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Using ACL2 in the Design of Efficient, Verifiable Data Structures for High-Assurance Systems 利用ACL2设计高效、可验证的高保证系统数据结构
Pub Date : 2018-10-10 DOI: 10.4204/EPTCS.280.5
D. Hardin, Konrad Slind
Verification of algorithms and data structures utilized in modern autonomous and semi-autonomous vehicles for land, sea, air, and space presents a significant challenge. Autonomy algorithms, e.g., route planning, pattern matching, and inference, are based on complex data structures such as directed graphs and algebraic data types. Proof techniques for these data structures exist, but are oriented to unbounded, functional realizations, which are not typically efficient in either space or time. Autonomous systems designers, on the other hand, generally limit the space and time allocations for any given function, and require that algorithms deliver results within a finite time, or suffer a watchdog timeout. Furthermore, high-assurance design rules frown on dynamic memory allocation, preferring simple array-based data structure implementations. In order to provide efficient implementations of high-level data structures used in autonomous systems with the high assurance needed for accreditation, we have developed a verifying compilation technique that supports the "natural" functional proof style, but yet applies to more efficient data structure implementations. Our toolchain features code generation to mainstream programming languages, as well as GPU-based and hardware-based realizations. We base the Intermediate Verification Language for our toolchain upon higher-order logic; however, we have used ACL2 to develop our efficient yet verifiable data structure design. ACL2 is particularly well-suited for this work, with its sophisticated libraries for reasoning about aggregate data structures of arbitrary size, efficient execution of formal specifications, as well as its support for "single-threaded objects" -- functional datatypes with imperative "under the hood" implementations. In this paper, we detail our high-assurance data structure design approach, including examples in ACL2 of common algebraic data types implemented using this design approach, proofs of correctness for those data types carried out in ACL2, as well as sample ACL2 implementations of relevant algorithms utilizing these efficient, high-assurance data structures.
验证用于陆地、海上、空中和太空的现代自主和半自主车辆的算法和数据结构提出了重大挑战。自治算法,如路线规划、模式匹配和推理,都是基于复杂的数据结构,如有向图和代数数据类型。这些数据结构的证明技术是存在的,但它们面向无界的功能实现,通常在空间或时间上都不是有效的。另一方面,自治系统设计者通常会限制任何给定功能的空间和时间分配,并要求算法在有限时间内交付结果,否则会遭受看门狗超时。此外,高保证设计规则不赞成动态内存分配,更喜欢简单的基于数组的数据结构实现。为了在具有认证所需的高保证的自治系统中提供高级数据结构的有效实现,我们开发了一种验证编译技术,该技术支持“自然”功能证明风格,但仍适用于更有效的数据结构实现。我们的工具链具有主流编程语言的代码生成功能,以及基于gpu和基于硬件的实现。我们将工具链的中间验证语言建立在高阶逻辑之上;然而,我们已经使用ACL2来开发我们高效且可验证的数据结构设计。ACL2特别适合这项工作,它有复杂的库来推断任意大小的聚合数据结构,有效地执行正式规范,以及它对“单线程对象”的支持——具有“底层”实现的命令式功能数据类型。在本文中,我们详细介绍了我们的高保证数据结构设计方法,包括在ACL2中使用这种设计方法实现的常见代数数据类型的示例,在ACL2中执行的这些数据类型的正确性证明,以及利用这些高效,高保证数据结构的相关算法的ACL2实现示例。
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引用次数: 3
A Simple Java Code Generator for ACL2 Based on a Deep Embedding of ACL2 in Java 基于ACL2在Java中的深度嵌入的简单的ACL2 Java代码生成器
Pub Date : 2018-10-10 DOI: 10.4204/EPTCS.280.1
A. Coglio
AIJ (ACL2 In Java) is a deep embedding in Java of an executable, side-effect-free, non-stobj-accessing subset of the ACL2 language without guards. ATJ (ACL2 To Java) is a simple Java code generator that turns ACL2 functions into AIJ representations that are evaluated by the AIJ interpreter. AIJ and ATJ enable possibly verified ACL2 code to run as, and interoperate with, Java code, without much of the ACL2 framework or any of the Lisp runtime. The current speed of the resulting Java code may be adequate to some applications.
AIJ (Java中的ACL2)是在Java中深度嵌入一个可执行的、无副作用的、不访问stobj的、没有保护的ACL2语言子集。ATJ (ACL2 To Java)是一个简单的Java代码生成器,它将ACL2函数转换为AIJ表示,并由AIJ解释器进行计算。AIJ和ATJ使可能经过验证的ACL2代码能够作为Java代码运行并与之互操作,而不需要太多的ACL2框架或Lisp运行时。当前生成的Java代码的速度对于某些应用程序来说可能已经足够了。
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引用次数: 3
Unfolding of Finite Concurrent Automata 有限并发自动机的展开
Pub Date : 2018-10-04 DOI: 10.4204/EPTCS.279.8
Alexandre Mansard
We consider recognizable trace rewriting systems with level-regular contexts (RTL). A trace language is level-regular if the set of Foata normal forms of its elements is regular. We prove that the rewriting graph of a RTL is word-automatic. Thus its first-order theory is decidable. Then, we prove that the concurrent unfolding of a finite concurrent automaton with the reachability relation is a RTL graph. It follows that the first-order theory with the reachability predicate (FO[Reach] theory) of such an unfolding is decidable. It is known that this property holds also for the ground term rewriting graphs. We provide examples of finite concurrent automata of which the concurrent unfoldings fail to be ground term rewriting graphs. The infinite grid tree (for each vertex of an infinite grid, there is an edge from this vertex to the origin of a copy of the infinite grid) is such an unfolding. We prove that the infinite grid tree is not a ground term rewriting graph. We have thus obtained a new class of graphs for with a decidable FO[Reach] theory.
我们考虑具有级别正则上下文(RTL)的可识别跟踪重写系统。如果跟踪语言元素的Foata范式集合是规则的,则该语言是级别规则的。证明了RTL的改写图是词自动的。因此它的一阶理论是可决定的。然后,证明了具有可达性关系的有限并发自动机的并发展开是RTL图。由此可见,具有可达性谓词的这种展开的一阶理论(FO[Reach]理论)是可决定的。众所周知,这个性质也适用于基项改写图。我们提供了有限并发自动机的例子,其中并发展开不是基项重写图。无限网格树(对于无限网格的每个顶点,从这个顶点到无限网格副本的原点都有一条边)就是这样一种展开。证明了无限网格树不是一个地项改写图。由此,我们得到了一类新的具有可判定FO[Reach]理论的图。
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引用次数: 1
Lower and Upper Conditioning in Quantum Bayesian Theory 量子贝叶斯理论中的上下条件作用
Pub Date : 2018-10-04 DOI: 10.4204/EPTCS.287.13
B. Jacobs
Updating a probability distribution in the light of new evidence is a very basic operation in Bayesian probability theory. It is also known as state revision or simply as conditioning. This paper recalls how locally updating a joint state can equivalently be described via inference using the channel extracted from the state (via disintegration). This paper also investigates the quantum analogues of conditioning, and in particular the analogues of this equivalence between updating a joint state and inference. The main finding is that in order to obtain a similar equivalence, we have to distinguish two forms of quantum conditioning, which we call lower and upper conditioning. They are known from the literature, but the common framework in which we describe them and the equivalence result are new.
根据新的证据更新概率分布是贝叶斯概率论中一项非常基本的操作。它也被称为状态修正或简单地称为条件反射。本文回顾了如何使用从状态中提取的通道(通过分解)通过推理等效地描述局部更新联合状态。本文还研究了条件作用的量子类似物,特别是这种更新联合状态和推理之间等价的类似物。主要的发现是,为了获得类似的等价,我们必须区分两种形式的量子条件作用,我们称之为下条件作用和上条件作用。它们在文献中是已知的,但我们描述它们的通用框架和等效结果是新的。
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引用次数: 3
Prototyping Formal System Models with Active Objects 用活动对象建立正式系统模型的原型
Pub Date : 2018-10-04 DOI: 10.4204/EPTCS.279.7
Eduard Kamburjan, Reiner Hähnle
We propose active object languages as a development tool for formal system models of distributed systems. Additionally to a formalization based on a term rewriting system, we use established Software Engineering concepts, including software product lines and object orientation that come with extensive tool support. We illustrate our modeling approach by prototyping a weak memory model. The resulting executable model is modular and has clear interfaces between communicating participants through object-oriented modeling. Relaxations of the basic memory model are expressed as self-contained variants of a software product line. As a modeling language we use the formal active object language ABS which comes with an extensive tool set. This permits rapid formalization of core ideas, early validity checks in terms of formal invariant proofs, and debugging support by executing test runs. Hence, our approach supports the prototyping of formal system models with early feedback.
我们提出活动对象语言作为分布式系统形式化系统模型的开发工具。除了基于术语重写系统的形式化之外,我们还使用了已建立的软件工程概念,包括软件产品线和具有广泛工具支持的面向对象。我们通过一个弱内存模型的原型来说明我们的建模方法。由此产生的可执行模型是模块化的,并且通过面向对象建模在通信参与者之间具有清晰的接口。基本内存模型的松弛被表示为软件产品线的自包含变体。作为一种建模语言,我们使用正式的活动对象语言ABS,它附带了一个广泛的工具集。这允许快速形式化核心思想,根据形式化不变证明进行早期有效性检查,并通过执行测试运行进行调试支持。因此,我们的方法支持具有早期反馈的正式系统模型的原型。
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引用次数: 8
Realisability of Pomsets via Communicating Automata 通过通信自动机实现集合的可实现性
Pub Date : 2018-10-01 DOI: 10.4204/EPTCS.279.6
R. Guanciale, E. Tuosto
Pomsets are a model of concurrent computations introduced by Pratt. They can provide a syntax-oblivious description of semantics of coordination models based on asynchronous message-passing, such a ...
pomset是Pratt引入的一种并发计算模型。它们可以提供基于异步消息传递的协调模型语义的语法无关描述,例如…
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引用次数: 4
Global Types for Open Systems 开放系统的全局类型
Pub Date : 2018-10-01 DOI: 10.4204/EPTCS.279.4
F. Barbanera, Ugo de'Liguoro, R. Hennicker
Global-type formalisms enable to describe the overall behaviour of distributed systems and at the same time to enforce safety properties for communications between system components. Our goal is that of amending a weakness of such formalisms: the difficulty in describing open systems, i.e. systems which can be connected and interact with other open systems. We parametrically extend, with the notion of interface role and interface connection, the syntax of global-type formalisms. Semantically, global types with interface roles denote open systems of communicating finite state machines connected by means of gateways obtained from compatible interfaces. We show that safety properties are preserved when open systems are connected that way.
全局类型的形式化能够描述分布式系统的整体行为,同时为系统组件之间的通信强制执行安全属性。我们的目标是修正这种形式化的弱点:描述开放系统的困难,即可以与其他开放系统连接和交互的系统。利用接口角色和接口连接的概念,对全局型形式化的语法进行了参数化扩展。在语义上,具有接口角色的全局类型表示通过从兼容接口获得的网关连接的通信有限状态机的开放系统。我们证明,当开放系统以这种方式连接时,安全属性是保留的。
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引用次数: 13
A Simple Functional Presentation and an Inductive Correctness Proof of the Horn Algorithm 霍恩算法的简单函数表示和归纳正确性证明
Pub Date : 2018-09-12 DOI: 10.4204/EPTCS.278.6
A. Ravara
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By defining the algorithm as a recursive function (computing a least fixed-point), we achieve: 1) a concise, yet rigorous, formalisation; 2) a clear form of visualising executions of the algorithm, step-by-step; 3) precise results, simple to state and with clean inductive proofs.
给出了决定命题子句可满足性的Horn算法的递推公式。命令式伪代码中通常的表示是非正式的,不适合简单地证明其主要属性。通过将算法定义为递归函数(计算最小不动点),我们实现了:1)简洁而严谨的形式化;2)清晰的可视化算法执行形式,一步一步;结果准确,表述简单,归纳证明清晰。
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引用次数: 0
A Framework for Rewriting Families of String Diagrams 改写弦图族的框架
Pub Date : 2018-09-11 DOI: 10.4204/EPTCS.288.6
Vladimir Zamdzhiev
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using context-free graph grammars. We model equations between infinite families of diagrams using rewrite rules between context-free grammars. Our framework represents equational reasoning about concrete string diagrams and context-free families of string diagrams using double-pushout rewriting on graphs and context-free graph grammars respectively. We prove that our representation is sound by showing that it respects the concrete semantics of string diagrammatic reasoning and we show that our framework is appropriate for software implementation by proving important decidability properties.
本文描述了一个适用于计算机自动化的无限族弦图方程推理的数学框架。该框架基于上下文无关的字符串图族,我们使用上下文无关的图语法表示这些字符串图族。我们使用上下文无关语法之间的重写规则对无限族图之间的方程进行建模。我们的框架分别使用双推出重写图和上下文无关的图语法来表示具体字符串图和上下文无关的字符串图族的方程推理。我们通过表明我们的表示尊重字符串图推理的具体语义来证明我们的表示是合理的,我们通过证明重要的可判定性属性来证明我们的框架适合于软件实现。
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引用次数: 1
A Comparison of BDD-Based Parity Game Solvers 基于bdd的奇偶博弈求解器的比较
Pub Date : 2018-09-07 DOI: 10.4204/EPTCS.277.8
L. Sanchez, Wieger Wesselink, T. Willemse
Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently deal with large games that arise from such applications. In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz. Zielonka's recursive algorithm, the more recent Priority Promotion algorithm, the Fixpoint-Iteration algorithm and the automata based APT algorithm. We compare their performance on several types of random games and on a number of cases taken from the Keiren benchmark set.
奇偶性游戏是在有限图上进行的具有- 3获胜条件的两人游戏。这类博弈在验证性、可满足性和综合性方面发挥着重要作用。因此,识别能够有效处理此类应用产生的大型游戏的算法非常重要。在本文中,我们描述了基于bdd实现的四种奇偶对策求解算法的实验,即Zielonka的递归算法,最新的优先级提升算法,不动点迭代算法和基于自动机的APT算法。我们比较了它们在不同类型的随机游戏中的表现,以及Keiren基准集中的许多情况。
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引用次数: 6
期刊
CoRR
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