In this case, the process of drawing up the model equations can be algorithmized and implemented in the computer algebra system. Furthermore, on the basis of these results a set of programs for numerical experiment can be obtained. Method. The computer algebra system Axiom is used for analytical calculations implementation. To perform the numerical experiment FORTRAN and Julia languages are used. The method Runge--Kutta method for stochastic differential equations is used as numerical method. Results. The program compex for creating stochastic one-step processes models is constructed. Its application is illustrated by the predator-prey population dynamic system. Conclusions. Computer algebra systems are very convenient for the purposes of rapid prototyping in mathematical models design and analysis.
We prove fixed point results for branched covering maps $f$ of the plane. For complex polynomials $P$ with Julia set $J_P$ these imply that periodic cutpoints of some invariant subcontinua of $J_P$ are also cutpoints of $J_P$. We deduce that, under c
ertain assumptions on invariant subcontinua $Q$ of $J_P$, every Riemann ray to $Q$ landing at a periodic repelling/parabolic point $xin Q$ is isotopic to a Riemann ray to $J_P$ relative to $Q$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
