Implementation Of Data Structure Research Articles

Simple & Optimal Quantile Sketch: Combining Greenwald-Khanna with Khanna-Greenwald

Estimating the ε-approximate quantiles or ranks of a stream is a fundamental task in data monitoring. Given a stream x_1,..., x_n from a universe \mathcalU with total order, an additive-error quantile sketch \mathcalM allows us to approximate the rank of any query y\in \mathcalU up to additive ε n error. In 2001, Greenwald and Khanna gave a deterministic algorithm (GK sketch) that solves the ε-approximate quantiles estimation problem using O(ε^-1 łog(ε n)) space \citegreenwald2001space ; recently, this algorithm was shown to be optimal by Cormode and Vesleý in 2020 \citecormode2020tight. However, due to the intricacy of the GK sketch and its analysis, over-simplified versions of the algorithm are implemented in practical applications, often without any known theoretical guarantees. In fact, it has remained an open question whether the GK sketch can be simplified while maintaining the optimal space bound. In this paper, we resolve this open question by giving a simplified deterministic algorithm that stores at most (2 + o(1))ε^-1 łog (ε n) elements and solves the additive-error quantile estimation problem; as a side benefit, our algorithm achieves a smaller constant factor than the \frac11 2 ε^-1 łog(ε n) space bound in the original GK sketch~\citegreenwald2001space. Our algorithm features an easier analysis and still achieves the same optimal asymptotic space complexity as the original GK sketch. Lastly, our simplification enables an efficient data structure implementation, with a worst-case runtime of O(łog(1/ε) + łog łog (ε n)) per-element for the ordinary ε-approximate quantile estimation problem. Also, for the related "weighted'' quantile estimation problem, we give efficient data structures for our simplified algorithm which guarantee a worst-case per-element runtime of O(łog(1/ε) + łog łog (ε W_n/w_\textrmmin )), achieving an improvement over the previous upper bound of \citeassadi2023generalizing.

Impact of algorithmic and data structure implementation to game development

Many game developers tend to build their proprietary game engines with various algorithmic and data structure implementations. This work discusses a game made using the Pygame library that utilizes a maze generation algorithm, collision detection algorithm, and 2d shadow drawing algorithm to analyze how programming implementation could impact the game's representation, optimization, and future development. In this paper, various algorithms and data structures are compared based on their characteristic and performance, which leads to an analysis of how the game would differ from its current state if alternative implementations are used. It also addresses the issues raised by algorithms and data structures based on their interdependence relationship.

Predecessor on the Ultra-Wide Word RAM

We consider the predecessor problem on the ultra-wide word RAM model of computation, which extends the word RAM model with ultrawords consisting of w2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w^2$$\\end{document} bits (TAMC, 2015). The model supports arithmetic and boolean operations on ultrawords, in addition to scattered memory operations that access or modify w (potentially non-contiguous) memory addresses simultaneously. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a simple, linear space data structure that supports predecessor in constant time and updates in amortized, expected constant time. This improves the space of the previous constant time solution that uses space in the order of the size of the universe. Our result holds even in a weaker model where ultrawords consist of w1+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w^{1+\\epsilon }$$\\end{document} bits for any ϵ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon > 0 $$\\end{document}. It is based on a new implementation of the classic x-fast trie data structure of Willard (Inform Process Lett 17(2):81–84, https://doi.org/10.1016/0020-0190(83)90075-3, 1983) combined with a new dictionary data structure that supports fast parallel lookups.

Three-dimensional partition-of-unity generalized node method for the simulation of fractured rock mass

A three-dimensional (3D) partition-of-unity (PU) generalized node method (GNM) is developed for the simulation of fractured rock mass. In the 3D PUGNM, generalized nodes with independent deformations are directly defined on the isolated blocks to simplify the construction of PU approximations in 3D problems. The explicitly representing of polyhedral blocks with complex geometric shapes by a proper topological structure, the computational geometric algorithms for block cutting, and the subdivision of integration tetrahedrons adapting to physical boundaries are totally avoided in the present 3D PUGNM, and thus the bottleneck problems encountered in the existing PU methods for three dimensions have been well solved. The present 3D PUGNM has the advantages of simple data structure, strong robustness, and convenient numerical implementation, and paves the way for promising application in various engineering problems. Several numerical examples are tested to demonstrate the accuracy, correctness and robustness of the proposed method.

GTMesh: A Highly Efficient C++ Template Library for Numerical Schemes on General Topology Meshes

This article introduces GTMesh, an open-source C++ library providing data structures and algorithms that facilitate the development of numerical schemes on general polytopal meshes. After discussing the features and limitations of the existing open-source alternatives, we focus on the theoretical description of geometry and the topology of conforming polytopal meshes in an arbitrary-dimensional space, using elements from graph theory. The data structure for mesh representation is explained. The main part of the article focuses on the implementation of data structures and algorithms (computation of measures, centers, normals, cell coloring) by using State-of-the-Art template metaprogramming techniques for maximum performance. The geometrical algorithms are designed to be valid regardless of the dimension of the underlying space. As an integral part of the library, a template implementation of class reflection in C++ has been created, which is sufficiently versatile and suitable for the development of numerical and data I/O algorithms working with generic data types. Finally, the use of GTMesh is demonstrated on a simple example of solving the heat equation by the finite volume method.

LeakageVerif: Efficient and Scalable Formal Verification of Leakage in Symbolic Expressions

Side-channel attacks are a powerful class of attacks targeting cryptographic devices. Masking is a popular protection technique to thwart such attacks as it can be theoretically proven secure. However, correctly implementing masking schemes is a non-trivial task and error-prone. If several techniques have been proposed to formally verify masked implementations, they all come with limitations regarding expressiveness, scalability or accuracy. In this work, we propose a symbolic approach, based on a variant of the classical substitution method, for formally verifying arithmetic and boolean masked programs. This approach is more accurate and scalable than existing approaches thanks to a careful design and implementation of key heuristics, algorithms and data structures involved in the verification process. We present all the details of this approach and the open-source tool called <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LeakageVerif</monospace> which implements it as a python library, and which offers constructions for symbolic expressions and functions for their verification. We compare <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LeakageVerif</monospace> to three existing state-of-the-art tools on a set of 46 masked programs, and we show that it has very good scalability and accuracy results while providing all the necessary constructs for describing algorithmic to assembly masking schemes. Finally, we also provide the set of 46 benchmarks, named <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MaskedVerifBenchs</monospace> and written for comparing the different verification tools, in the hope that they will be useful to the community for future comparisons.

GitHub Copilot AI pair programmer: Asset or Liability?

Automatic program synthesis is a long-lasting dream in software engineering. Recently, a promising Deep Learning (DL) based solution, called Copilot, has been proposed by OpenAI and Microsoft as an industrial product. Although some studies evaluate the correctness of Copilot solutions and report its issues, more empirical evaluations are necessary to understand how developers can benefit from it effectively. In this paper, we study the capabilities of Copilot in two different programming tasks: (i) generating (and reproducing) correct and efficient solutions for fundamental algorithmic problems, and (ii) comparing Copilot’s proposed solutions with those of human programmers on a set of programming tasks. For the former, we assess the performance and functionality of Copilot in solving selected fundamental problems in computer science, like sorting and implementing data structures. In the latter, a dataset of programming problems with human-provided solutions is used. The results show that Copilot is capable of providing solutions for almost all fundamental algorithmic problems, however, some solutions are buggy and non-reproducible. Moreover, Copilot has some difficulties in combining multiple methods to generate a solution. Comparing Copilot to humans, our results show that the correct ratio of humans’ solutions is greater than Copilot’s suggestions, while the buggy solutions generated by Copilot require less effort to be repaired. Based on our findings, if Copilot is used by expert developers in software projects, it can become an asset since its suggestions could be comparable to humans’ contributions in terms of quality. However, Copilot can become a liability if it is used by novice developers who may fail to filter its buggy or non-optimal solutions due to a lack of expertise.

Hardware/Software Co-Assurance for the Rust Programming Language Applied to Zero Trust Architecture Development

Zero Trust Architecture requirements are of increasing importance in critical systems development. Zero trust tenets hold that no implicit trust be granted to assets based on their physical or network location. Zero Trust development focuses on authentication, authorization, and shrinking implicit trust zones to the most granular level possible, while maintaining availability and minimizing authentication latency. Performant, high-assurance cryptographic primitives are thus central to successfully realizing a Zero Trust Architecture. The Rust programming language has garnered significant interest and use as a modern, type-safe, memory-safe, and potentially formally analyzable programming language. Our interest in Rust particularly stems from its potential as a hardware/software co-assurance language for developing Zero Trust Architectures. We describe a novel environment enabling Rust to be used as a High-Level Synthesis (HLS) language, suitable for secure and performant Zero Trust application development. Many incumbent HLS languages are a subset of C, and inherit many of the well-known security shortcomings of that language. A Rust-based HLS brings a single modern, type-safe, memory-safe, high-assurance development language for both hardware and software. To study the benefits of this approach, we crafted a Rust HLS subset, and developed a frontend to the hardware/software co-assurance toolchain due to Russinoff and colleagues at Arm, used primarily for floating-point hardware formal verification. This allows us to leverage a number of existing hardware/software co-assurance tools with a minimum investment of time and effort. In this paper, we describe our Rust subset, detail our prototype toolchain, and describe the implementation, performance analysis, formal verification and validation of representative Zero Trust algorithms and data structures written in Rust, emphasizing cryptographic primitives and common data structures.

The splay-list: a distribution-adaptive concurrent skip-list

The design and implementation of efficient concurrent data structures has seen significant attention. However, most of this work has focused on concurrent data structures providing good worst-case guarantees, although, in real workloads, objects are often accessed at different rates. Efficient distribution-adaptive data structures, such as splay-trees, are known in the sequential case; however, they often are hard to translate efficiently to the concurrent case. We investigate distribution-adaptive concurrent data structures, and propose a new design called the splay-list. At a high level, the splay-list is similar to a standard skip-list, with the key distinction that the height of each element adapts dynamically to its access rate: popular elements “move up,” whereas rarely-accessed elements decrease in height. We show that the splay-list provides order-optimal amortized complexity bounds for a subset of operations, while being amenable to efficient concurrent implementation. Experiments show that the splay-list can leverage distribution-adaptivity for performance, and can outperform the only previously-known distribution-adaptive concurrent design in certain workloads.

Can Learned Models Replace Hash Functions?

Hashing is a fundamental operation in database management, playing a key role in the implementation of numerous core database data structures and algorithms. Traditional hash functions aim to mimic a function that maps a key to a random value, which can result in collisions, where multiple keys are mapped to the same value. There are many well-known schemes like chaining, probing, and cuckoo hashing to handle collisions. In this work, we aim to study if using learned models instead of traditional hash functions can reduce collisions and whether such a reduction translates to improved performance, particularly for indexing and joins. We show that learned models reduce collisions in some cases, which depend on how the data is distributed. To evaluate the effectiveness of learned models as hash function, we test them with bucket chaining, linear probing, and cuckoo hash tables. We find that learned models can (1) yield a 1.4x lower probe latency, and (2) reduce the non-partitioned hash join runtime with 28% over the next best baseline for certain datasets. On the other hand, if the data distribution is not suitable, we either do not see gains or see worse performance. In summary, we find that learned models can indeed outperform hash functions, but only for certain data distributions.

Tower: data structures in Quantum superposition

Emerging quantum algorithms for problems such as element distinctness, subset sum, and closest pair demonstrate computational advantages by relying on abstract data structures. Practically realizing such an algorithm as a program for a quantum computer requires an efficient implementation of the data structure whose operations correspond to unitary operators that manipulate quantum superpositions of data. To correctly operate in superposition, an implementation must satisfy three properties --- reversibility, history independence, and bounded-time execution. Standard implementations, such as the representation of an abstract set as a hash table, fail these properties, calling for tools to develop specialized implementations. In this work, we present Core Tower, the first language for quantum programming with random-access memory. Core Tower enables the developer to implement data structures as pointer-based, linked data. It features a reversible semantics enabling every valid program to be translated to a unitary quantum circuit. We present Boson, the first memory allocator that supports reversible, history-independent, and constant-time dynamic memory allocation in quantum superposition. We also present Tower, a language for quantum programming with recursively defined data structures. Tower features a type system that bounds all recursion using classical parameters as is necessary for a program to execute on a quantum computer. Using Tower, we implement Ground, the first quantum library of data structures, including lists, stacks, queues, strings, and sets. We provide the first executable implementation of sets that satisfies all three mandated properties of reversibility, history independence, and bounded-time execution.

Configurable Open-source Data Structure for Distributed Conforming Unstructured Homogeneous Meshes with GPU Support

A general multi-purpose data structure for an efficient representation of conforming unstructured homogeneous meshes for scientific computations on CPU and GPU-based systems is presented. The data structure is provided as open-source software as part of the TNL library (https://tnl-project.org/). The abstract representation supports almost any cell shape and common 2D quadrilateral, 3D hexahedron and arbitrarily dimensional simplex shapes are currently built into the library. The implementation is highly configurable via templates of the C++ language, which allows avoiding the storage of unnecessary dynamic data. The internal memory layout is based on state-of-the-art sparse matrix storage formats, which are optimized for different hardware architectures in order to provide high-performance computations. The proposed data structure is also suitable for meshes decomposed into several subdomains and distributed computing using the Message Passing Interface (MPI). The efficiency of the implemented data structure on CPU and GPU hardware architectures is demonstrated on several benchmark problems and a comparison with another library. Its applicability to advanced numerical methods is demonstrated with an example problem of two-phase flow in porous media using a numerical scheme based on the mixed-hybrid finite element method (MHFEM). We show GPU speed-ups that rise above 20 in 2D and 50 in 3D when compared to sequential CPU computations, and above 2 in 2D and 9 in 3D when compared to 12-threaded CPU computations.

Local refinement strategy and implementation in the Numerical Manifold Method (NMM) for two-dimensional geotechnical problems

Complex geometric features contained in rock masses and its induced continuous-discontinuous deformation field pose great challenges for Finite Element Analysis to generate high-quality fitting meshes. Proposing the splitting of physical covers, the Numerical Manifold Method (NMM) simulates the complex geometries and the continuous-discontinuous deformation using a simply generated structured mesh. Locally refining the NMM’s structured mesh to meet different accuracy needs of various engineering part, or to solve stress concentrations (singularities) is, therefore, a critical issue for large scale engineering simulation. In this work, a multi-level local refinement is realized on a structured mesh with square elements. To ensure the continuity between the large and small elements, the degree of freedoms (DOFs) are present at the hanging node’s physical covers, and the mean value coordinates are employed as the weight functions of the hanging node’s mathematical cover. Different from the conventional recursive quadtree/octree algorithm, the mathematical group composed of one or more square elements is introduced to generate the 1-irregular mesh. The proposed approach features concise algorithm, simple data structure and convenient numerical implementation, which automatically realizes a local refinement with arbitrary level for complex geotechnical problems. Three numerical examples demonstrate the correctness, convergence and efficiency of the present NMM.

IMPLEMENTASI STRUKTUR DATA TREE PADA WEB BLOG SEBAGAI MEDIA PEMBELAJARAN

In writing this study aims to review the implementation of tree data structures on web blogs as learning media, starting from a discussion of the implementation of data structures. After that, it was continued with the use of blogs as an applied learning medium. The use of tree data structures is one of the most common data structures used in the development of a web. One of the efforts to streamline and provide a variation in the realm of learning media is to create a web blog, especially in the era of globalization, everyone who lives in that era should at least know about one of the results of technological and communication advances. This study will see how the description or description of the application of tree data structures on blogs as learning media. The making of this research uses a qualitative descriptive method in which the data is obtained from observation and documentation of matters relating to the topic under study. The core discussion of this research is the implementation of data structures on blogs as learning media.

Hardware/Software Co-Assurance using the Rust Programming Language and ACL2

The Rust programming language has garnered significant interest and use as a modern, type-safe, memory-safe, and potentially formally analyzable programming language. Our interest in Rust stems from its potential as a hardware/software co-assurance language, with application to critical systems such as autonomous vehicles. We report on the first known use of Rust as a High-Level Synthesis (HLS) language. Most incumbent HLS languages are a subset of C. A Rust-based HLS brings a single modern, type-safe, and memory-safe expression language for both hardware and software realizations with high assurance. As a a study of the suitability of Rust as an HLS, we have crafted a Rust subset, inspired by Russinoff's Restricted Algorithmic C (RAC), which we have imaginatively named Restricted Algorithmic Rust, or RAR. In our first implementation of a RAR toolchain, we simply transpile the RAR source into RAC. By so doing, we leverage a number of existing hardware/software co-assurance tools with a minimum investment of time and effort. In this paper, we describe the RAR Rust subset, detail our prototype RAR toolchain, and describe the implementation and verification of several representative algorithms and data structures written in RAR, with proofs of correctness conducted using the ACL2 theorem prover.

Combinatorial BLAS 2.0: Scaling Combinatorial Algorithms on Distributed-Memory Systems

Combinatorial algorithms such as those that arise in graph analysis, modeling of discrete systems, bioinformatics, and chemistry, are often hard to parallelize. The Combinatorial BLAS library implements key computational primitives for rapid development of combinatorial algorithms in distributed-memory systems. During the decade since its first introduction, the Combinatorial BLAS library has evolved and expanded significantly. This article details many of the key technical features of Combinatorial BLAS version 2.0, such as communication avoidance, hierarchical parallelism via in-node multithreading, accelerator support via GPU kernels, generalized semiring support, implementations of key data structures and functions, and scalable distributed I/O operations for human-readable files. Our article also presents several rules of thumb for choosing the right data structures and functions in Combinatorial BLAS 2.0, under various common application scenarios.

Application of the Blockchain Technology in the Vertical Value Chain Management of Enterprises

This paper studies how the blockchain technology applies the enterprise’s vertical value chain management and specifically studies how the blockchain technology is applied to the management of various transaction information involved in the enterprise’s vertical value chain management. This paper first analyzes the basic needs of the enterprise vertical value chain management, analyzes the decentralization, integrity, and authenticity of relevant transaction information in management, and designs and implements enterprise value chain management solution based on the blockchain technology, including the design and implementation of organizations, consensus mechanisms, data structures, and business processes. The simulation data is used for testing, and finally, the solution is evaluated in terms of security, transparency, efficiency, and scalability. The research in this paper shows that the blockchain technology can be applied to the enterprise’s vertical value chain management, which can ensure the authenticity, transparency, tamper resistance, and security of various transaction information of enterprises, thus improving the quality and reliability of the vertical value chain management of enterprises.

Hierarchical change-point regression models including random effects to estimate empirical critical loads for nitrogen using Bayesian Regression Models (brms) and JAGS

The concept of critical loads is used in the framework of the Convention on Long-range Transboundary Air Pollution (UNECE) to define thresholds below which no damaging effects on habitats occur based on the latest scientific knowledge. Change-point regression models applied in a Bayesian framework are useful statistical tools to estimate critical empirical loads. While hierarchical study designs are common in ecological research, previous methods to estimate critical loads using change-point regression did not allow to analyse data collected under such a design. This method update provides an implementation of hierarchical data structure by including random effects such as study sites or as in this example tree species within the Bayesian approach of change-point regression models using two different approaches. The example data set is an European wide gradient study of the impact of climate change and air pollution on forest tree health assessed by foliar nutrient status of nitrogen (N) to phosphorus (P) from 10 different conifer tree species originated from 88 forest sites and 9 countries covering 22 years (1995-2017). Both modelling approaches using JAGS and Bayesian Regression Models using ‘Stan’ (brms) resulted in reasonable and similar estimations of the critical empirical load for nitrogen (CLempN) for temperate forests. These methodological examples of using different approaches of Bayesian change-point regression models dealing with random effects could prove useful to infer CLempN for other ecosystems and long-term data sets.•Hierarchical change-point regression models are suitable for estimating critical empirical loads.•The Bayesian framework of these models provides the inclusion of the current critical load and various confounding or modifying variables.•Here we present two ways of implementing hierarchical data sets in Bayesian change-point regression models using JAGS and brms.

Designing and Implementing a Database for Thesis Data Management by Using the Python Flask Framework

This study aims to implement the database design used in thesis data processing using Flask. The results of the database design produce four tables, namely the lecturer table is used to store lecturer data, the student table is used to store student data, the title of thesis table is used to store data related to student thesis and the guidance table contains history during guidance with the supervisor, The design of the thesis data processing database was developed using Flask. Flask is a web framework written in Python. Flask serves as the application framework and the interface of the web-based flask application. In this research, the methodology used is to implement database development which consists of system analysis, logical design, physical design and implementation. The database design methodology is carried out by 1. Building a local conceptual data design based on user views, 2. Building and validating local logical data models, 3. Building and validating logical data models, 4. Translating logical data models for the database management system, 5. Designing and implementation of physical representation. The results show that the process of creating a thesis data management database can be done using the Flask framework. The development process using the flask framework includes the process of creating databases, tables and reading, adding, repairing and deleting data. In making the application, the application is divided into 2, namely the application used for database management and the application used to display website-based results that are used to display the results of data processing from the application. Implementation of data structures in the database design and applications used include programming language: Python 3.7.0, framework for displaying web-based data: Flask 1.1.2, and database management system using SQLite.

VECTOR-DRIVEN LOGIC AND STRUCTURE FOR TESTING AND DEDUCTIVE FAULT SIMULATION

Context. It is known that data structures are decisive for the creation of efficient parallel algorithms and high-performance computing devices. Therefore, the development of mathematically perfect and technologically simple data structures takes about 80 percent of the design time, when about 20 percent of time and material resources are spent on algorithms and their hardware-software coding. This lead to search for such primitives of data structures that will significantly simplify the parallel high-performance algorithms which are working on them. Models and methods for testing and simulation of digital systems are proposed, which containing certain advantages of quantum computing in terms of implementation of vector qubit data structures in technology of classical computational processes.&#x0D; Objective. The goal of the work is development of an innovative technology for qubit-vector synthesis and deductive analysis of tests for their verification based on vector data structures that greatly simplify algorithms that can be embedded as BIST components in digital systems on chips.&#x0D; Method. The deductive faults simulation is used to obtain analytical expressions focused on transporting fault lists through a functional or logical element based on the xor-operation, which serves as a measure of similarity-difference between a test, a function and faults which is specified in the same way in one of the formats − a table, graph, equation. A binary vector is proposed as the most technologically advanced primitive of data structures for setting logical functionality for the purpose of parallel synthesis and analysis of digital systems. The parallelism of solving combinatorial problems is a physical property of quantum computing, which in classical computing, for parallel simulation and faults diagnostics, is provided by unitary-coded data structures due to excess memory.&#x0D; Results. 1) A method of analytical synthesis of deductive logic for functional elements on the gate level and register transfer level has been developed. 2) A deductive processor for faults simulation based on transporting input lists or faults vectors to external outputs of digital circuits was proposed. 3) The qubit-vector form of logic setting and methods of qubit synthesis of deductive equations for faults simulation were described. 4) A qubit-vector method for the tests’ synthesis which is using derivatives calculated by vector coverage of logic has been developed. 5) Models and methods verification is performed on test examples in the software implementation of structures and algorithms.&#x0D; Conclusions. The scientific novelty lies in the new paradigm of the technology for the synthesis of deductive RTL logic based on metric test equation, which forms the. A vector form for structures description is introduced, which makes it possible to apply wellknown technologies for the synthesis and analysis of logical circuits tests to effectively solve the problems of graph structures testing and state machine models of digital devices. The practical significance is reflected in the examples of analytical synthesis of deductive logic for functional elements on gate level and register transfer level. A deductive processor for faults simulation which is focused on implementation as a BIST tool, which is used in online testing, simulation and fault diagnosis for digital systems on chips is proposed. A qubit-vector form of the digital systems description is proposed, which surpasses the existing methods of computing devices development in terms of the metric: manufacturability, compactness, speed and quality. A software application has been developed that implements the main testing, simulation and diagnostics services which are used in the educational process to study the advantages of qubit-vector data structures and algorithms. The computational complexity of synthesis processes and deductive formulas for logic and their usage in fault simulation are given.