arXiv subjects

Zinovy Diskin

Publications and source records attributed to Zinovy Diskin.

6 recordsLinked to original sources

arXiv2023

Cartesian institutions with evidence: Data and system modelling with diagrammatic constraints and generalized sketches

Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are important as both a theoretical concepts and a practically convenient device. The paper shows that basic formal constraint management can well be developed within a finitely complete category (hence the reference to Cartesianity in the title). In the data modelling context, objects of such a category can be thought of as graphs, while their morphisms play two roles: of data instances and (when being additionally labelled) of constraints. Specifically, a generalized sketch $S$ consists of a graph $G_S$ and a set of constraints $C_S$ declared over $G_S$, and appears as a pattern for typical data schemas (in databases, XML, and UML class diagrams). Interoperability of data modelling frameworks (and tools based on them) very much depends on the laws regulating the transformation of satisfaction relations between data instances and schemas when the schema graph changes: then constraints are translated co- whereas instances contra-variantly. Investigation of this transformation pattern is the main mathematical subject of the paper

cs.LO↗

arXiv2021

Is the Rush to Machine Learning Jeopardizing Safety? Results of a Survey

Machine learning (ML) is finding its way into safety-critical systems (SCS). Current safety standards and practice were not designed to cope with ML techniques, and it is difficult to be confident that SCSs that contain ML components are safe. Our hypothesis was that there has been a rush to deploy ML techniques at the expense of a thorough examination as to whether the use of ML techniques introduces safety problems that we are not yet adequately able to detect and mitigate against. We thus conducted a targeted literature survey to determine the research effort that has been expended in applying ML to SCS compared with that spent on evaluating the safety of SCSs that deploy ML components. This paper presents the (surprising) results of the survey.

cs.LG↗

arXiv2021

General supervised learning as change propagation with delta lenses

Delta lenses are an established mathematical framework for modelling and designing bidirectional model transformations. Following the recent observations by Fong et al, the paper extends the delta lens framework with a a new ingredient: learning over a parameterized space of model transformations seen as functors. We define a notion of an asymmetric learning delta lens with amendment (ala-lens), and show how ala-lenses can be organized into a symmetric monoidal (sm) category. We also show that sequential and parallel composition of well-behaved ala-lenses are also well-behaved so that well-behaved ala-lenses constitute a full sm-subcategory of ala-lenses.

cs.LO↗

arXiv2019

Assurance via workflow+ modelling and conformance

We propose considering assurance as a model management enterprise: saying that a system is safe amounts to specifying three workflows modelling how the safety engineering process is defined and executed, and checking their conformance. These workflows are based on precise data modelling as in functional block diagrams, but their distinctive feature is the presence of relationships between the output data of a process and its input data; hence, the name ``WorkflowPlus'', WF+ . A typical WP^+ model comprises three layers: (i) process and control flow, (ii) dataflow (with input-output relationships), and (iii) argument flow or constraint derivation. Precise dataflow modelling signifies a crucial distinction of (WP+)-based and GSN-based assurance, in which the data layer is mainly implicit. We provide a detailed comparative analysis of the two formalisms and conclude that GSN does not fulfil its promises.

cs.SE↗

arXiv2019

Multiple Model Synchronization with Multiary Delta Lenses with Amendment and K-Putput

Multiple (more than 2) model synchronization is ubiquitous and important for model driven engineering, but its theoretical underpinning gained much less attention than the binary case. Specifically, the latter was extensively studied by the bx community in the framework of algebraic models for update propagation called lenses. Now we make a step to restore the balance and propose a notion of multiary delta lens. Besides multiarity, our lenses feature {\em reflective} updates, when consistency restoration requires some amendment of the update that violated consistency. We emphasize the importance of various ways of lens composition for practical applications of the framework, and prove several composition results.

cs.LO↗

arXiv2012

Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.

cs.SE↗