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Comparing session type systems derived from linear logic 比较源自线性逻辑的会话类型系统
IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-08-22 DOI: 10.1016/j.jlamp.2024.101004
Bas van den Heuvel , Jorge A. Pérez

Session types are a typed approach to message-passing concurrency, where types describe sequences of intended exchanges over channels. Session type systems have been given strong logical foundations via Curry-Howard correspondences with linear logic, a resource-aware logic that naturally captures structured interactions. These logical foundations provide an elegant framework to specify and (statically) verify message-passing processes.

In this paper, we rigorously compare different type systems for concurrency derived from the Curry-Howard correspondence between linear logic and session types. We address the main divide between these type systems: the classical and intuitionistic presentations of linear logic. Over the years, these presentations have given rise to separate research strands on logical foundations for concurrency; the differences between their derived type systems have only been addressed informally.

To formally assess these differences, we develop πULL, a session type system that encompasses type systems derived from classical and intuitionistic interpretations of linear logic. Based on a fragment of Girard's Logic of Unity, πULL provides a basic reference framework: we compare existing session type systems by characterizing fragments of πULL that coincide with classical and intuitionistic formulations. We analyze the significance of our characterizations by considering the locality principle (enforced by intuitionistic interpretations but not by classical ones) and forms of process composition induced by the interpretations.

会话类型是一种消息传递并发的类型化方法,其中的类型描述了在通道上的预期交换序列。会话类型系统通过与线性逻辑的库里-霍华德对应关系获得了坚实的逻辑基础,线性逻辑是一种资源感知逻辑,能自然地捕捉结构化的交互。这些逻辑基础为指定和(静态)验证消息传递过程提供了一个优雅的框架。在本文中,我们严格比较了从线性逻辑和会话类型之间的 Curry-Howard 对应关系中衍生出来的不同并发类型系统。我们讨论了这些类型系统之间的主要分歧:线性逻辑的经典表述和直觉表述。为了正式评估这些差异,我们开发了会话类型系统 πULL,它包含了从线性逻辑的经典解释和直觉解释中派生出来的类型系统。πULL以吉拉德的《统一逻辑》(Logic of Unity)的一个片段为基础,提供了一个基本的参考框架:我们通过描述πULL中与经典和直觉主义表述相吻合的片段来比较现有的会话类型系统。我们通过考虑局部性原则(直观解释强制执行,而经典解释不强制执行)和解释所诱导的流程组成形式,来分析我们的特征描述的意义。
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引用次数: 0
Towards an efficient implementation of a tableau method for reactive safety specifications 高效实施反应式安全规范的表法
IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-08-08 DOI: 10.1016/j.jlamp.2024.101003
Ander Alonso , Montserrat Hermo , Josu Oca

In this paper, we will show how to handle a new normal form called terse normal form (TNF), which is crucial to the development of a novel tableau method that solves realizability and synthesis for specifications expressed in a safety fragment of LTL. The construction of these tableaux is based on the conversion of LTL formulas into TNF, which is one of the most computationally expensive parts of the method. We will explain how to efficiently extract the relevant information required by the tableaux without having to compute the entire TNF of a safety formula. We present a correct algorithm for carrying out this task as well as its implementation.

在本文中,我们将展示如何处理一种名为terse normal form(TNF)的新正则表达式,这对于开发一种新颖的表法至关重要,这种表法可以解决以 LTL 安全片段表达的规范的可实现性和合成问题。这些表法的构建基于将 LTL 公式转换为 TNF,这是该方法中计算成本最高的部分之一。我们将解释如何有效地提取表格所需的相关信息,而无需计算安全公式的整个 TNF。我们将介绍执行这项任务的正确算法及其实现方法。
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引用次数: 0
Towards the exact complexity of realizability for Safety LTL 实现安全 LTL 可实现性的精确复杂性
IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-07-31 DOI: 10.1016/j.jlamp.2024.101002
Noel Arteche , Montserrat Hermo

We study the realizability and strong satisfiability problems for Safety LTL, a syntactic fragment of Linear Temporal Logic (

) capturing safe formulas. While it is well-known that realizability for this fragment lies in
, the best-known lower bound is
-hardness. Surprisingly, closing this gap has proven an elusive task. Previous works have claimed first
-completeness [1] and later
-completeness [2] for this problem, but both of these proofs turned out to be incorrect.

We revisit the problem of the exact classification of the complexity of realizability for

through the lens of seemingly weaker fragments. While we cannot settle the question for
, we study a subfragment of it consisting of formulas of the form
, where α is a present formula over system variables and ψ contains Next as the only temporal operator. We prove that the realizability problem for this new fragment, which we call
, is
-complete, and observe that this fragment is equirealizable to existing more expressive fragments, such as the class
[3].

Furthermore, we revisit the techniques used in the purported proof of

-completeness of Arteche and Hermo [1], and observe that, while incorrect in their original claims, their proofs can be modified to classify the complexity of strong satisfiability, a necessary condition for realizability introduced by Kupferman, Sadigh, and Seshia [4]. We prove that, with regards to strong satisfiability, the fragments
and
are in fact equivalent under polynomial-time many-one reductions.

我们研究了线性时态逻辑 (▪) 的一个语法片段--捕捉安全公式的可实现性和强可满足性问题。众所周知,该语法片段的可实现性在▪范围内,而最著名的下限是▪-硬度。令人惊讶的是,缩小这一差距已被证明是一项难以实现的任务。以前的著作先是声称这个问题具有 ▪ 可完备性,后来又声称它具有 ▪ 可完备性,但结果证明这两个证明都是不正确的。
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引用次数: 0
Efficient analysis of belief properties in process algebra 过程代数中信念属性的高效分析
IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-07-08 DOI: 10.1016/j.jlamp.2024.101001
Zahra Moezkarimi , Fatemeh Ghassemi

Protocols are typically specified in an operational manner by specifying the communication patterns among the different involved principals. However, many properties are of epistemic nature, e.g., what each principal believes after having seen a run of the protocol. We elaborate on a unified algebraic framework suitable for epistemic reasoning about operational protocols. This reasoning framework is based on a logic of beliefs and allows for the operational specification of untruthful communications. The information recorded in the semantic models to support reasoning about the interaction between the operational and epistemic aspects intensifies the state-space explosion. We propose an efficient on-the-fly reduction for such a unifying framework by providing a set of operational rules. These operational rules automatically generate efficient reduced semantics for a class of epistemic properties, specified in a rich extension of modal μ-calculus with past and belief modality, and can potentially reduce an infinite state space into a finite one. We reformulate and prove criteria that guarantee belief consistency for credulous agents, i.e., agents that are ready to believe what is told unless it is logically inconsistent. We adjust our reduction so that the belief consistency of an original model is preserved. We prove the soundness and completeness result for the specified class of properties.

协议通常是通过指定不同参与主体之间的通信模式,以可操作的方式指定的。然而,许多属性是认识论性质的,例如,每个委托人在看到协议运行后相信什么。我们阐述了一个适用于对运行协议进行认识论推理的统一代数框架。这个推理框架以信念逻辑为基础,允许对不真实的通信进行操作规范。语义模型中记录的用于支持操作和认识方面交互推理的信息加剧了状态空间爆炸。我们通过提供一系列操作规则,为这样一个统一框架提出了一种高效的即时还原方法。这些运算规则能自动为一类认识论属性生成高效的还原语义,并在具有过去和信念模态的模态μ计算的丰富扩展中加以指定,从而有可能将无限的状态空间还原为有限的状态空间。我们重新制定并证明了保证可信代理的信念一致性的标准,即除非逻辑上不一致,否则代理愿意相信别人所说的话。我们调整了还原方法,从而保留了原始模型的信念一致性。我们证明了指定属性类别的健全性和完备性结果。
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引用次数: 0
When causality meets fairness: A survey 当因果关系遇上公平一项调查
IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-06-20 DOI: 10.1016/j.jlamp.2024.101000
Karima Makhlouf , Sami Zhioua , Catuscia Palamidessi

Addressing the problem of fairness is crucial to safely using machine learning algorithms to support decisions that have a critical impact on people's lives, such as job hiring, child maltreatment, disease diagnosis, loan granting, etc. Several notions of fairness have been defined and examined in the past decade, such as statistical parity and equalized odds. However, the most recent notions of fairness are causal-based and reflect the now widely accepted idea that using causality is necessary to appropriately address the problem of fairness. This paper examines an exhaustive list of causal-based fairness notions and studies their applicability in real-world scenarios. As most causal-based fairness notions are defined in terms of non-observable quantities (e.g., interventions and counterfactuals), their deployment in practice requires computing or estimating those quantities using observational data. This paper offers a comprehensive report of the different approaches to infer causal quantities from observational data, including identifiability (Pearl's SCM framework) and estimation (potential outcome framework). The main contributions of this survey paper are (1) a guideline to help select a suitable causal fairness notion given a specific real-world scenario and (2) a ranking of the fairness notions according to Pearl's causation ladder, indicating how difficult it is to deploy each notion in practice.

要安全地使用机器学习算法来支持对人们生活有重要影响的决策,如工作招聘、儿童虐待、疾病诊断、贷款发放等,解决公平性问题至关重要。过去十年间,人们定义并研究了几种公平概念,如统计均等和赔率均等。不过,最近的公平概念都是基于因果关系的,反映了现在被广泛接受的观点,即要恰当地解决公平问题,就必须使用因果关系。本文详尽列举了基于因果关系的公平概念,并研究了它们在现实世界中的适用性。由于大多数基于因果关系的公平概念都是以不可观测的量(如干预和反事实)来定义的,因此在实际应用中需要利用观测数据来计算或估计这些量。本文全面报告了从观察数据中推断因果量的不同方法,包括可识别性(珀尔的单片机框架)和估算(潜在结果框架)。本调查报告的主要贡献在于:(1) 提供了一个指南,帮助人们在特定的现实世界场景中选择合适的因果公平概念;(2) 根据珀尔的因果关系阶梯对公平概念进行了排序,指出了在实践中采用每种概念的难度。
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引用次数: 0
Formal definitions and proofs for partial (co)recursive functions 部分(共)递归函数的形式定义和证明
IF 0.9 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-06-17 DOI: 10.1016/j.jlamp.2024.100999
Horaţiu Cheval , David Nowak , Vlad Rusu

Partial functions are a key concept in programming. Without partiality a programming language has limited expressiveness – it is not Turing-complete, hence, it excludes some constructs such as while-loops. In functional programming languages, partiality mostly originates from the non-termination of recursive functions. Corecursive functions are another source of partiality: here, the issue is not termination, but the inability to produce arbitrary large, finite approximations of a theoretically infinite output.

Partial functions have been formally studied in the branch of theoretical computer science called domain theory. In this paper we propose to step up the level of formality by using the Coq proof assistant. The main difficulty is that Coq requires all functions to be total, since partiality would break the soundness of its underlying logic. We propose practical solutions for this issue, and others, which appear when one attempts to define and reason about partial (co)recursive functions in a total functional language.

偏函数是编程中的一个关键概念。如果没有部分性,编程语言的表达能力就会受到限制--它不是图灵完备的,因此,它排除了一些构造,如 while-loops。在函数式编程语言中,偏倚性主要源于递归函数的非终结性。核心递归函数是偏倚性的另一个来源:在这里,问题不在于终止,而在于无法对理论上无限的输出产生任意大的、有限的近似值。在本文中,我们建议使用 Coq 证明助手来提高正式程度。主要困难在于,Coq 要求所有函数都是全函数,因为偏函数会破坏其底层逻辑的健全性。我们针对这个问题和其他问题提出了切实可行的解决方案,这些问题会在人们尝试用完全函数式语言定义和推理部分(共)递归函数时出现。
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引用次数: 0
Advancing orchestration synthesis for contract automata 推进合约自动机的协调合成
IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-06-15 DOI: 10.1016/j.jlamp.2024.100998
Davide Basile, Maurice H. ter Beek

Contract automata allow to formally define the behaviour of service contracts in terms of service offers and requests, some of which are moreover optional and some of which are necessary. A composition of contracts is said to be in agreement if all service requests are matched by corresponding offers. Whenever a composition of contracts is not in agreement, it can be refined to reach an agreement using the orchestration synthesis algorithm. This algorithm is a variant of the synthesis algorithm used in supervisory control theory and it is based on the fact that optional transitions are controllable, whereas necessary transitions are at most semi-controllable and cannot always be controlled. In this paper, we present advancements of the orchestration synthesis for contract automata. Notably, we identify the existing limits of the orchestration synthesis and propose a novel orchestration synthesis along with additional constructs to enhance the expressiveness and scalability of contract automata. The proposed advancements have been implemented and experimented on two case studies, one of which originates from the railway domain and the other is a card game.

合约自动机可以用服务提议和请求来正式定义服务合约的行为,其中有些是可选的,有些是必须的。如果所有服务请求都与相应的提议相匹配,就可以说合同组合是一致的。如果合同组合不一致,可以使用协调合成算法对其进行完善,以达成一致。该算法是监督控制理论中使用的合成算法的一种变体,它基于以下事实:可选的转换是可控的,而必要的转换最多是半可控的,不可能总是可控的。在本文中,我们介绍了合同自动机协调合成的进展。值得注意的是,我们发现了协调合成的现有限制,并提出了一种新的协调合成和附加结构,以增强合约自动机的表达能力和可扩展性。我们在两个案例研究中实施并实验了所提出的改进措施,其中一个来自铁路领域,另一个是纸牌游戏。
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引用次数: 0
A logical approach to graph databases 图形数据库的逻辑方法
IF 0.9 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-06-13 DOI: 10.1016/j.jlamp.2024.100997
Elvira Pino, Fernando Orejas, Nikos Mylonakis, Edelmira Pasarella

Graph databases are now playing an important role because they allow us to overcome some limitations of relational databases. In particular, in graph databases we are interested not only on the data contained but also on its topology. As a consequence, most graph database queries are navigational, asking whether some nodes are connected by edges or paths.

Up to now, most foundational work has concentrated on the study of computational models and query languages, analyzing their expressivity, computability, and complexity. However, in our work we address a different kind of foundational work. We are not concerned with expressibility, efficiency or feasibility issues, but with correctness. More precisely, given an algorithm or an implementation for solving queries, how can we be sure that the answers obtained are correct (soundness) and that all possible correct answers are obtained by our implementation (completeness).

In this sense, in this paper we first present a core query language, similar to Cypher or G-Core. Then, we define a simple logic whose formulas are precisely the database queries, and whose satisfaction relation defines what is a correct answer. Finally, we define an operational semantics, which could be seen as an abstract implementation of our language, showing that the semantics is correct, i.e. sound and complete with respect to our logic.

图数据库现在正发挥着重要作用,因为它能让我们克服关系数据库的一些局限性。特别是,在图数据库中,我们不仅对所包含的数据感兴趣,还对其拓扑结构感兴趣。因此,大多数图数据库查询都是导航性的,询问某些节点是否由边或路径连接。迄今为止,大多数基础性工作都集中在计算模型和查询语言的研究上,分析它们的表达性、可计算性和复杂性。然而,在我们的工作中,我们要解决的是另一种基础性工作。我们关注的不是可表达性、效率或可行性问题,而是正确性。更确切地说,给定一个用于解决查询的算法或实现,我们如何才能确保得到的答案是正确的(正确性),以及我们的实现得到了所有可能的正确答案(完备性)。在这个意义上,本文首先提出了一种核心查询语言,类似于 Cypher 或 G-Core。然后,我们定义了一个简单的逻辑,其公式正是数据库查询,其满足关系定义了什么是正确答案。最后,我们定义了一种操作语义,它可以看作是我们语言的抽象实现,并表明该语义是正确的,即相对于我们的逻辑而言是健全和完整的。
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引用次数: 0
Optimizing term rewriting with creeper trace transducers 利用爬行跟踪转换器优化术语重写
IF 0.9 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-05-31 DOI: 10.1016/j.jlamp.2024.100987
Rick Erkens

In the context of functional programming/term normalization algorithms we discuss the optimization problem of constructing the result of a sequence of rewrite steps, without computing all the intermediate terms. From a rewrite system we construct a creeper trace transducer, which reads a sequence of backwards overlapping rewrite steps while producing the desired answer. The transducer writes each symbol of the output only once, skipping overlap between each pair of subsequent rules. In some cases a part of the trace can be disregarded altogether.

在函数式编程/术语规范化算法的背景下,我们讨论了在不计算所有中间术语的情况下构建一系列重写步骤结果的优化问题。我们从一个重写系统中构建了一个爬行跟踪转换器,它可以读取一连串向后重叠的重写步骤,同时生成所需的答案。转换器只写入输出的每个符号一次,跳过每对后续规则之间的重叠。在某些情况下,可以完全忽略部分跟踪。
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引用次数: 0
A logical account of subtyping for session types 会话类型子类型的逻辑说明
IF 0.9 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-05-28 DOI: 10.1016/j.jlamp.2024.100986
Ross Horne , Luca Padovani

We study iso-recursive and equi-recursive subtyping for session types in a logical setting, where session types are propositions of multiplicative/additive linear logic extended with least and greatest fixed points. Both subtyping relations admit a simple characterization that can be roughly spelled out as the following lapalissade: every session type is larger than the smallest session type and smaller than the largest session type. We observe that, because of the logical setting in which they arise, these subtyping relations preserve termination in addition to the usual safety properties of sessions.

我们研究了逻辑环境中会话类型的等递归和等递归子类型,其中会话类型是乘法/加法线性逻辑的命题,扩展有最小和最大定点。这两种子类型关系都有一个简单的表征,大致可以表述为:每个会话类型都比最小的会话类型大,比最大的会话类型小。我们注意到,由于它们产生的逻辑环境,这些子类型关系除了保留会话的通常安全属性外,还保留了终止属性。
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引用次数: 0
期刊
Journal of Logical and Algebraic Methods in Programming
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