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. 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. 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. 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. 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.
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. 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. 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. 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. 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.
Quantum data structures, methods, algorithms and software applications for parallel solution of combinatorial problems, including design and test, on classical computers by using extra memory are proposed. Quantum models and methods for design and test of specific logic functionalities are developed based on the use of vector qubit data structures and memory-driven architectures for parallel computing algorithms, in order to significantly improve the performance of testing and deductive simulation of digital systems-on-chips. A new quantum method of test generation for single stuck-at faults of logic functions through taking Boolean derivatives with respect to their qubit coverages is proposed. The quantum method of deductive simulation of stuck-at faults of logical functions through the synthesis of matrices of Boolean derivatives with respect to their qubit coverage has been developed. The performance of methods for test synthesis and their analysis has no analogues in algorithmic performance.
An overview of the technologies of cyber-physical culture is proposed that is aimed at solving practical problems in the field of quantum parallel synthesis and analysis of digital systems based on qubit models and algorithms for design, testing, and simulation. Algorithms for deductive analysis of digital logic circuits leveraging qubit data structures, which significantly improve the processing performance of large scale digital systems are presented. Software and hardware solutions for the simulation of stuck-at faults based on the use of qubit vector descriptions of logic circuits are proposed. Algorithms for the synthesis of deductive expressions focused on fault simulation of x-functions, which are characterized by a high level of testability, are developed. Practical examples, proving the effectiveness of models, methods and algorithms for processing modern digital systems-on-chips, are described.
Context. Nature is the relation among processes and phenomena. Nothing exists in the universe without relations. Computer is transactions of relations between data with the help of control and execution mechanisms. Quantum relations are a superposition of particles and their states. Superposition and entanglement are equivalent concepts. Entanglement is a non-local superposition of deterministic states. A quantum computer is unconditional transactions of relations between qubit data. Quantum computer is an analog device for parallel solution of combinatorial problems. Practically oriented definitions of the quantum computer concepts are the path to development of scalable quantum parallel algorithms for combinatorial problems solving. Any algorithm can be reduced to a sequence of operations without conditions, because any truth table is a collection of a complete system of conditions-states. Any sequence of actions can always be reduced to one parallel operation. Conditions and sequences arise only when the developer wants to use previously created primitive constructs to build an always non-optimal computing unit. The paradigm of quantum computer creation is determined through the use of photonic transactions on the electrons of an atom may exclude the use of quantum logic. The evolutionary path of a quantum computer from the classical one: “memory-address-transaction” (MAT) → “electron-addresstransaction” → “electron-address-quantaction” (EAQ) → state-superposition-logic. The meeting point of classical and quantum computers is photon transactions on the structure of electrons. Everything that is calculated on a quantum computer can be calculated in parallel on a classical one on account of memory redundancy. The given example is a memory-driven algorithm for modeling digital products based on qubit-vector forms of functionality description for significant performance boost of computing processes by parallel execution of logical operations. Objective. Simulation of the correct SoC-component behavior based on vector representation of the logic. Formation of the triggering development of a computing based on the superposition of the classical, quantum and analog computing process, which in its development should be based on technological qubit, tabular and vector data structures for the parallel solution of combinatorial problems. Method. MAT-computing implements any algorithms on account of transactions (read-write) in memory. Qubit-vector models for describing functionalities, which differ from known truth tables in compactness of description and manufacturability for the implementation of parallel algorithms of the synthesis and analysis of digital devices and SoC-components. Results. 1) The metric of the technological data structures, focused on parallel troubleshooting in digital systems based on the usage of two logical vector operations, was proposed for the first time. 2) The metric of relations between the individual components of QC, allowing organizing a quantum deterministic computer, has been further developed. 3) Quantum architectural solutions, that allow solving coverage problems in a quasi-parallel mode, were proposed for the first time. 4) Architectural solutions based on an analog-to-digital computing, which can be used to solve the problems of the digital systems parallel analysis, have been further developed. 5) Vector-qubit structures of the logic data, that allow a quasi-parallel simulation of digital circuits, were proposed. Conclusions. Qubit models, quantum methods and combinatorial algorithms for technical diagnostics of digital devices have been implemented, which can significantly (up to 25%) reduce the time of test synthesis, deductive modeling of faulty and correct behavior, search for defective states by introducing an innovative idea of using qubit-vector data structures for describing logical components. Comparative assessments of qubit models and methods usage show an increase in the efficiency of algorithms for modeling digital devices compared to tabular ones. The superposition of a classical, quantum and analog computer is integrally represented, which allows to find the best solutions for recognition and decision making.
"Quantum " data structures for synthesis of digital system are proposed. They are based on transactions between addressable memory components to implement any functionality. The new approach of logic function minimization for synthesis of digital systems is proposed. It is supposed to apply vector form (quantum) of description logic and sequential structures implemented into memory elements. This approach remarkably differs from the common synthesis theory of discrete devices based on truth tables of components. It is based on an opportunity of applying quantum or qubit data structures [1-5] in modern computers when doing calculating processes with the purpose of unary coding states of input, internal and output variables, and also on the technology of qubit-vectors implementation into memory elements FPGA, which realize combinational and sequential primitives. The use of quantum memory-based only models for describing digital components when computer systems design would allow us to increase yield, enhance reliability of computers, make the process of design and production of devices cheaper, and also provides human-free repairing in remote & online mode.
Context. Nature is the relation among processes and phenomena. Nothing exists in the universe without relations. Computer is transactions of relations between data with the help of control and execution mechanisms. Quantum relations are a superposition of particles and their states. Superposition and entanglement are equivalent concepts. Entanglement is a non-local superposition of deterministic states. A quantum computer is unconditional transactions of relations between qubit data. Quantum computer is an analog device for parallel solution of combinatorial problems. Practically oriented definitions of the quantum computer concepts are the path to development of scalable quantum parallel algorithms for combinatorial problems solving. Any algorithm can be reduced to a sequence of operations without conditions, because any truth table is a collection of a complete system of conditions-states. Any sequence of actions can always be reduced to one parallel operation. Conditions and sequences arise only when the developer wants to use previously created primitive constructs to build an always non-optimal computing unit. The paradigm of quantum computer creation is determined through the use of photonic transactions on the electrons of an atom may exclude the use of quantum logic. The evolutionary path of a quantum computer from the classical one: “memory-address-transaction” (MAT) → “electron-addresstransaction” → “electron-address-quantaction” (EAQ) → state-superposition-logic. The meeting point of classical and quantum computers is photon transactions on the structure of electrons. Everything that is calculated on a quantum computer can be calculated in parallel on a classical one on account of memory redundancy. The given example is a memory-driven algorithm for modeling digital products based on qubit-vector forms of functionality description for significant performance boost of computing processes by parallel execution of logical operations. Objective. Simulation of the correct SoC-component behavior based on vector representation of the logic. Formation of the triggering development of a computing based on the superposition of the classical, quantum and analog computing process, which in its development should be based on technological qubit, tabular and vector data structures for the parallel solution of combinatorial problems. Method. MAT-computing implements any algorithms on account of transactions (read-write) in memory. Qubit-vector models for describing functionalities, which differ from known truth tables in compactness of description and manufacturability for the implementation of parallel algorithms of the synthesis and analysis of digital devices and SoC-components. Results. 1) The metric of the technological data structures, focused on parallel troubleshooting in digital systems based on the usage of two logical vector operations, was proposed for the first time. 2) The metric of relations between the individual components of QC, allowing organizing a quantum deterministic computer, has been further developed. 3) Quantum architectural solutions, that allow solving coverage problems in a quasi-parallel mode, were proposed for the first time. 4) Architectural solutions based on an analog-to-digital computing, which can be used to solve the problems of the digital systems parallel analysis, have been further developed. 5) Vector-qubit structures of the logic data, that allow a quasi-parallel simulation of digital circuits, were proposed. Conclusions. Qubit models, quantum methods and combinatorial algorithms for technical diagnostics of digital devices have been implemented, which can significantly (up to 25%) reduce the time of test synthesis, deductive modeling of faulty and correct behavior, search for defective states by introducing an innovative idea of using qubit-vector data structures for describing logical components. Comparative assessments of qubit models and methods usage show an increase in the efficiency of algorithms for modeling digital devices compared to tabular ones. The superposition of a classical, quantum and analog computer is integrally represented, which allows to find the best solutions for recognition and decision making.
Qubit (quantum) structures of data and computational processes for significantly improving performance when solving problems of discrete optimization and fault-tolerant design are proposed. We describe a hardware-focused models for parallel (one cycle) calculating the power set (the set of all subsets) on the universe of n primitives for solving coverage problems, minimization of Boolean functions, data compression, analysis and synthesis of digital systems through the implementation of the processor structure in the form of the Hasse diagram. A prototype of quantum device, implemented by programmable logic, is described.