Journal of Logical and Algebraic Methods in Programming最新文献

{"title":"Coherent modal transition systems refinement","authors":"Davide Basile ,&nbsp;Maurice H. ter Beek ,&nbsp;Alessandro Fantechi ,&nbsp;Stefania Gnesi","doi":"10.1016/j.jlamp.2024.100954","DOIUrl":"https://doi.org/10.1016/j.jlamp.2024.100954","url":null,"abstract":"<div><p>Modal Transition Systems (MTS) are a well-known formalism that extend Labelled Transition Systems (LTS) with the possibility of specifying necessary and permitted behaviour. Coherent MTS (CMTS) have been introduced to model Software Product Lines (SPL) based on a correspondence between the necessary and permitted modalities of MTS transitions and their associated actions, and the core and optional features of SPL. In this paper, we address open problems of the coherent fragment of MTS and introduce the notions of refinement and thorough refinement of CMTS. Most notably, we prove that refinement and thorough refinement coincide for CMTS, while it is known that this is not the case for MTS. We also define (thorough) equivalence and strong bisimilarity of both MTS and CMTS. We show their relations and, in particular, we prove that also strong bisimilarity and equivalence coincide for CMTS, whereas they do not for MTS. Finally, we extend our investigation to CMTS equipped with Constraints (MTSC), originally introduced to express alternative behaviour, and we prove that novel notions of refinement and strong thorough refinement coincide for MTSC, and so do their extensions to strong (thorough) equivalence and strong bisimilarity.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"138 ","pages":"Article 100954"},"PeriodicalIF":0.9,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220824000129/pdfft?md5=f3454b411ac825e2a7452e39b5a346f5&pid=1-s2.0-S2352220824000129-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139992455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trace preservation in B and Event-B refinements","authors":"Sebastian Stock ,&nbsp;Atif Mashkoor ,&nbsp;Michael Leuschel ,&nbsp;Alexander Egyed","doi":"10.1016/j.jlamp.2024.100943","DOIUrl":"10.1016/j.jlamp.2024.100943","url":null,"abstract":"<div><p>Refinement guarantees that the concrete version of a model does not violate the constraints introduced at the abstract level. The peculiarity of refinement, however, is that we have no guarantee about the preservation of the behavior of the model. For example, a trace (a set of desirable states and transitions) created on the abstract model may not replay on the concrete model. Its manual recreation, usually via animation, is necessary to run the trace, as the model may have changed significantly during refinement. However, this is a labor-intensive and error-prone task. To this end, this article presents an automatic trace refining technique and tool called <em>BERT</em> (<u>B</u> and <u>E</u>vent-B Trace <u>R</u>efinement <u>T</u>echnique) that allows modelers to ensure the behavioral integrity of high-level traces at the concrete level. The cost- and time-effectiveness of BERT are shown in industrial-strength case studies from the automotive and aviation domains.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100943"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220824000014/pdfft?md5=014ec80e27c6d35f0f8d4a7e25c9564e&pid=1-s2.0-S2352220824000014-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On proving that an unsafe controller is not proven safe","authors":"Yuvaraj Selvaraj ,&nbsp;Jonas Krook ,&nbsp;Wolfgang Ahrendt ,&nbsp;Martin Fabian","doi":"10.1016/j.jlamp.2023.100939","DOIUrl":"10.1016/j.jlamp.2023.100939","url":null,"abstract":"<div><p>Cyber-physical systems are often safety-critical and their correctness is crucial, such as in the case of automated driving. Using formal mathematical methods is one way to guarantee correctness and improve safety. Although these methods have shown their usefulness, care must be taken because modelling errors might result in proving a faulty controller safe, which is potentially catastrophic in practice. This paper deals with two such modelling errors in <em>differential dynamic logic</em>, a formal specification and verification language for <em>hybrid systems</em>, which are mathematical models of cyber-physical systems. The main contributions are to provide conditions under which these two modelling errors cannot cause a faulty controller to be proven safe, and to show how these conditions can be proven with help of the interactive theorem prover KeYmaera X. The problems are illustrated with a real world example of a safety controller for automated driving, and it is shown that the formulated conditions have the intended effect both for a faulty and a correct controller. It is also shown how the formulated conditions aid in finding a <em>loop invariant</em> candidate to prove properties of hybrid systems with feedback loops. Furthermore, the relation between such a loop invariant and the characterisation of the <em>maximal control invariant set</em> is discussed.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100939"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220823000937/pdfft?md5=a0255d67f0ba6855c0bca13111b7ef6d&pid=1-s2.0-S2352220823000937-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138816599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bridging formal methods and machine learning with model checking and global optimisation","authors":"Saddek Bensalem ,&nbsp;Xiaowei Huang ,&nbsp;Wenjie Ruan ,&nbsp;Qiyi Tang ,&nbsp;Changshun Wu ,&nbsp;Xingyu Zhao","doi":"10.1016/j.jlamp.2023.100941","DOIUrl":"10.1016/j.jlamp.2023.100941","url":null,"abstract":"<div><p>Formal methods and machine learning are two research fields with drastically different foundations and philosophies. Formal methods utilise mathematically rigorous techniques for software and hardware systems' specification, development and verification. Machine learning focuses on pragmatic approaches to gradually improve a parameterised model by observing a training data set. While historically, the two fields lack communication, this trend has changed in the past few years with an outburst of research interest in the robustness verification of neural networks. This paper will briefly review these works, and focus on the urgent need for broader and more in-depth communication between the two fields, with the ultimate goal of developing learning-enabled systems with excellent performance and acceptable safety and security. We present a specification language, MLS², and show that it can express a set of known safety and security properties, including generalisation, uncertainty, robustness, data poisoning, backdoor, model stealing, membership inference, model inversion, interpretability, and fairness. To verify MLS² properties, we promote the global optimisation-based methods, which have provable guarantees on the convergence to the optimal solution. Many of them have theoretical bounds on the gap between current solutions and the optimal solution.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100941"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220823000950/pdfft?md5=524bb8cc97eab39538606c56c0fd3849&pid=1-s2.0-S2352220823000950-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139068888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounded model checking for interval probabilistic timed graph transformation systems against properties of probabilistic metric temporal graph logic","authors":"Sven Schneider,&nbsp;Maria Maximova,&nbsp;Holger Giese","doi":"10.1016/j.jlamp.2023.100938","DOIUrl":"10.1016/j.jlamp.2023.100938","url":null,"abstract":"<div><p>Cyber-physical systems often encompass complex concurrent behavior with timing constraints and probabilistic failures on demand. The analysis whether such systems with probabilistic timed behavior adhere to a given specification is essential. The formalism of Interval Probabilistic Timed Graph Transformation Systems (IPTGTSs) is often a suitable choice to model cyber-physical systems because <em>(a)</em> its rule-based approach to graph transformation can capture a wide range of system's structure dynamics when the states of the system can be represented by graphs while <em>(b)</em><span> it employs interval specifications for probabilistic behavior as well as lower and upper bounds on delays of steps to support systems where precise probabilities and delays are not known or may change during the runtime of the system. Probabilistic Metric Temporal Graph Logic (PMTGL) has been introduced as a powerful specification language to express worst-case/best-case probabilistic timed requirements such as actor-based soft deadlines using </span><em>(a)</em> path properties relying on its Metric Temporal Graph Logic fragment to track individual graph elements and <em>(b)</em><span> an operator inherited from Probabilistic Timed Computation Tree Logic to express worst-case/best-case probabilistic requirements identifying worst-case/best-case resolutions of non-determinism. Bounded Model Checking (BMC) support for Probabilistic Timed Graph Transformation Systems (PTGTSs) w.r.t. properties specified using PMTGL has been already presented. However, for IPTGTSs no analysis support w.r.t. PMTGL properties has been developed for stating metric temporal properties on identified subgraphs and their structural changes over time.</span></p><p>In this paper, we adapt the BMC approach developed for PTGTSs to the case of IPTGTSs extending modeling and analysis support to the usage of probability intervals more appropriately covering cyber-physical systems where probabilistic effects cannot be specified precisely and need to be approximated instead. In our evaluation, we apply an implementation of our BMC approach in <span>AutoGraph</span> to a novel running example demonstrating the effect of using probability intervals instead of precise probability values.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100938"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Formally verified animation for RoboChart using interaction trees","authors":"Kangfeng Ye,&nbsp;Simon Foster,&nbsp;Jim Woodcock","doi":"10.1016/j.jlamp.2023.100940","DOIUrl":"10.1016/j.jlamp.2023.100940","url":null,"abstract":"<div><p>RoboChart is a core notation in the RoboStar framework. It is a timed and probabilistic domain-specific and state machine-based language for robotics. RoboChart supports shared variables and communication across entities in its component model. It has formal denotational semantics given in CSP. The semantic technique of Interaction Trees (ITrees) represents behaviours of reactive and concurrent programs interacting with their environments. Recent mechanisation of ITrees, ITree-based CSP semantics and a Z mathematical toolkit in Isabelle/HOL bring new applications of verification and animation for state-rich process languages, such as RoboChart. In this paper, we use ITrees to give RoboChart novel operational semantics, implement it in Isabelle, and use Isabelle's code generator to generate verified and executable animations. We illustrate our approach using an autonomous chemical detector and patrol robot models, exhibiting nondeterminism and using shared variables. With animation, we show two concrete scenarios for the chemical detector when the robot encounters different environmental inputs and three for the patrol robot when its calibrated position is in other corridor sections. We also verify that the animated scenarios are trace refinements of the CSP denotational semantics of the RoboChart models using FDR, a refinement model checker for CSP. This ensures that our approach to resolve nondeterminism using CSP operators with priority is sound and correct.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100940"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220823000949/pdfft?md5=5312a452edca31ae541827e9147a0d84&pid=1-s2.0-S2352220823000949-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139067982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Protocol choice and iteration for the free cornering","authors":"Chad Nester ,&nbsp;Niels Voorneveld","doi":"10.1016/j.jlamp.2023.100942","DOIUrl":"10.1016/j.jlamp.2023.100942","url":null,"abstract":"<div><p>We extend the free cornering of a symmetric monoidal category, a double categorical model of concurrent interaction, to support branching communication protocols and iterated communication protocols. We validate our constructions by showing that they inherit significant categorical structure from the free cornering, including that they form monoidal double categories. We also establish some elementary properties of the novel structure they contain. Further, we give a model of the free cornering in terms of strong functors and strong natural transformations, inspired by the literature on computational effects.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100942"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139068328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Back to the format: A survey on SOS for probabilistic processes","authors":"Valentina Castiglioni ,&nbsp;Ruggero Lanotte ,&nbsp;Simone Tini","doi":"10.1016/j.jlamp.2023.100929","DOIUrl":"10.1016/j.jlamp.2023.100929","url":null,"abstract":"<div><p>In probabilistic process algebras the classic qualitative description of process behaviour is enriched with quantitative information on it, usually modelled in terms of probabilistic weights and/or distributions over the qualitative behaviour. In this setting, we use behavioural equivalences to check whether two processes show exactly the same behaviour, and, if this is not the case, we can use behavioural metrics to measure the distance between them. Compositional reasoning requires that equivalence, or closeness, of behaviour of two processes are not destroyed when language operators are applied on top of them in order to build larger processes. Formally, the equivalence must be a congruence, and the metric must be uniformly continuous, with respect to language operators. Instead of verifying these compositional properties by hand, operator-by-operator, it is much more convenient to prove them for a class of operators once for all, and to check that the operators one is dealing with are in that class. This is achieved by means of SOS specification formats: they consist in a set of syntactical constraints characterising a class of operators on the patterns of SOS rules, that define the operational semantics of languages. With this survey, we aim to collect and describe the specification formats that have been proposed in the literature to guarantee the compositional properties of (variants of) bisimulation equivalences and bisimulation metrics in the probabilistic setting.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"137 ","pages":"Article 100929"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220823000834/pdfft?md5=ce48feb3ed771dee50dbe8f80129e90b&pid=1-s2.0-S2352220823000834-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135715196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum encoding of dynamic directed graphs","authors":"D. Della Giustina,&nbsp;C. Londero,&nbsp;C. Piazza,&nbsp;B. Riccardi,&nbsp;R. Romanello","doi":"10.1016/j.jlamp.2023.100925","DOIUrl":"https://doi.org/10.1016/j.jlamp.2023.100925","url":null,"abstract":"<div><p>In application domains such as routing, network analysis, scheduling, and planning, directed graphs are widely used as both formal models and core data structures for the development of efficient algorithmic solutions. In these areas, graphs are often evolving in time: for example, connection links may fail due to temporary technical issues, meaning that edges of the graph cannot be traversed for some time interval and alternative paths have to be followed.</p><p>In classical computation graphs have been implemented both explicitly through adjacency matrices/lists and symbolically as ordered binary decision diagrams. Moreover, ad-hoc visit procedures have been developed to deal with dynamically evolving graphs.</p><p>Quantum computation, exploiting interference and entanglement, has provided an exponential speed-up for specific problems, e.g., database search and integer factorization. In the quantum framework everything must be represented and manipulated using reversible operators. This poses a challenge when one has to deal with traversals of dynamically evolving directed graphs. Graph traversals are not intrinsically reversible because of converging paths. In the case of dynamically evolving graphs also the creation/destruction of paths comes into play against reversibility.</p><p>In this paper we propose a novel high level graph representation in quantum computation supporting dynamic connectivity typical of real-world network applications. Our procedure allows to encode any <em>multigraph</em> into a unitary matrix. We devise algorithms for computing the encoding that are optimal in terms of time and space and we show the effectiveness of the proposal with some examples. We describe how to react to edge/node failures in constant time. Furthermore, we present two methods to perform quantum random walks taking advantage of this encoding: with and without <em>projectors</em>. We implement and test our encoding obtaining that the theoretical bounds for the running time are confirmed by the empirical results and providing more details on the behavior of the algorithms over graphs of different densities.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"136 ","pages":"Article 100925"},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2352220823000792/pdfft?md5=c55a5be4601cbf982b84a0ffbe5997ec&pid=1-s2.0-S2352220823000792-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92096451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On algebraic array theories","authors":"Rodrigo Raya,&nbsp;Viktor Kunčak","doi":"10.1016/j.jlamp.2023.100906","DOIUrl":"10.1016/j.jlamp.2023.100906","url":null,"abstract":"<div><p>Automatic verification of programs manipulating arrays relies on specialised decision procedures. A methodology to classify the theories handled by these procedures is introduced. It is based on decomposition theorems in the style of Feferman and Vaught. The method is applied to obtain an extension of combinatory array logic that is closed under propositional operations and Hoare triples. A classification according to expressiveness of six different fragments studied in the literature is given.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"136 ","pages":"Article 100906"},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47384064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}